Glossary · word list
English terms: Math
1,230 words and terms, A–Z, from School Launch lessons. Each links to the lesson where it is taught.
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10% conditionEnglish
When sampling without replacement, the sample size n is at most 10% of the population size, so the draws are nearly independent.
Statistics, Lesson 10.2 (grade 11–12) · Statistics, Lesson 8.2 (grade 11–12) · Statistics, Lesson 9.2 (grade 11–12)
When sampling without replacement, the sample size n is at most 10% of the population size, so the draws are nearly independent.
Statistics, Lesson 10.2 (grade 11–12) · Statistics, Lesson 8.2 (grade 11–12) · Statistics, Lesson 9.2 (grade 11–12)
30-60-90 triangleEnglish
A right triangle whose acute angles are 30^\circ and 60^\circ; it is exactly half of an equilateral triangle.
Trigonometry, Lesson 2.2 (grade 11–12)
A right triangle whose acute angles are 30^\circ and 60^\circ; it is exactly half of an equilateral triangle.
Trigonometry, Lesson 2.2 (grade 11–12)
30^\circ-60^\circ-90^\circ triangleEnglish
A right triangle whose acute angles measure 30^\circ and 60^\circ.
Geometry, Lesson 9.4 (grade 9–10)
A right triangle whose acute angles measure 30^\circ and 60^\circ.
Geometry, Lesson 9.4 (grade 9–10)
45-45-90 triangleEnglish
A right triangle whose two acute angles are both 45^\circ; it is also called an isosceles right triangle because its two legs are equal.
Trigonometry, Lesson 2.1 (grade 11–12)
A right triangle whose two acute angles are both 45^\circ; it is also called an isosceles right triangle because its two legs are equal.
Trigonometry, Lesson 2.1 (grade 11–12)
45^\circ-45^\circ-90^\circ triangleEnglish
An isosceles right triangle; its acute angles are both 45^\circ and its legs are congruent.
Geometry, Lesson 9.4 (grade 9–10)
An isosceles right triangle; its acute angles are both 45^\circ and its legs are congruent.
Geometry, Lesson 9.4 (grade 9–10)
68–95–99.7 ruleEnglish
In any normal distribution, about 68% of values lie within 1\sigma of the mean, about 95% within 2\sigma, and about 99.7% within 3\sigma. It is also called the empirical rule.
Statistics, Lesson 3.3 (grade 11–12)
In any normal distribution, about 68% of values lie within 1\sigma of the mean, about 95% within 2\sigma, and about 99.7% within 3\sigma. It is also called the empirical rule.
Statistics, Lesson 3.3 (grade 11–12)
A
AAAEnglish
Three angles and no side. Such data fix only the shape of a triangle, not its size, so they cannot be solved for lengths.
Trigonometry, Lesson 7.5 (grade 11–12)
Three angles and no side. Such data fix only the shape of a triangle, not its size, so they cannot be solved for lengths.
Trigonometry, Lesson 7.5 (grade 11–12)
AASEnglish
Given data of two angles and a side that is not between them.
Trigonometry, Lesson 7.2 (grade 11–12)
Given data of two angles and a side that is not between them.
Trigonometry, Lesson 7.2 (grade 11–12)
absolute valueEnglish
The distance of a number from 0 on the number line, written |x|. Because it is a distance, it is never negative: |5| = 5 and |-5| = 5.
Algebra I, Lesson 3.4 (grade 8–9) · Algebra II, Lesson 1.3 (grade 10–11) · Pre-Algebra, Lesson 5.1 (grade 6–8)
The distance of a number from 0 on the number line, written |x|. Because it is a distance, it is never negative: |5| = 5 and |-5| = 5.
Algebra I, Lesson 3.4 (grade 8–9) · Algebra II, Lesson 1.3 (grade 10–11) · Pre-Algebra, Lesson 5.1 (grade 6–8)
absolute value equationEnglish
An equation with the variable inside absolute value bars, such as |2x - 5| = 9.
Algebra I, Lesson 3.4 (grade 8–9)
An equation with the variable inside absolute value bars, such as |2x - 5| = 9.
Algebra I, Lesson 3.4 (grade 8–9)
absolute value (modulus)English
The distance from a + bi to 0 in the complex plane: |a + bi| = \sqrt{a^2 + b^2}.
Algebra II, Lesson 3.3 (grade 10–11)
The distance from a + bi to 0 in the complex plane: |a + bi| = \sqrt{a^2 + b^2}.
Algebra II, Lesson 3.3 (grade 10–11)
ac methodEnglish
A way to factor ax^2 + bx + c: find two numbers whose product is a \cdot c and whose sum is b, use them to split the middle term into two terms, then factor by grouping.
Algebra I, Lesson 9.3 (grade 8–9)
A way to factor ax^2 + bx + c: find two numbers whose product is a \cdot c and whose sum is b, use them to split the middle term into two terms, then factor by grouping.
Algebra I, Lesson 9.3 (grade 8–9)
Acute, right, obtuse and equiangular trianglesEnglish
A triangle is acute if all three angles are acute, right if it has a right angle, obtuse if it has an obtuse angle, and equiangular if all three angles are congruent.
Geometry, Lesson 4.1 (grade 9–10)
A triangle is acute if all three angles are acute, right if it has a right angle, obtuse if it has an obtuse angle, and equiangular if all three angles are congruent.
Geometry, Lesson 4.1 (grade 9–10)
acute, right, obtuse and straight anglesEnglish
An acute angle measures between 0^\circ and 90^\circ; a right angle measures exactly 90^\circ; an obtuse angle measures between 90^\circ and 180^\circ; a straight angle is formed by opposite rays and measures 180^\circ.
Geometry, Lesson 2.3 (grade 9–10)
An acute angle measures between 0^\circ and 90^\circ; a right angle measures exactly 90^\circ; an obtuse angle measures between 90^\circ and 180^\circ; a straight angle is formed by opposite rays and measures 180^\circ.
Geometry, Lesson 2.3 (grade 9–10)
acute, right, obtuse, straightEnglish
An acute angle is less than 90^\circ. A right angle is exactly 90^\circ (a square corner). An obtuse angle is between 90^\circ and 180^\circ. A straight angle is exactly 180^\circ (a straight line).
Pre-Algebra, Lesson 12.1 (grade 6–8)
An acute angle is less than 90^\circ. A right angle is exactly 90^\circ (a square corner). An obtuse angle is between 90^\circ and 180^\circ. A straight angle is exactly 180^\circ (a straight line).
Pre-Algebra, Lesson 12.1 (grade 6–8)
acute, right, obtuse triangleEnglish
Names for triangles by their angles: an acute triangle has three acute angles, a right triangle has one 90^\circ angle, and an obtuse triangle has one angle greater than 90^\circ.
Pre-Algebra, Lesson 12.2 (grade 6–8)
Names for triangles by their angles: an acute triangle has three acute angles, a right triangle has one 90^\circ angle, and an obtuse triangle has one angle greater than 90^\circ.
Pre-Algebra, Lesson 12.2 (grade 6–8)
Acute triangleEnglish
A triangle whose three angles are all acute (less than 90^\circ).
Geometry, Lesson 9.2 (grade 9–10)
A triangle whose three angles are all acute (less than 90^\circ).
Geometry, Lesson 9.2 (grade 9–10)
adding the oppositeEnglish
Rewriting a subtraction as an addition by changing the number being subtracted to its opposite: a - b = a + (-b).
Pre-Algebra, Lesson 5.3 (grade 6–8)
Rewriting a subtraction as an addition by changing the number being subtracted to its opposite: a - b = a + (-b).
Pre-Algebra, Lesson 5.3 (grade 6–8)
addition property of equalityEnglish
If a = b and c = d, then a + c = b + d: adding equal amounts to both sides keeps an equation true.
Algebra I, Lesson 6.3 (grade 8–9)
If a = b and c = d, then a + c = b + d: adding equal amounts to both sides keeps an equation true.
Algebra I, Lesson 6.3 (grade 8–9)
additive inverseEnglish
Another name for the opposite of a number. A number plus its additive inverse is always 0, as in 6 + (-6) = 0.
Pre-Algebra, Lesson 5.2 (grade 6–8)
Another name for the opposite of a number. A number plus its additive inverse is always 0, as in 6 + (-6) = 0.
Pre-Algebra, Lesson 5.2 (grade 6–8)
adjacent anglesEnglish
Two angles in a plane that share a vertex and a side but have no interior points in common, such as \angle ABD and \angle DBC when D is in the interior of \angle ABC.
Geometry, Lesson 2.4 (grade 9–10) · Pre-Algebra, Lesson 12.1 (grade 6–8)
Two angles in a plane that share a vertex and a side but have no interior points in common, such as \angle ABD and \angle DBC when D is in the interior of \angle ABC.
Geometry, Lesson 2.4 (grade 9–10) · Pre-Algebra, Lesson 12.1 (grade 6–8)
Adjacent legEnglish
For an acute angle of a right triangle, the leg that forms one side of the angle (the side of the angle that is not the hypotenuse).
Geometry, Lesson 9.5 (grade 9–10)
For an acute angle of a right triangle, the leg that forms one side of the angle (the side of the angle that is not the hypotenuse).
Geometry, Lesson 9.5 (grade 9–10)
Adjacent segmentEnglish
For a leg of the right triangle, the segment of the hypotenuse that touches that leg (for leg \overline{AC} it is \overline{AD}).
Geometry, Lesson 9.3 (grade 9–10)
For a leg of the right triangle, the segment of the hypotenuse that touches that leg (for leg \overline{AC} it is \overline{AD}).
Geometry, Lesson 9.3 (grade 9–10)
adjacent sideEnglish
For an acute angle of a right triangle, the leg that forms the angle together with the hypotenuse.
Trigonometry, Lesson 1.2 (grade 11–12)
For an acute angle of a right triangle, the leg that forms the angle together with the hypotenuse.
Trigonometry, Lesson 1.2 (grade 11–12)
affirming the conclusionEnglish
The invalid argument “p \to q is true and q is true, so p is true.” It treats the converse as if it were true.
Geometry, Lesson 1.4 (grade 9–10)
The invalid argument “p \to q is true and q is true, so p is true.” It treats the converse as if it were true.
Geometry, Lesson 1.4 (grade 9–10)
Algebraic expressionEnglish
A combination of numbers, variables and operations with no equal sign, such as 2n - 5.
Algebra I, Lesson 1.5 (grade 8–9) · Pre-Algebra, Lesson 9.1 (grade 6–8)
A combination of numbers, variables and operations with no equal sign, such as 2n - 5.
Algebra I, Lesson 1.5 (grade 8–9) · Pre-Algebra, Lesson 9.1 (grade 6–8)
al-jabrEnglish
Arabic for "restoring"; from the title of al-Khwarizmi's book, it gave us the word algebra.
Algebra I, Lesson 11.4 (grade 8–9)
Arabic for "restoring"; from the title of al-Khwarizmi's book, it gave us the word algebra.
Algebra I, Lesson 11.4 (grade 8–9)
all real numbersEnglish
The answer when an inequality is true no matter what number replaces the variable, such as 2x + 6 > 2x.
Algebra I, Lesson 3.2 (grade 8–9)
The answer when an inequality is true no matter what number replaces the variable, such as 2x + 6 > 2x.
Algebra I, Lesson 3.2 (grade 8–9)
alternate exterior anglesEnglish
Two angles that lie outside the two lines, on opposite sides of the transversal, at different intersection points.
Geometry, Lesson 3.1 (grade 9–10)
Two angles that lie outside the two lines, on opposite sides of the transversal, at different intersection points.
Geometry, Lesson 3.1 (grade 9–10)
alternate interior anglesEnglish
Two angles that lie between the two lines, on opposite sides of the transversal, at different intersection points.
Geometry, Lesson 3.1 (grade 9–10)
Two angles that lie between the two lines, on opposite sides of the transversal, at different intersection points.
Geometry, Lesson 3.1 (grade 9–10)
alternative hypothesis (H_a)English
The claim we are looking for evidence for. It is one-sided if it says the parameter is greater than (or less than) the null value, and two-sided if it says only that the parameter is different (\ne).
Statistics, Lesson 11.1 (grade 11–12)
The claim we are looking for evidence for. It is one-sided if it says the parameter is greater than (or less than) the null value, and two-sided if it says only that the parameter is different (\ne).
Statistics, Lesson 11.1 (grade 11–12)
altitude of a triangleEnglish
The perpendicular segment from a vertex to the line containing the opposite side. Its length is the height of the triangle for that side.
Geometry, Lesson 5.3 (grade 9–10)
The perpendicular segment from a vertex to the line containing the opposite side. Its length is the height of the triangle for that side.
Geometry, Lesson 5.3 (grade 9–10)
Altitude to the hypotenuseEnglish
The segment from the vertex of the right angle perpendicular to the hypotenuse.
Geometry, Lesson 9.3 (grade 9–10)
The segment from the vertex of the right angle perpendicular to the hypotenuse.
Geometry, Lesson 9.3 (grade 9–10)
ambiguous caseEnglish
The SSA situation, so called because the data may fit no triangle, exactly one triangle, or two different triangles.
Trigonometry, Lesson 7.3 (grade 11–12)
The SSA situation, so called because the data may fit no triangle, exactly one triangle, or two different triangles.
Trigonometry, Lesson 7.3 (grade 11–12)
amortization tableEnglish
A table showing, for each loan payment, how much goes to interest, how much reduces the principal, and the balance that remains.
Algebra II, Lesson 9.5 (grade 10–11)
A table showing, for each loan payment, how much goes to interest, how much reduces the principal, and the balance that remains.
Algebra II, Lesson 9.5 (grade 10–11)
amount of changeEnglish
How much the amount went up or down: the larger amount minus the smaller amount.
Pre-Algebra, Lesson 8.4 (grade 6–8)
How much the amount went up or down: the larger amount minus the smaller amount.
Pre-Algebra, Lesson 8.4 (grade 6–8)
angle between a line and a planeEnglish
The angle between the line and its projection on the plane.
Trigonometry, Lesson 8.4 (grade 11–12)
The angle between the line and its projection on the plane.
Trigonometry, Lesson 8.4 (grade 11–12)
angle between two planesEnglish
For a sloping face meeting a horizontal base along an edge, the angle between two lines, one in each plane, both perpendicular to that edge at the same point.
Trigonometry, Lesson 8.4 (grade 11–12)
For a sloping face meeting a horizontal base along an edge, the angle between two lines, one in each plane, both perpendicular to that edge at the same point.
Trigonometry, Lesson 8.4 (grade 11–12)
angle bisectorEnglish
A ray in the interior of an angle, starting at the vertex, that divides the angle into two congruent angles.
Geometry, Lesson 2.3 (grade 9–10) · Geometry, Lesson 5.1 (grade 9–10)
A ray in the interior of an angle, starting at the vertex, that divides the angle into two congruent angles.
Geometry, Lesson 2.3 (grade 9–10) · Geometry, Lesson 5.1 (grade 9–10)
Angle formed by two chordsEnglish
An angle whose vertex is the point where two chords cross inside the circle. It intercepts one arc, and its vertical angle intercepts another.
Geometry, Lesson 10.5 (grade 9–10)
An angle whose vertex is the point where two chords cross inside the circle. It intercepts one arc, and its vertical angle intercepts another.
Geometry, Lesson 10.5 (grade 9–10)
Angle of depressionEnglish
The angle between the horizontal and the line of sight when an observer looks DOWN at an object.
Geometry, Lesson 9.7 (grade 9–10) · Trigonometry, Lesson 8.1 (grade 11–12)
The angle between the horizontal and the line of sight when an observer looks DOWN at an object.
Geometry, Lesson 9.7 (grade 9–10) · Trigonometry, Lesson 8.1 (grade 11–12)
Angle of elevationEnglish
The angle between the horizontal and the line of sight when an observer looks UP at an object.
Geometry, Lesson 9.7 (grade 9–10) · Trigonometry, Lesson 8.1 (grade 11–12)
The angle between the horizontal and the line of sight when an observer looks UP at an object.
Geometry, Lesson 9.7 (grade 9–10) · Trigonometry, Lesson 8.1 (grade 11–12)
Angle of elevation (depression)English
The angle between a horizontal line and a line of sight to an object above (below) the horizontal.
Algebra II, Lesson 13.1 (grade 10–11)
The angle between a horizontal line and a line of sight to an object above (below) the horizontal.
Algebra II, Lesson 13.1 (grade 10–11)
angle of rotationEnglish
The angle \theta through which every ray from the center is turned.
Geometry, Lesson 7.3 (grade 9–10)
The angle \theta through which every ray from the center is turned.
Geometry, Lesson 7.3 (grade 9–10)
Angle-Angle (AA) Similarity PostulateEnglish
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Geometry, Lesson 8.3 (grade 9–10)
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Geometry, Lesson 8.3 (grade 9–10)
Angle-Angle-Side (AAS)English
If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the triangles are congruent.
Geometry, Lesson 4.4 (grade 9–10)
If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the triangles are congruent.
Geometry, Lesson 4.4 (grade 9–10)
Angle-Side-Angle (ASA)English
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Geometry, Lesson 4.4 (grade 9–10)
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Geometry, Lesson 4.4 (grade 9–10)
angular speedEnglish
The angle turned per unit of time, \omega = \dfrac{\theta}{t}, usually in radians per second or radians per minute. The symbol \omega is the Greek letter omega.
Trigonometry, Lesson 3.5 (grade 11–12)
The angle turned per unit of time, \omega = \dfrac{\theta}{t}, usually in radians per second or radians per minute. The symbol \omega is the Greek letter omega.
Trigonometry, Lesson 3.5 (grade 11–12)
annual rateEnglish
The yearly interest rate r, written as a decimal in formulas (5% is r = 0.05). Each compounding period uses the rate \frac{r}{n}.
Algebra II, Lesson 7.2 (grade 10–11)
The yearly interest rate r, written as a decimal in formulas (5% is r = 0.05). Each compounding period uses the rate \frac{r}{n}.
Algebra II, Lesson 7.2 (grade 10–11)
annuityEnglish
A series of equal payments or deposits made at equal time intervals, such as $300 at the end of every month.
Algebra II, Lesson 9.5 (grade 10–11) · Accounting, Lesson 10.4 (grade 9–12) · Insurance Agent Exam Prep: Life, Health, Property & Casualty, Lesson 4.4 (grade 9–12) · +1 more
A series of equal payments or deposits made at equal time intervals, such as $300 at the end of every month.
Algebra II, Lesson 9.5 (grade 10–11) · Accounting, Lesson 10.4 (grade 9–12) · Insurance Agent Exam Prep: Life, Health, Property & Casualty, Lesson 4.4 (grade 9–12) · +1 more
apothemEnglish
The perpendicular segment from the center to a side, or its length a. It is the same length for every side.
Geometry, Lesson 11.3 (grade 9–10)
The perpendicular segment from the center to a side, or its length a. It is the same length for every side.
Geometry, Lesson 11.3 (grade 9–10)
arc lengthEnglish
The distance along an arc, measured in units of length (inches, feet). It is different from the arc's degree measure, which is measured in degrees.
Geometry, Lesson 11.4 (grade 9–10) · Trigonometry, Lesson 3.4 (grade 11–12)
The distance along an arc, measured in units of length (inches, feet). It is different from the arc's degree measure, which is measured in degrees.
Geometry, Lesson 11.4 (grade 9–10) · Trigonometry, Lesson 3.4 (grade 11–12)
Arc of a chordEnglish
The minor arc whose endpoints are the endpoints of the chord. The chord and its arc are said to subtend (stand on) each other, and they share the same central angle.
Geometry, Lesson 10.2 (grade 9–10)
The minor arc whose endpoints are the endpoints of the chord. The chord and its arc are said to subtend (stand on) each other, and they share the same central angle.
Geometry, Lesson 10.2 (grade 9–10)
Area Addition PostulateEnglish
If a region is split into non-overlapping parts, its area is the sum of the areas of the parts.
Geometry, Lesson 11.1 (grade 9–10)
If a region is split into non-overlapping parts, its area is the sum of the areas of the parts.
Geometry, Lesson 11.1 (grade 9–10)
Area Congruence PostulateEnglish
Congruent figures have equal areas.
Geometry, Lesson 11.1 (grade 9–10)
Congruent figures have equal areas.
Geometry, Lesson 11.1 (grade 9–10)
area modelEnglish
A rectangle split into smaller rectangles, used to picture a product. The area of the whole equals the sum of the areas of the parts.
Algebra I, Lesson 8.2 (grade 8–9) · Pre-Algebra, Lesson 1.3 (grade 6–8) · Pre-Algebra, Lesson 3.5 (grade 6–8)
A rectangle split into smaller rectangles, used to picture a product. The area of the whole equals the sum of the areas of the parts.
Algebra I, Lesson 8.2 (grade 8–9) · Pre-Algebra, Lesson 1.3 (grade 6–8) · Pre-Algebra, Lesson 3.5 (grade 6–8)
argumentEnglish
The number x whose logarithm is taken in \log_b x; it must be positive.
Algebra II, Lesson 8.1 (grade 10–11) · Algebra II, Lesson 8.2 (grade 10–11) · Grade 6 Composition & Creative Writing: Maxim, Refutation and Confirmation, Lesson 6.1 (grade 6) · +1 more
The number x whose logarithm is taken in \log_b x; it must be positive.
Algebra II, Lesson 8.1 (grade 10–11) · Algebra II, Lesson 8.2 (grade 10–11) · Grade 6 Composition & Creative Writing: Maxim, Refutation and Confirmation, Lesson 6.1 (grade 6) · +1 more
arithmetic meansEnglish
The terms that fill in between two given terms so that all of them together form an arithmetic sequence. A single arithmetic mean of a and b is their average \dfrac{a + b}{2}.
Algebra II, Lesson 9.2 (grade 10–11)
The terms that fill in between two given terms so that all of them together form an arithmetic sequence. A single arithmetic mean of a and b is their average \dfrac{a + b}{2}.
Algebra II, Lesson 9.2 (grade 10–11)
arithmetic sequenceEnglish
A sequence in which you add the same number each time to get the next term.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra II, Lesson 9.2 (grade 10–11)
A sequence in which you add the same number each time to get the next term.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra II, Lesson 9.2 (grade 10–11)
arithmetic seriesEnglish
The sum of the terms of an arithmetic sequence. S_n stands for the sum of the first n terms.
Algebra II, Lesson 9.2 (grade 10–11)
The sum of the terms of an arithmetic sequence. S_n stands for the sum of the first n terms.
Algebra II, Lesson 9.2 (grade 10–11)
Assessing normalityEnglish
Using graphs and the 68–95–99.7 rule to decide whether a normal model fits a data set well enough to use.
Statistics, Lesson 3.6 (grade 11–12)
Using graphs and the 68–95–99.7 rule to decide whether a normal model fits a data set well enough to use.
Statistics, Lesson 3.6 (grade 11–12)
AssociationEnglish
Two variables are associated if knowing the value of one tells you something about the value of the other; in a two-way table, the conditional distributions differ from group to group.
Statistics, Lesson 1.3 (grade 11–12) · Statistics, Lesson 13.2 (grade 11–12)
Two variables are associated if knowing the value of one tells you something about the value of the other; in a two-way table, the conditional distributions differ from group to group.
Statistics, Lesson 1.3 (grade 11–12) · Statistics, Lesson 13.2 (grade 11–12)
Associative propertyEnglish
Changing the grouping of three numbers does not change a sum or product: (a + b) + c = a + (b + c) and (ab)c = a(bc).
Algebra I, Lesson 1.2 (grade 8–9) · Pre-Algebra, Lesson 1.2 (grade 6–8)
Changing the grouping of three numbers does not change a sum or product: (a + b) + c = a + (b + c) and (ab)c = a(bc).
Algebra I, Lesson 1.2 (grade 8–9) · Pre-Algebra, Lesson 1.2 (grade 6–8)
ASTCEnglish
A memory aid ("All Students Take Calculus") for the functions that are positive in Quadrants I, II, III, IV: All, Sine, Tangent, Cosine.
Trigonometry, Lesson 3.7 (grade 11–12)
A memory aid ("All Students Take Calculus") for the functions that are positive in Quadrants I, II, III, IV: All, Sine, Tangent, Cosine.
Trigonometry, Lesson 3.7 (grade 11–12)
asymptotes of a hyperbolaEnglish
The two lines through the center that the branches get closer and closer to as they move away from the center.
Algebra II, Lesson 11.3 (grade 10–11)
The two lines through the center that the branches get closer and closer to as they move away from the center.
Algebra II, Lesson 11.3 (grade 10–11)
at leastEnglish
That number or more; written with \ge. "At least 10" includes 10.
Algebra I, Lesson 3.2 (grade 8–9)
That number or more; written with \ge. "At least 10" includes 10.
Algebra I, Lesson 3.2 (grade 8–9)
at least oneEnglish
One or more of the events happen; its complement is “none of them happen.”
Statistics, Lesson 6.4 (grade 11–12)
One or more of the events happen; its complement is “none of them happen.”
Statistics, Lesson 6.4 (grade 11–12)
at most / no more thanEnglish
That number or less; written with \le. "No more than $50" includes $50.
Algebra I, Lesson 3.2 (grade 8–9)
That number or less; written with \le. "No more than $50" includes $50.
Algebra I, Lesson 3.2 (grade 8–9)
augmented matrixEnglish
The coefficient matrix with the column of constants attached on the right, usually set off by a vertical bar.
Algebra II, Lesson 12.4 (grade 10–11)
The coefficient matrix with the column of constants attached on the right, usually set off by a vertical bar.
Algebra II, Lesson 12.4 (grade 10–11)
auxiliary lineEnglish
A line added to a figure to help with a proof or a calculation. Every auxiliary line must be justified: we must know that it exists and what it is (for example, by Playfair's Axiom, the one line through a point parallel to a given line).
Geometry, Lesson 3.3 (grade 9–10) · Geometry, Lesson 4.1 (grade 9–10)
A line added to a figure to help with a proof or a calculation. Every auxiliary line must be justified: we must know that it exists and what it is (for example, by Playfair's Axiom, the one line through a point parallel to a given line).
Geometry, Lesson 3.3 (grade 9–10) · Geometry, Lesson 4.1 (grade 9–10)
average costEnglish
Total cost divided by the number of items made: \overline{C}(x) = \dfrac{\text{fixed cost} + (\text{cost per item})x}{x}.
Algebra II, Lesson 5.3 (grade 10–11) · Grade 6 Business & Finance, Lesson 3.4 (grade 6) · Grade 7 Business & Finance, Lesson 3.3 (grade 7)
Total cost divided by the number of items made: \overline{C}(x) = \dfrac{\text{fixed cost} + (\text{cost per item})x}{x}.
Algebra II, Lesson 5.3 (grade 10–11) · Grade 6 Business & Finance, Lesson 3.4 (grade 6) · Grade 7 Business & Finance, Lesson 3.3 (grade 7)
average rate of changeEnglish
For a function f from x = a to x = b, the change in output divided by the change in input: \dfrac{f(b) - f(a)}{b - a}.
Algebra II, Lesson 1.6 (grade 10–11)
For a function f from x = a to x = b, the change in output divided by the change in input: \dfrac{f(b) - f(a)}{b - a}.
Algebra II, Lesson 1.6 (grade 10–11)
axis of symmetryEnglish
The vertical line through the vertex that cuts the parabola into two mirror-image halves.
Algebra I, Lesson 11.1 (grade 8–9) · Algebra II, Lesson 3.1 (grade 10–11)
The vertical line through the vertex that cuts the parabola into two mirror-image halves.
Algebra I, Lesson 11.1 (grade 8–9) · Algebra II, Lesson 3.1 (grade 10–11)
B
back-substituteEnglish
After finding one variable, put its value into an equation to find the other variable.
Algebra I, Lesson 6.2 (grade 8–9)
After finding one variable, put its value into an equation to find the other variable.
Algebra I, Lesson 6.2 (grade 8–9)
back-substitutionEnglish
After finding the last variable, substituting it into earlier equations, one at a time, to find the other variables.
Algebra II, Lesson 2.4 (grade 10–11)
After finding the last variable, substituting it into earlier equations, one at a time, to find the other variables.
Algebra II, Lesson 2.4 (grade 10–11)
Back-to-back stemplotEnglish
Two stemplots that share one column of stems, with one group's leaves to the left and the other's to the right, used to compare two groups.
Statistics, Lesson 1.4 (grade 11–12)
Two stemplots that share one column of stems, with one group's leaves to the left and the other's to the right, used to compare two groups.
Statistics, Lesson 1.4 (grade 11–12)
bar notationEnglish
A bar drawn over the repetend to show that it repeats forever: 0.\overline{3} = 0.333\ldots and 0.8\overline{3} = 0.8333\ldots
Pre-Algebra, Lesson 4.5 (grade 6–8)
A bar drawn over the repetend to show that it repeats forever: 0.\overline{3} = 0.333\ldots and 0.8\overline{3} = 0.8333\ldots
Pre-Algebra, Lesson 4.5 (grade 6–8)
baseEnglish
The number or variable being multiplied by itself; in 5^3 the base is 5.
Algebra I, Lesson 7.1 (grade 8–9) · Algebra II, Lesson 8.1 (grade 10–11) · Grade 2 Earth Science: The Earth's Surface, Lesson 3.2 (grade 2) · +3 more
The number or variable being multiplied by itself; in 5^3 the base is 5.
Algebra I, Lesson 7.1 (grade 8–9) · Algebra II, Lesson 8.1 (grade 10–11) · Grade 2 Earth Science: The Earth's Surface, Lesson 3.2 (grade 2) · +3 more
base and heightEnglish
The base is the side you choose to measure along the bottom. The height is the straight-up (perpendicular) distance from the base to the opposite side or corner, measured at a right angle to the base, not along a slanted side.
Pre-Algebra, Lesson 12.3 (grade 6–8)
The base is the side you choose to measure along the bottom. The height is the straight-up (perpendicular) distance from the base to the opposite side or corner, measured at a right angle to the base, not along a slanted side.
Pre-Algebra, Lesson 12.3 (grade 6–8)
base and height of a parallelogramEnglish
Any side may be chosen as the base; the height is the perpendicular distance between the base and the opposite side (the line containing it).
Geometry, Lesson 11.1 (grade 9–10)
Any side may be chosen as the base; the height is the perpendicular distance between the base and the opposite side (the line containing it).
Geometry, Lesson 11.1 (grade 9–10)
base and height of a triangleEnglish
Any side may be chosen as the base; the height (altitude) is the perpendicular distance from the opposite vertex to the line containing the base.
Geometry, Lesson 11.1 (grade 9–10)
Any side may be chosen as the base; the height (altitude) is the perpendicular distance from the opposite vertex to the line containing the base.
Geometry, Lesson 11.1 (grade 9–10)
Base anglesEnglish
The two angles of an isosceles triangle that have the base as a side; each lies opposite a leg.
Geometry, Lesson 4.6 (grade 9–10)
The two angles of an isosceles triangle that have the base as a side; each lies opposite a leg.
Geometry, Lesson 4.6 (grade 9–10)
base angles of a trapezoidEnglish
A pair of angles whose vertices are the endpoints of the same base. A trapezoid has two pairs of base angles.
Geometry, Lesson 6.5 (grade 9–10)
A pair of angles whose vertices are the endpoints of the same base. A trapezoid has two pairs of base angles.
Geometry, Lesson 6.5 (grade 9–10)
base caseEnglish
The proof that the statement is true for the first value, usually n = 1.
Algebra II, Lesson 9.6 (grade 10–11)
The proof that the statement is true for the first value, usually n = 1.
Algebra II, Lesson 9.6 (grade 10–11)
bases of a trapezoidEnglish
The two parallel sides of a trapezoid, often called b_1 and b_2. The other two sides are the legs.
Geometry, Lesson 11.2 (grade 9–10)
The two parallel sides of a trapezoid, often called b_1 and b_2. The other two sides are the legs.
Geometry, Lesson 11.2 (grade 9–10)
benchmark percentEnglish
An easy percent such as 10%, 50% or 25% that you can find in your head and use to build other percents.
Pre-Algebra, Lesson 8.2 (grade 6–8)
An easy percent such as 10%, 50% or 25% that you can find in your head and use to build other percents.
Pre-Algebra, Lesson 8.2 (grade 6–8)
better buyEnglish
The choice with the lower unit price, so you pay less for each unit.
Pre-Algebra, Lesson 7.2 (grade 6–8)
The choice with the lower unit price, so you pay less for each unit.
Pre-Algebra, Lesson 7.2 (grade 6–8)
betweenEnglish
Point B is between A and C when A, B and C are different collinear points and B lies on \overline{AC}.
Geometry, Lesson 2.2 (grade 9–10)
Point B is between A and C when A, B and C are different collinear points and B lies on \overline{AC}.
Geometry, Lesson 2.2 (grade 9–10)
between the same parallelsEnglish
Euclid's phrase for figures whose bases lie on one line and whose opposite sides or vertices lie on a second line parallel to it, so that all of them have the same height.
Geometry, Lesson 11.1 (grade 9–10)
Euclid's phrase for figures whose bases lie on one line and whose opposite sides or vertices lie on a second line parallel to it, so that all of them have the same height.
Geometry, Lesson 11.1 (grade 9–10)
biconditionalEnglish
A statement of the form “p if and only if q,” written p \leftrightarrow q. It means both p \to q and q \to p, and it is true exactly when both of those conditionals are true.
Geometry, Lesson 1.3 (grade 9–10)
A statement of the form “p if and only if q,” written p \leftrightarrow q. It means both p \to q and q \to p, and it is true exactly when both of those conditionals are true.
Geometry, Lesson 1.3 (grade 9–10)
binomialEnglish
A polynomial with two terms, such as a + b, x - 2 or 2y - 1.
Algebra II, Lesson 10.3 (grade 10–11)
A polynomial with two terms, such as a + b, x - 2 or 2y - 1.
Algebra II, Lesson 10.3 (grade 10–11)
binomial and trinomialEnglish
A binomial is a polynomial with two terms (x + 4); a trinomial is a polynomial with three terms (x^2 - 3x + 2).
Algebra I, Lesson 8.1 (grade 8–9)
A binomial is a polynomial with two terms (x + 4); a trinomial is a polynomial with three terms (x^2 - 3x + 2).
Algebra I, Lesson 8.1 (grade 8–9)
binomial coefficientEnglish
The number C(n, k) = \binom{n}{k}, which is the coefficient of a^{n-k}b^k in the expansion of (a + b)^n.
Algebra II, Lesson 10.3 (grade 10–11) · Statistics, Lesson 8.1 (grade 11–12)
The number C(n, k) = \binom{n}{k}, which is the coefficient of a^{n-k}b^k in the expansion of (a + b)^n.
Algebra II, Lesson 10.3 (grade 10–11) · Statistics, Lesson 8.1 (grade 11–12)
binomial denominatorEnglish
A denominator with two terms, such as 3 - \sqrt{5}.
Algebra II, Lesson 6.3 (grade 10–11)
A denominator with two terms, such as 3 - \sqrt{5}.
Algebra II, Lesson 6.3 (grade 10–11)
Binomial meanEnglish
\mu = np, the long-run average number of successes in many repetitions of n trials.
Statistics, Lesson 8.2 (grade 11–12)
\mu = np, the long-run average number of successes in many repetitions of n trials.
Statistics, Lesson 8.2 (grade 11–12)
binomial probabilityEnglish
The probability of exactly k successes in n independent trials, each with success probability p: C(n, k)\,p^k(1-p)^{n-k}.
Algebra II, Lesson 10.4 (grade 10–11)
The probability of exactly k successes in n independent trials, each with success probability p: C(n, k)\,p^k(1-p)^{n-k}.
Algebra II, Lesson 10.4 (grade 10–11)
Binomial random variableEnglish
X = the number of successes in a binomial setting. Its possible values are 0, 1, 2, ..., n. We write X is B(n, p).
Statistics, Lesson 8.1 (grade 11–12)
X = the number of successes in a binomial setting. Its possible values are 0, 1, 2, ..., n. We write X is B(n, p).
Statistics, Lesson 8.1 (grade 11–12)
Binomial settingEnglish
A chance process with Binary outcomes, Independent trials, a fixed Number n of trials, and the Same probability p of success on every trial (BINS).
Statistics, Lesson 8.1 (grade 11–12)
A chance process with Binary outcomes, Independent trials, a fixed Number n of trials, and the Same probability p of success on every trial (BINS).
Statistics, Lesson 8.1 (grade 11–12)
Binomial standard deviationEnglish
\sigma = \sqrt{np(1 - p)}, the typical distance between the number of successes and the mean np.
Statistics, Lesson 8.2 (grade 11–12)
\sigma = \sqrt{np(1 - p)}, the typical distance between the number of successes and the mean np.
Statistics, Lesson 8.2 (grade 11–12)
Binomial TheoremEnglish
The formula (a + b)^n = \sum_{k=0}^{n} C(n, k)\,a^{n-k}b^k for multiplying out any power of a binomial.
Algebra II, Lesson 10.3 (grade 10–11)
The formula (a + b)^n = \sum_{k=0}^{n} C(n, k)\,a^{n-k}b^k for multiplying out any power of a binomial.
Algebra II, Lesson 10.3 (grade 10–11)
blueprintEnglish
A scale drawing that shows the plan of a building, used by carpenters and builders.
Pre-Algebra, Lesson 7.4 (grade 6–8)
A scale drawing that shows the plan of a building, used by carpenters and builders.
Pre-Algebra, Lesson 7.4 (grade 6–8)
boundaryEnglish
The curve or points where the two sides are equal. It is included (solid or closed) for \le and \ge, and left out (dashed or open) for < and >.
Algebra II, Lesson 3.5 (grade 10–11) · Grade 2 Earth Science: The Earth's Surface, Lesson 6.4 (grade 2) · Geography and History: Why Borders Fall Where They Do, Lesson 1.4 (grade 9–12)
The curve or points where the two sides are equal. It is included (solid or closed) for \le and \ge, and left out (dashed or open) for < and >.
Algebra II, Lesson 3.5 (grade 10–11) · Grade 2 Earth Science: The Earth's Surface, Lesson 6.4 (grade 2) · Geography and History: Why Borders Fall Where They Do, Lesson 1.4 (grade 9–12)
boundary lineEnglish
The line you get by replacing the inequality symbol with an equal sign. It splits the plane into two sides.
Algebra I, Lesson 6.6 (grade 8–9) · Algebra II, Lesson 2.2 (grade 10–11)
The line you get by replacing the inequality symbol with an equal sign. It splits the plane into two sides.
Algebra I, Lesson 6.6 (grade 8–9) · Algebra II, Lesson 2.2 (grade 10–11)
bounded regionEnglish
A region that can be enclosed in a circle; a region that goes on forever in some direction is unbounded.
Algebra II, Lesson 2.2 (grade 10–11)
A region that can be enclosed in a circle; a region that goes on forever in some direction is unbounded.
Algebra II, Lesson 2.2 (grade 10–11)
box modelEnglish
A rectangle divided into a grid, with the terms of one polynomial along the top and the terms of the other down the side. Each cell holds the product of its row term and column term, and the sum of all cells is the product.
Algebra I, Lesson 8.3 (grade 8–9)
A rectangle divided into a grid, with the terms of one polynomial along the top and the terms of the other down the side. Each cell holds the product of its row term and column term, and the sum of all cells is the product.
Algebra I, Lesson 8.3 (grade 8–9)
BoxplotEnglish
A graph of the five-number summary: a box from Q1 to Q3 with a line at the median, and whiskers reaching out toward the smallest and largest values.
Statistics, Lesson 2.3 (grade 11–12)
A graph of the five-number summary: a box from Q1 to Q3 with a line at the median, and whiskers reaching out toward the smallest and largest values.
Statistics, Lesson 2.3 (grade 11–12)
branch probabilityEnglish
The probability written on a branch. Second-stage branches carry conditional probabilities: the probability of that outcome given the branch it grows from.
Statistics, Lesson 6.5 (grade 11–12)
The probability written on a branch. Second-stage branches carry conditional probabilities: the probability of that outcome given the branch it grows from.
Statistics, Lesson 6.5 (grade 11–12)
break-even pointEnglish
The number of items at which a business's total income (revenue) equals its total cost, so it has neither gained nor lost money.
Algebra I, Lesson 6.5 (grade 8–9) · Accounting, Lesson 10.1 (grade 9–12) · Entrepreneurship & Sales, Lesson 4.3 (grade 9–12) · +3 more
The number of items at which a business's total income (revenue) equals its total cost, so it has neither gained nor lost money.
Algebra I, Lesson 6.5 (grade 8–9) · Accounting, Lesson 10.1 (grade 9–12) · Entrepreneurship & Sales, Lesson 4.3 (grade 9–12) · +3 more
C
cancelingEnglish
Dividing a numerator and a denominator by a common factor before you multiply, so the numbers stay small.
Pre-Algebra, Lesson 3.5 (grade 6–8)
Dividing a numerator and a denominator by a common factor before you multiply, so the numbers stay small.
Pre-Algebra, Lesson 3.5 (grade 6–8)
candidateEnglish
A number on the list of possible rational zeros \pm\dfrac{p}{q}. Each one must be tested; most will not be zeros.
Algebra II, Lesson 4.6 (grade 10–11)
A number on the list of possible rational zeros \pm\dfrac{p}{q}. Each one must be tested; most will not be zeros.
Algebra II, Lesson 4.6 (grade 10–11)
cardioidEnglish
A heart-shaped curve with equation r = a(1 \pm \cos\theta) or r = a(1 \pm \sin\theta); it passes through the pole with a point (cusp) there.
Trigonometry, Lesson 9.3 (grade 11–12)
A heart-shaped curve with equation r = a(1 \pm \cos\theta) or r = a(1 \pm \sin\theta); it passes through the pole with a point (cusp) there.
Trigonometry, Lesson 9.3 (grade 11–12)
carrying capacityEnglish
The number L that a logistic model approaches but never reaches: the largest population the pond, valley or town can support.
Algebra II, Lesson 7.4 (grade 10–11) · Explore Horses and Ponies · Expert, Stop 1.7 (Ages 14+) · Explore Horses and Ponies · Expert, Stop 4.5 (Ages 14+) · +3 more
The number L that a logistic model approaches but never reaches: the largest population the pond, valley or town can support.
Algebra II, Lesson 7.4 (grade 10–11) · Explore Horses and Ponies · Expert, Stop 1.7 (Ages 14+) · Explore Horses and Ponies · Expert, Stop 4.5 (Ages 14+) · +3 more
caseEnglish
One of the two possibilities you solve separately: the expression inside the bars equals c, or it equals -c.
Algebra I, Lesson 3.4 (grade 8–9) · English Grammar, Lesson 10.3 (grade 3–8) · Grade 5 Greek, Lesson 4.1 (grade 5) · +2 more
One of the two possibilities you solve separately: the expression inside the bars equals c, or it equals -c.
Algebra I, Lesson 3.4 (grade 8–9) · English Grammar, Lesson 10.3 (grade 3–8) · Grade 5 Greek, Lesson 4.1 (grade 5) · +2 more
case of a triangleEnglish
The pattern of the three given parts: AAS, ASA, SSA, SAS or SSS.
Trigonometry, Lesson 7.5 (grade 11–12)
The pattern of the three given parts: AAS, ASA, SSA, SAS or SSS.
Trigonometry, Lesson 7.5 (grade 11–12)
Categorical variableEnglish
A variable that places each individual into a group or category, such as breed, color or voice part. Numbers used only as labels (jersey numbers, ZIP codes) are categorical.
Statistics, Lesson 1.1 (grade 11–12)
A variable that places each individual into a group or category, such as breed, color or voice part. Numbers used only as labels (jersey numbers, ZIP codes) are categorical.
Statistics, Lesson 1.1 (grade 11–12)
CausationEnglish
Changing the explanatory variable actually produces a change in the response variable.
Statistics, Lesson 4.5 (grade 11–12)
Changing the explanatory variable actually produces a change in the response variable.
Statistics, Lesson 4.5 (grade 11–12)
Cavalieri's PrincipleEnglish
If two solids have the same height and the cross sections at every level have equal areas, then the two solids have equal volumes.
Geometry, Lesson 12.4 (grade 9–10)
If two solids have the same height and the cross sections at every level have equal areas, then the two solids have equal volumes.
Geometry, Lesson 12.4 (grade 9–10)
centerEnglish
The midpoint of the segment joining the foci; it is also the midpoint of both axes.
Algebra II, Lesson 11.2 (grade 10–11) · Grade 3 Composition & Creative Writing: The Fable and the First Story, Lesson 6.4 (grade 3) · Tactics & Strategy, Lesson 2.2 (grade 4–7)
The midpoint of the segment joining the foci; it is also the midpoint of both axes.
Algebra II, Lesson 11.2 (grade 10–11) · Grade 3 Composition & Creative Writing: The Fable and the First Story, Lesson 6.4 (grade 3) · Tactics & Strategy, Lesson 2.2 (grade 4–7)
Center and spreadEnglish
The center is a typical or middle value (for now, the median: the middle value when the data are in order). The spread describes how far the values vary, for now from the smallest to the largest.
Statistics, Lesson 1.5 (grade 11–12)
The center is a typical or middle value (for now, the median: the middle value when the data are in order). The spread describes how far the values vary, for now from the smallest to the largest.
Statistics, Lesson 1.5 (grade 11–12)
center of a regular polygonEnglish
The point that is the same distance from every vertex; it is the center of the circle through all the vertices.
Geometry, Lesson 11.3 (grade 9–10)
The point that is the same distance from every vertex; it is the center of the circle through all the vertices.
Geometry, Lesson 11.3 (grade 9–10)
center of dilationEnglish
The fixed point O from which all distances are stretched or shrunk.
Geometry, Lesson 7.5 (grade 9–10)
The fixed point O from which all distances are stretched or shrunk.
Geometry, Lesson 7.5 (grade 9–10)
center of rotationEnglish
The fixed point O about which a rotation turns the plane.
Geometry, Lesson 7.3 (grade 9–10)
The fixed point O about which a rotation turns the plane.
Geometry, Lesson 7.3 (grade 9–10)
Central angleEnglish
An angle whose vertex is the center of a circle.
Geometry, Lesson 10.1 (grade 9–10) · Trigonometry, Lesson 3.2 (grade 11–12)
An angle whose vertex is the center of a circle.
Geometry, Lesson 10.1 (grade 9–10) · Trigonometry, Lesson 3.2 (grade 11–12)
central angle of a regular polygonEnglish
An angle whose vertex is the center and whose sides pass through two consecutive vertices. A regular n-gon has n of them, each \dfrac{360^\circ}{n}.
Geometry, Lesson 11.3 (grade 9–10)
An angle whose vertex is the center and whose sides pass through two consecutive vertices. A regular n-gon has n of them, each \dfrac{360^\circ}{n}.
Geometry, Lesson 11.3 (grade 9–10)
Central limit theorem (CLT)English
When n is large, the sampling distribution of \bar{x} is approximately normal, with mean \mu and standard deviation \dfrac{\sigma}{\sqrt{n}}, whatever the shape of the population.
Statistics, Lesson 9.4 (grade 11–12)
When n is large, the sampling distribution of \bar{x} is approximately normal, with mean \mu and standard deviation \dfrac{\sigma}{\sqrt{n}}, whatever the shape of the population.
Statistics, Lesson 9.4 (grade 11–12)
central rectangleEnglish
The rectangle centered at the center of the hyperbola with sides 2a and 2b; its diagonals, extended, are the asymptotes.
Algebra II, Lesson 11.3 (grade 10–11)
The rectangle centered at the center of the hyperbola with sides 2a and 2b; its diagonals, extended, are the asymptotes.
Algebra II, Lesson 11.3 (grade 10–11)
centroidEnglish
The point where the three medians of a triangle meet. It is the triangle's balance point (center of gravity).
Geometry, Lesson 5.3 (grade 9–10)
The point where the three medians of a triangle meet. It is the triangle's balance point (center of gravity).
Geometry, Lesson 5.3 (grade 9–10)
change-of-base formulaEnglish
The rule \log_b x = \dfrac{\log_c x}{\log_c b}, which turns a logarithm in any base b into logarithms in a base c your calculator has (usually 10 or e).
Algebra II, Lesson 8.3 (grade 10–11)
The rule \log_b x = \dfrac{\log_c x}{\log_c b}, which turns a logarithm in any base b into logarithms in a base c your calculator has (usually 10 or e).
Algebra II, Lesson 8.3 (grade 10–11)
cherry-pickingEnglish
Reporting only the data or results that support the conclusion you want, and leaving out the rest.
Statistics, Lesson 13.3 (grade 11–12)
Reporting only the data or results that support the conclusion you want, and leaving out the rest.
Statistics, Lesson 13.3 (grade 11–12)
chi-square distributionEnglish
A family of right-skewed density curves that take only values of 0 or more; each one is named by its degrees of freedom, and its mean equals its degrees of freedom.
Statistics, Lesson 13.1 (grade 11–12)
A family of right-skewed density curves that take only values of 0 or more; each one is named by its degrees of freedom, and its mean equals its degrees of freedom.
Statistics, Lesson 13.1 (grade 11–12)
chi-square statisticEnglish
The number \chi^2 = \sum \dfrac{(\text{observed} - \text{expected})^2}{\text{expected}}, which measures how far all the observed counts are from the expected counts, taken together.
Statistics, Lesson 13.1 (grade 11–12)
The number \chi^2 = \sum \dfrac{(\text{observed} - \text{expected})^2}{\text{expected}}, which measures how far all the observed counts are from the expected counts, taken together.
Statistics, Lesson 13.1 (grade 11–12)
chi-square test for homogeneityEnglish
A test that compares the distribution of one categorical variable across several populations or treatments, using separate random samples or groups formed by random assignment. H_0: the distribution is the same in every population (or for every treatment).
Statistics, Lesson 13.2 (grade 11–12)
A test that compares the distribution of one categorical variable across several populations or treatments, using separate random samples or groups formed by random assignment. H_0: the distribution is the same in every population (or for every treatment).
Statistics, Lesson 13.2 (grade 11–12)
chi-square test for independenceEnglish
A test that uses ONE random sample in which two categorical variables are recorded for each individual. H_0: there is no association between the two variables in the population.
Statistics, Lesson 13.2 (grade 11–12)
A test that uses ONE random sample in which two categorical variables are recorded for each individual. H_0: there is no association between the two variables in the population.
Statistics, Lesson 13.2 (grade 11–12)
Chord and diameterEnglish
A chord is a segment whose endpoints both lie on the circle. A diameter is a chord that passes through the center; its length is twice the radius.
Geometry, Lesson 10.1 (grade 9–10)
A chord is a segment whose endpoints both lie on the circle. A diameter is a chord that passes through the center; its length is twice the radius.
Geometry, Lesson 10.1 (grade 9–10)
circumcenterEnglish
The point where the three perpendicular bisectors of the sides of a triangle meet. It is equidistant from the three vertices.
Geometry, Lesson 5.2 (grade 9–10)
The point where the three perpendicular bisectors of the sides of a triangle meet. It is equidistant from the three vertices.
Geometry, Lesson 5.2 (grade 9–10)
circumcircleEnglish
The circle passing through all three vertices of a triangle; its radius is the circumradius R.
Trigonometry, Lesson 7.2 (grade 11–12)
The circle passing through all three vertices of a triangle; its radius is the circumradius R.
Trigonometry, Lesson 7.2 (grade 11–12)
circumscribed circleEnglish
The circle that passes through all three vertices of a triangle (its circumcircle). Its center is the circumcenter and its radius is the circumradius.
Geometry, Lesson 5.2 (grade 9–10)
The circle that passes through all three vertices of a triangle (its circumcircle). Its center is the circumcenter and its radius is the circumradius.
Geometry, Lesson 5.2 (grade 9–10)
Circumscribed polygonEnglish
A polygon whose sides are all tangent to a circle. The circle is then inscribed in the polygon.
Geometry, Lesson 10.3 (grade 9–10)
A polygon whose sides are all tangent to a circle. The circle is then inscribed in the polygon.
Geometry, Lesson 10.3 (grade 9–10)
clearing decimalsEnglish
Multiplying every term on both sides by 10, 100 or 1000 so that every decimal becomes a whole number.
Algebra I, Lesson 2.4 (grade 8–9)
Multiplying every term on both sides by 10, 100 or 1000 so that every decimal becomes a whole number.
Algebra I, Lesson 2.4 (grade 8–9)
clearing fractionsEnglish
Multiplying every term on both sides of an equation by the LCD so that no fractions remain.
Algebra I, Lesson 2.4 (grade 8–9)
Multiplying every term on both sides of an equation by the LCD so that no fractions remain.
Algebra I, Lesson 2.4 (grade 8–9)
clinometerEnglish
A simple instrument for measuring angles of elevation and depression, often a protractor with a weighted string or a level and sighting tube.
Trigonometry, Lesson 8.1 (grade 11–12)
A simple instrument for measuring angles of elevation and depression, often a protractor with a weighted string or a level and sighting tube.
Trigonometry, Lesson 8.1 (grade 11–12)
closed and open endpointsEnglish
A solid dot shows that an endpoint belongs to a piece of the graph; a hollow dot shows that it does not.
Algebra II, Lesson 1.3 (grade 10–11)
A solid dot shows that an endpoint belongs to a piece of the graph; a hollow dot shows that it does not.
Algebra II, Lesson 1.3 (grade 10–11)
closed circleEnglish
A filled-in dot on a number line graph showing that the endpoint IS a solution (used with \le and \ge).
Algebra I, Lesson 3.1 (grade 8–9)
A filled-in dot on a number line graph showing that the endpoint IS a solution (used with \le and \ge).
Algebra I, Lesson 3.1 (grade 8–9)
ClosureEnglish
A set is closed under an operation if doing that operation on any two members of the set always gives another member of the set.
Algebra I, Lesson 1.2 (grade 8–9)
A set is closed under an operation if doing that operation on any two members of the set always gives another member of the set.
Algebra I, Lesson 1.2 (grade 8–9)
cluster sampleEnglish
A sample chosen by dividing the population into groups (clusters) that are each a mix of individuals, choosing an SRS of clusters, and including every individual in the chosen clusters.
Statistics, Lesson 5.2 (grade 11–12)
A sample chosen by dividing the population into groups (clusters) that are each a mix of individuals, choosing an SRS of clusters, and including every individual in the chosen clusters.
Statistics, Lesson 5.2 (grade 11–12)
Clusters and gapsEnglish
A cluster is a group of values close together; a gap is a stretch of the number line with no values, separating clusters.
Statistics, Lesson 1.5 (grade 11–12)
A cluster is a group of values close together; a gap is a stretch of the number line with no values, separating clusters.
Statistics, Lesson 1.5 (grade 11–12)
C(n, r) or \binom{n}{r}English
Read "n choose r": the number of ways to choose r objects from n different objects when order does not matter.
Algebra II, Lesson 10.2 (grade 10–11)
Read "n choose r": the number of ways to choose r objects from n different objects when order does not matter.
Algebra II, Lesson 10.2 (grade 10–11)
CoefficientEnglish
The number multiplying the variable part of a term. In 4x^2 it is 4; in -x it is -1.
Algebra I, Lesson 1.4 (grade 8–9) · Algebra I, Lesson 11.5 (grade 8–9) · Algebra I, Lesson 2.2 (grade 8–9) · +3 more
The number multiplying the variable part of a term. In 4x^2 it is 4; in -x it is -1.
Algebra I, Lesson 1.4 (grade 8–9) · Algebra I, Lesson 11.5 (grade 8–9) · Algebra I, Lesson 2.2 (grade 8–9) · +3 more
coefficient matrixEnglish
The matrix A of the coefficients of the variables in a system, one row per equation and one column per variable.
Algebra II, Lesson 12.4 (grade 10–11)
The matrix A of the coefficients of the variables in a system, one row per equation and one column per variable.
Algebra II, Lesson 12.4 (grade 10–11)
Coefficient of determination (r^2)English
The fraction of the variation in y that is accounted for by the linear relationship with x.
Statistics, Lesson 4.4 (grade 11–12)
The fraction of the variation in y that is accounted for by the linear relationship with x.
Statistics, Lesson 4.4 (grade 11–12)
cofunctionEnglish
Cosine is the sine of the complementary angle: the name comes from complementi sinus, "sine of the complement."
Trigonometry, Lesson 4.2 (grade 11–12)
Cosine is the sine of the complementary angle: the name comes from complementi sinus, "sine of the complement."
Trigonometry, Lesson 4.2 (grade 11–12)
cofunction identitiesEnglish
Identities such as \sin(90^\circ - \theta) = \cos\theta that relate a function of an angle to its cofunction of the complementary angle.
Trigonometry, Lesson 5.1 (grade 11–12)
Identities such as \sin(90^\circ - \theta) = \cos\theta that relate a function of an angle to its cofunction of the complementary angle.
Trigonometry, Lesson 5.1 (grade 11–12)
cofunction identityEnglish
An equation such as \sin\theta = \cos(90^\circ - \theta) that is true for every acute angle \theta.
Trigonometry, Lesson 2.3 (grade 11–12)
An equation such as \sin\theta = \cos(90^\circ - \theta) that is true for every acute angle \theta.
Trigonometry, Lesson 2.3 (grade 11–12)
CofunctionsEnglish
Sine and cosine are cofunctions: the sine of an angle equals the cosine of its complement. “Cosine” means “complement's sine.”
Geometry, Lesson 9.6 (grade 9–10) · Trigonometry, Lesson 2.3 (grade 11–12)
Sine and cosine are cofunctions: the sine of an angle equals the cosine of its complement. “Cosine” means “complement's sine.”
Geometry, Lesson 9.6 (grade 9–10) · Trigonometry, Lesson 2.3 (grade 11–12)
collect variable termsEnglish
Use addition or subtraction on both sides so that all the variable terms end up on one side of the equation.
Algebra I, Lesson 2.3 (grade 8–9)
Use addition or subtraction on both sides so that all the variable terms end up on one side of the equation.
Algebra I, Lesson 2.3 (grade 8–9)
collinear pointsEnglish
Points that lie on one line. Points that do not all lie on one line are noncollinear.
Geometry, Lesson 2.1 (grade 9–10)
Points that lie on one line. Points that do not all lie on one line are noncollinear.
Geometry, Lesson 2.1 (grade 9–10)
column vectorEnglish
A matrix with just one column, such as \begin{bmatrix} 3 \\ 4 \end{bmatrix}.
Algebra II, Lesson 12.2 (grade 10–11)
A matrix with just one column, such as \begin{bmatrix} 3 \\ 4 \end{bmatrix}.
Algebra II, Lesson 12.2 (grade 10–11)
combinationEnglish
A selection of objects in which order does not matter, such as a committee or a set of pizza toppings.
Algebra II, Lesson 10.2 (grade 10–11) · Playing the Odds, Lesson 1.2 (grade 8–12) · Statistics, Lesson 6.6 (grade 11–12)
A selection of objects in which order does not matter, such as a committee or a set of pizza toppings.
Algebra II, Lesson 10.2 (grade 10–11) · Playing the Odds, Lesson 1.2 (grade 8–12) · Statistics, Lesson 6.6 (grade 11–12)
combined variationEnglish
A mix of direct and inverse variation, such as y = \dfrac{kx}{z^2} (y varies directly as x and inversely as the square of z).
Algebra II, Lesson 5.6 (grade 10–11)
A mix of direct and inverse variation, such as y = \dfrac{kx}{z^2} (y varies directly as x and inversely as the square of z).
Algebra II, Lesson 5.6 (grade 10–11)
common baseEnglish
A single base, such as 2, in which both sides of an equation can be written, as in 8^x = (2^3)^x = 2^{3x}.
Algebra II, Lesson 8.4 (grade 10–11)
A single base, such as 2, in which both sides of an equation can be written, as in 8^x = (2^3)^x = 2^{3x}.
Algebra II, Lesson 8.4 (grade 10–11)
common binomial factorEnglish
A binomial, such as (x - 4), that appears as a factor in every term of an expression, so it can be factored out just like a number.
Algebra I, Lesson 9.1 (grade 8–9)
A binomial, such as (x - 4), that appears as a factor in every term of an expression, so it can be factored out just like a number.
Algebra I, Lesson 9.1 (grade 8–9)
common denominatorEnglish
A denominator that two or more fractions share, so their pieces are the same size.
Pre-Algebra, Lesson 3.2 (grade 6–8)
A denominator that two or more fractions share, so their pieces are the same size.
Pre-Algebra, Lesson 3.2 (grade 6–8)
common differenceEnglish
The fixed number d added each time in an arithmetic sequence; d = a_{n} - a_{n-1} for every term after the first.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra II, Lesson 9.2 (grade 10–11)
The fixed number d added each time in an arithmetic sequence; d = a_{n} - a_{n-1} for every term after the first.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra II, Lesson 9.2 (grade 10–11)
common factorEnglish
A number that is a factor of two or more numbers. 3 is a common factor of 12 and 18.
Pre-Algebra, Lesson 2.4 (grade 6–8)
A number that is a factor of two or more numbers. 3 is a common factor of 12 and 18.
Pre-Algebra, Lesson 2.4 (grade 6–8)
common logarithmEnglish
The logarithm with base 10, written \log x with no base shown, so \log x = \log_{10} x.
Algebra II, Lesson 8.1 (grade 10–11)
The logarithm with base 10, written \log x with no base shown, so \log x = \log_{10} x.
Algebra II, Lesson 8.1 (grade 10–11)
common multipleEnglish
A number that is a multiple of each of two or more numbers. 24 and 48 are common multiples of 6 and 8.
Pre-Algebra, Lesson 2.6 (grade 6–8)
A number that is a multiple of each of two or more numbers. 24 and 48 are common multiples of 6 and 8.
Pre-Algebra, Lesson 2.6 (grade 6–8)
common notionEnglish
Euclid's name for a general truth about quantities that is accepted without proof, such as “things equal to the same thing are equal to each other.”
Geometry, Lesson 1.1 (grade 9–10)
Euclid's name for a general truth about quantities that is accepted without proof, such as “things equal to the same thing are equal to each other.”
Geometry, Lesson 1.1 (grade 9–10)
common ratioEnglish
In a table with equally spaced x-values, the number you get by dividing any output by the one before it.
Algebra I, Lesson 7.4 (grade 8–9) · Algebra I, Lesson 7.6 (grade 8–9) · Algebra II, Lesson 9.3 (grade 10–11)
In a table with equally spaced x-values, the number you get by dividing any output by the one before it.
Algebra I, Lesson 7.4 (grade 8–9) · Algebra I, Lesson 7.6 (grade 8–9) · Algebra II, Lesson 9.3 (grade 10–11)
Common tangentEnglish
A line that is tangent to two circles, such as the straight part of a belt running around two pulleys.
Geometry, Lesson 10.3 (grade 9–10)
A line that is tangent to two circles, such as the straight part of a belt running around two pulleys.
Geometry, Lesson 10.3 (grade 9–10)
Commutative propertyEnglish
Changing the order of two numbers does not change a sum or product: a + b = b + a and ab = ba.
Algebra I, Lesson 1.2 (grade 8–9) · Pre-Algebra, Lesson 1.2 (grade 6–8)
Changing the order of two numbers does not change a sum or product: a + b = b + a and ab = ba.
Algebra I, Lesson 1.2 (grade 8–9) · Pre-Algebra, Lesson 1.2 (grade 6–8)
Comparison Property of InequalityEnglish
If a = b + c and c > 0, then a > b. This is Euclid's Common Notion 5: the whole is greater than the part.
Geometry, Lesson 5.5 (grade 9–10)
If a = b + c and c > 0, then a > b. This is Euclid's Common Notion 5: the whole is greater than the part.
Geometry, Lesson 5.5 (grade 9–10)
compass bearingEnglish
A direction given by starting at north or south and turning a stated angle toward east or west, such as N40^\circE or S25^\circW. The angle is between 0^\circ and 90^\circ.
Trigonometry, Lesson 8.2 (grade 11–12)
A direction given by starting at north or south and turning a stated angle toward east or west, such as N40^\circE or S25^\circW. The angle is between 0^\circ and 90^\circ.
Trigonometry, Lesson 8.2 (grade 11–12)
compatible numbersEnglish
Numbers that are easy to work with together, such as 25 and 4 (they multiply to 100) or 37 and 63 (they add to 100).
Pre-Algebra, Lesson 1.2 (grade 6–8) · Pre-Algebra, Lesson 1.5 (grade 6–8)
Numbers that are easy to work with together, such as 25 and 4 (they multiply to 100) or 37 and 63 (they add to 100).
Pre-Algebra, Lesson 1.2 (grade 6–8) · Pre-Algebra, Lesson 1.5 (grade 6–8)
complementEnglish
The event "E does not happen," written "not E"; its probability is 1 - P(E).
Algebra II, Lesson 10.4 (grade 10–11) · Grade 6 Art, Lesson 3.1 (grade 6) · Playing the Odds, Lesson 1.1 (grade 8–12) · +3 more
The event "E does not happen," written "not E"; its probability is 1 - P(E).
Algebra II, Lesson 10.4 (grade 10–11) · Grade 6 Art, Lesson 3.1 (grade 6) · Playing the Odds, Lesson 1.1 (grade 8–12) · +3 more
complementary and supplementary anglesEnglish
Two angles are complementary if they add to 90^\circ, and supplementary if they add to 180^\circ.
Pre-Algebra, Lesson 12.1 (grade 6–8)
Two angles are complementary if they add to 90^\circ, and supplementary if they add to 180^\circ.
Pre-Algebra, Lesson 12.1 (grade 6–8)
complementary anglesEnglish
Two angles whose measures add to 90^\circ. Each is the complement of the other.
Geometry, Lesson 2.4 (grade 9–10) · Trigonometry, Lesson 2.3 (grade 11–12)
Two angles whose measures add to 90^\circ. Each is the complement of the other.
Geometry, Lesson 2.4 (grade 9–10) · Trigonometry, Lesson 2.3 (grade 11–12)
completely randomized designEnglish
An experimental design in which all the experimental units are assigned to the treatments completely at random.
Statistics, Lesson 5.5 (grade 11–12)
An experimental design in which all the experimental units are assigned to the treatments completely at random.
Statistics, Lesson 5.5 (grade 11–12)
completing the squareEnglish
Adding the number \left(\dfrac{b}{2}\right)^2 to x^2 + bx so that it becomes a perfect-square trinomial \left(x + \dfrac{b}{2}\right)^2.
Algebra I, Lesson 11.4 (grade 8–9) · Algebra II, Lesson 11.4 (grade 10–11) · Algebra II, Lesson 3.2 (grade 10–11) · +1 more
Adding the number \left(\dfrac{b}{2}\right)^2 to x^2 + bx so that it becomes a perfect-square trinomial \left(x + \dfrac{b}{2}\right)^2.
Algebra I, Lesson 11.4 (grade 8–9) · Algebra II, Lesson 11.4 (grade 10–11) · Algebra II, Lesson 3.2 (grade 10–11) · +1 more
complex conjugateEnglish
The conjugate of a + bi is a - bi: the same real part, the opposite imaginary part.
Algebra II, Lesson 3.3 (grade 10–11)
The conjugate of a + bi is a - bi: the same real part, the opposite imaginary part.
Algebra II, Lesson 3.3 (grade 10–11)
complex fractionEnglish
A fraction that has a fraction in its numerator, its denominator, or both, such as \dfrac{\frac{1}{x} + \frac{1}{2}}{\frac{1}{x} - \frac{1}{2}}.
Algebra II, Lesson 5.2 (grade 10–11)
A fraction that has a fraction in its numerator, its denominator, or both, such as \dfrac{\frac{1}{x} + \frac{1}{2}}{\frac{1}{x} - \frac{1}{2}}.
Algebra II, Lesson 5.2 (grade 10–11)
complex numberEnglish
A number a + bi where a and b are real. The real number a is the real part and the real number b is the imaginary part.
Algebra II, Lesson 3.3 (grade 10–11)
A number a + bi where a and b are real. The real number a is the real part and the real number b is the imaginary part.
Algebra II, Lesson 3.3 (grade 10–11)
complex planeEnglish
A coordinate plane where a + bi is plotted as the point (a, b): the horizontal axis is the real axis and the vertical axis is the imaginary axis.
Algebra II, Lesson 3.3 (grade 10–11)
A coordinate plane where a + bi is plotted as the point (a, b): the horizontal axis is the real axis and the vertical axis is the imaginary axis.
Algebra II, Lesson 3.3 (grade 10–11)
componentEnglish
One entry of a vector. In \langle 3, 1 \rangle the x-component is 3 and the y-component is 1.
Algebra II, Lesson 12.5 (grade 10–11) · Graphic Design & Illustration, Lesson 9.2 (grade 9–12) · Graphic Design & Illustration, Lesson 9.5 (grade 9–12) · +1 more
One entry of a vector. In \langle 3, 1 \rangle the x-component is 3 and the y-component is 1.
Algebra II, Lesson 12.5 (grade 10–11) · Graphic Design & Illustration, Lesson 9.2 (grade 9–12) · Graphic Design & Illustration, Lesson 9.5 (grade 9–12) · +1 more
Components of a vectorEnglish
The horizontal and vertical parts of a vector; a vector of length r at angle \theta above the positive x-axis has components r\cos\theta and r\sin\theta.
Algebra II, Lesson 13.1 (grade 10–11)
The horizontal and vertical parts of a vector; a vector of length r at angle \theta above the positive x-axis has components r\cos\theta and r\sin\theta.
Algebra II, Lesson 13.1 (grade 10–11)
composite figureEnglish
A figure made of simpler figures, such as rectangles, triangles and trapezoids. Its area is found by adding the areas of non-overlapping pieces or subtracting the areas of cut-out pieces.
Geometry, Lesson 11.2 (grade 9–10) · Pre-Algebra, Lesson 12.3 (grade 6–8)
A figure made of simpler figures, such as rectangles, triangles and trapezoids. Its area is found by adding the areas of non-overlapping pieces or subtracting the areas of cut-out pieces.
Geometry, Lesson 11.2 (grade 9–10) · Pre-Algebra, Lesson 12.3 (grade 6–8)
composite numberEnglish
A whole number greater than 1 that has at least one factor other than 1 and itself. Examples: 4, 9, 15.
Pre-Algebra, Lesson 2.2 (grade 6–8)
A whole number greater than 1 that has at least one factor other than 1 and itself. Examples: 4, 9, 15.
Pre-Algebra, Lesson 2.2 (grade 6–8)
composite regionEnglish
A region built from simpler shapes (polygons, circles, sectors) by joining them or cutting some away.
Geometry, Lesson 11.6 (grade 9–10)
A region built from simpler shapes (polygons, circles, sectors) by joining them or cutting some away.
Geometry, Lesson 11.6 (grade 9–10)
composite solidEnglish
A solid made of two or more simpler solids joined together or with one removed from another.
Geometry, Lesson 12.4 (grade 9–10)
A solid made of two or more simpler solids joined together or with one removed from another.
Geometry, Lesson 12.4 (grade 9–10)
compositionEnglish
The function (f \circ g)(x) = f(g(x)): apply g first, then apply f to the result. Read "f of g of x."
Algebra II, Lesson 1.4 (grade 10–11) · Grade 1 Art, Lesson 7.4 (grade 1) · Grade 3 Art, Lesson 8.1 (grade 3) · +3 more
The function (f \circ g)(x) = f(g(x)): apply g first, then apply f to the result. Read "f of g of x."
Algebra II, Lesson 1.4 (grade 10–11) · Grade 1 Art, Lesson 7.4 (grade 1) · Grade 3 Art, Lesson 8.1 (grade 3) · +3 more
composition of transformationsEnglish
Doing one transformation and then another. Its matrix is the product of the two matrices, with the first step on the right.
Algebra II, Lesson 12.6 (grade 10–11)
Doing one transformation and then another. Its matrix is the product of the two matrices, with the first step on the right.
Algebra II, Lesson 12.6 (grade 10–11)
compound eventEnglish
An event made of two or more simple events, such as flipping a coin and then rolling a number cube.
Pre-Algebra, Lesson 13.4 (grade 6–8)
An event made of two or more simple events, such as flipping a coin and then rolling a number cube.
Pre-Algebra, Lesson 13.4 (grade 6–8)
compound inequalityEnglish
Two inequalities joined by the word "and" or the word "or."
Algebra I, Lesson 3.3 (grade 8–9)
Two inequalities joined by the word "and" or the word "or."
Algebra I, Lesson 3.3 (grade 8–9)
compound interestEnglish
Interest paid on both the original money (the principal) and on the interest already earned.
Algebra I, Lesson 7.5 (grade 8–9) · Grade 3 Business & Finance, Lesson 8.2 (grade 3) · Grade 4 Business & Finance, Lesson 8.2 (grade 4) · +3 more
Interest paid on both the original money (the principal) and on the interest already earned.
Algebra I, Lesson 7.5 (grade 8–9) · Grade 3 Business & Finance, Lesson 8.2 (grade 3) · Grade 4 Business & Finance, Lesson 8.2 (grade 4) · +3 more
compoundingEnglish
Adding the interest earned to the balance so that later interest is earned on the interest too. Compounding n times a year means the interest is added n times each year.
Algebra II, Lesson 7.2 (grade 10–11) · Personal Finance & Investing, Lesson 8.5 (grade 9–12)
Adding the interest earned to the balance so that later interest is earned on the interest too. Compounding n times a year means the interest is added n times each year.
Algebra II, Lesson 7.2 (grade 10–11) · Personal Finance & Investing, Lesson 8.5 (grade 9–12)
concave polygonEnglish
A polygon that is not convex; at least one interior angle is greater than 180^\circ, so the polygon 'caves in'.
Geometry, Lesson 6.1 (grade 9–10)
A polygon that is not convex; at least one interior angle is greater than 180^\circ, so the polygon 'caves in'.
Geometry, Lesson 6.1 (grade 9–10)
concentric circlesEnglish
Circles in the same plane with the same center and different radii.
Geometry, Lesson 11.5 (grade 9–10)
Circles in the same plane with the same center and different radii.
Geometry, Lesson 11.5 (grade 9–10)
concurrentEnglish
Three or more lines are concurrent when they all pass through one point, called the point of concurrency.
Geometry, Lesson 5.2 (grade 9–10)
Three or more lines are concurrent when they all pass through one point, called the point of concurrency.
Geometry, Lesson 5.2 (grade 9–10)
condenseEnglish
To rewrite a sum, difference or multiple of logarithms with the same base as a single logarithm.
Algebra II, Lesson 8.3 (grade 10–11) · Grade 3 Composition & Creative Writing: The Fable and the First Story, Lesson 9.2 (grade 3) · Grade 4 Composition & Creative Writing: The Fable Grown Up, and Narrative, Lesson 1.3 (grade 4) · +1 more
To rewrite a sum, difference or multiple of logarithms with the same base as a single logarithm.
Algebra II, Lesson 8.3 (grade 10–11) · Grade 3 Composition & Creative Writing: The Fable and the First Story, Lesson 9.2 (grade 3) · Grade 4 Composition & Creative Writing: The Fable Grown Up, and Narrative, Lesson 1.3 (grade 4) · +1 more
Conditional distributionEnglish
The distribution of one variable among only the individuals who share a given value of the other variable, such as "among the sheep raisers only".
Statistics, Lesson 1.3 (grade 11–12)
The distribution of one variable among only the individuals who share a given value of the other variable, such as "among the sheep raisers only".
Statistics, Lesson 1.3 (grade 11–12)
conditional statementEnglish
A statement of the form “if p, then q,” written p \to q. The part after “if” (p) is the hypothesis; the part after “then” (q) is the conclusion.
Geometry, Lesson 1.3 (grade 9–10)
A statement of the form “if p, then q,” written p \to q. The part after “if” (p) is the hypothesis; the part after “then” (q) is the conclusion.
Geometry, Lesson 1.3 (grade 9–10)
confidence intervalEnglish
An interval, estimate ± margin of error, computed from sample data, that gives a range of plausible values for a parameter.
Statistics, Lesson 10.1 (grade 11–12)
An interval, estimate ± margin of error, computed from sample data, that gives a range of plausible values for a parameter.
Statistics, Lesson 10.1 (grade 11–12)
confidence levelEnglish
The percent of all possible samples for which the method gives an interval that captures the true parameter (for example 95%).
Statistics, Lesson 10.1 (grade 11–12)
The percent of all possible samples for which the method gives an interval that captures the true parameter (for example 95%).
Statistics, Lesson 10.1 (grade 11–12)
ConfoundingEnglish
Two variables are confounded when their effects on a response cannot be told apart, so we cannot say which one caused a change.
Statistics, Lesson 4.5 (grade 11–12) · Statistics, Lesson 5.4 (grade 11–12)
Two variables are confounded when their effects on a response cannot be told apart, so we cannot say which one caused a change.
Statistics, Lesson 4.5 (grade 11–12) · Statistics, Lesson 5.4 (grade 11–12)
Congruence statementEnglish
A statement such as \triangle ABC \cong \triangle DEF, in which the order of the letters tells which vertices correspond: A \leftrightarrow D, B \leftrightarrow E, C \leftrightarrow F.
Geometry, Lesson 4.2 (grade 9–10)
A statement such as \triangle ABC \cong \triangle DEF, in which the order of the letters tells which vertices correspond: A \leftrightarrow D, B \leftrightarrow E, C \leftrightarrow F.
Geometry, Lesson 4.2 (grade 9–10)
congruent anglesEnglish
Angles that have the same measure. \angle A \cong \angle B means exactly m\angle A = m\angle B.
Geometry, Lesson 2.3 (grade 9–10)
Angles that have the same measure. \angle A \cong \angle B means exactly m\angle A = m\angle B.
Geometry, Lesson 2.3 (grade 9–10)
Congruent circles, concentric circles, congruent arcsEnglish
Congruent circles have congruent radii. Concentric circles lie in the same plane and have the same center. Congruent arcs are arcs of the same circle or of congruent circles that have equal measures.
Geometry, Lesson 10.1 (grade 9–10)
Congruent circles have congruent radii. Concentric circles lie in the same plane and have the same center. Congruent arcs are arcs of the same circle or of congruent circles that have equal measures.
Geometry, Lesson 10.1 (grade 9–10)
congruent figures (rigid-motion definition)English
Two figures are congruent if some sequence of rigid motions maps one onto the other.
Geometry, Lesson 7.4 (grade 9–10)
Two figures are congruent if some sequence of rigid motions maps one onto the other.
Geometry, Lesson 7.4 (grade 9–10)
Congruent polygonsEnglish
Two polygons are congruent if and only if their vertices can be matched so that every pair of corresponding sides is congruent and every pair of corresponding angles is congruent. Informally: same size and same shape.
Geometry, Lesson 4.2 (grade 9–10)
Two polygons are congruent if and only if their vertices can be matched so that every pair of corresponding sides is congruent and every pair of corresponding angles is congruent. Informally: same size and same shape.
Geometry, Lesson 4.2 (grade 9–10)
congruent segmentsEnglish
Segments that have the same length. \overline{AB} \cong \overline{CD} means exactly AB = CD.
Geometry, Lesson 2.2 (grade 9–10)
Segments that have the same length. \overline{AB} \cong \overline{CD} means exactly AB = CD.
Geometry, Lesson 2.2 (grade 9–10)
congruent segments and anglesEnglish
Segments are congruent (\cong) if they have equal lengths; angles are congruent if they have equal measures. (\overline{AB} \cong \overline{CD} means AB = CD; \angle A \cong \angle B means m\angle A = m\angle B.) These definitions are studied further in Lessons 2.2 and 2.3.
Geometry, Lesson 1.5 (grade 9–10)
Segments are congruent (\cong) if they have equal lengths; angles are congruent if they have equal measures. (\overline{AB} \cong \overline{CD} means AB = CD; \angle A \cong \angle B means m\angle A = m\angle B.) These definitions are studied further in Lessons 2.2 and 2.3.
Geometry, Lesson 1.5 (grade 9–10)
conic sectionEnglish
A curve made by slicing a double cone (two cones joined tip to tip) with a flat plane: a circle, an ellipse, a parabola or a hyperbola.
Algebra II, Lesson 11.1 (grade 10–11)
A curve made by slicing a double cone (two cones joined tip to tip) with a flat plane: a circle, an ellipse, a parabola or a hyperbola.
Algebra II, Lesson 11.1 (grade 10–11)
conjectureEnglish
An unproved statement based on observation; an educated guess that may be true or false.
Geometry, Lesson 1.2 (grade 9–10)
An unproved statement based on observation; an educated guess that may be true or false.
Geometry, Lesson 1.2 (grade 9–10)
conjugateEnglish
For an expression a + b, the expression a - b (and the reverse). Their product a^2 - b^2 often turns into a single term by a Pythagorean identity.
Trigonometry, Lesson 5.3 (grade 11–12)
For an expression a + b, the expression a - b (and the reverse). Their product a^2 - b^2 often turns into a single term by a Pythagorean identity.
Trigonometry, Lesson 5.3 (grade 11–12)
conjugate axisEnglish
The segment of length 2b through the center, perpendicular to the transverse axis.
Algebra II, Lesson 11.3 (grade 10–11)
The segment of length 2b through the center, perpendicular to the transverse axis.
Algebra II, Lesson 11.3 (grade 10–11)
conjugate pairEnglish
Two numbers p + qi and p - qi that are complex conjugates of each other.
Algebra II, Lesson 3.4 (grade 10–11) · Algebra II, Lesson 4.6 (grade 10–11)
Two numbers p + qi and p - qi that are complex conjugates of each other.
Algebra II, Lesson 3.4 (grade 10–11) · Algebra II, Lesson 4.6 (grade 10–11)
conjugatesEnglish
Two binomials that are the same except for the sign in the middle, such as 5 + \sqrt{3} and 5 - \sqrt{3}. Their product has no radical in it.
Algebra I, Lesson 10.3 (grade 8–9) · Algebra II, Lesson 6.3 (grade 10–11)
Two binomials that are the same except for the sign in the middle, such as 5 + \sqrt{3} and 5 - \sqrt{3}. Their product has no radical in it.
Algebra I, Lesson 10.3 (grade 8–9) · Algebra II, Lesson 6.3 (grade 10–11)
consecutive anglesEnglish
Two angles of a polygon whose vertices are the endpoints of the same side, such as \angle A and \angle B in quadrilateral ABCD.
Geometry, Lesson 6.2 (grade 9–10)
Two angles of a polygon whose vertices are the endpoints of the same side, such as \angle A and \angle B in quadrilateral ABCD.
Geometry, Lesson 6.2 (grade 9–10)
consecutive even (or odd) integersEnglish
Even (or odd) integers that follow one after another, such as 36, 38, 40 or 23, 25; written n, n + 2, n + 4.
Algebra I, Lesson 2.6 (grade 8–9) · Pre-Algebra, Lesson 10.6 (grade 6–8)
Even (or odd) integers that follow one after another, such as 36, 38, 40 or 23, 25; written n, n + 2, n + 4.
Algebra I, Lesson 2.6 (grade 8–9) · Pre-Algebra, Lesson 10.6 (grade 6–8)
consecutive integersEnglish
Integers that follow one after another, such as 28, 29, 30; written n, n + 1, n + 2.
Algebra I, Lesson 2.6 (grade 8–9) · Pre-Algebra, Lesson 10.6 (grade 6–8)
Integers that follow one after another, such as 28, 29, 30; written n, n + 1, n + 2.
Algebra I, Lesson 2.6 (grade 8–9) · Pre-Algebra, Lesson 10.6 (grade 6–8)
consecutive whole numbersEnglish
Whole numbers that come one right after the other, like 7 and 8.
Pre-Algebra, Lesson 6.5 (grade 6–8)
Whole numbers that come one right after the other, like 7 and 8.
Pre-Algebra, Lesson 6.5 (grade 6–8)
Conservative degrees of freedomEnglish
In this course, df = the smaller of n_1 - 1 and n_2 - 1. It gives a slightly wider interval and a slightly larger P-value than technology, so it errs on the safe side.
Statistics, Lesson 12.2 (grade 11–12)
In this course, df = the smaller of n_1 - 1 and n_2 - 1. It gives a slightly wider interval and a slightly larger P-value than technology, so it errs on the safe side.
Statistics, Lesson 12.2 (grade 11–12)
consistency checkEnglish
A test that a finished solution fits together: the angles sum to 180^\circ, the longest side faces the largest angle, and all three ratios \dfrac{a}{\sin A}, \dfrac{b}{\sin B}, \dfrac{c}{\sin C} agree.
Trigonometry, Lesson 7.5 (grade 11–12)
A test that a finished solution fits together: the angles sum to 180^\circ, the longest side faces the largest angle, and all three ratios \dfrac{a}{\sin A}, \dfrac{b}{\sin B}, \dfrac{c}{\sin C} agree.
Trigonometry, Lesson 7.5 (grade 11–12)
consistent and inconsistentEnglish
A system is consistent if it has at least one solution and inconsistent if it has no solution.
Algebra I, Lesson 6.1 (grade 8–9)
A system is consistent if it has at least one solution and inconsistent if it has no solution.
Algebra I, Lesson 6.1 (grade 8–9)
consistent systemEnglish
A system with at least one solution (exactly one, or infinitely many).
Algebra II, Lesson 2.1 (grade 10–11)
A system with at least one solution (exactly one, or infinitely many).
Algebra II, Lesson 2.1 (grade 10–11)
ConstantEnglish
A term with no variable, such as 9.
Algebra I, Lesson 1.4 (grade 8–9) · Electronics & Microcontrollers, Lesson 7.2 (grade 9–12) · Pre-Algebra, Lesson 9.1 (grade 6–8)
A term with no variable, such as 9.
Algebra I, Lesson 1.4 (grade 8–9) · Electronics & Microcontrollers, Lesson 7.2 (grade 9–12) · Pre-Algebra, Lesson 9.1 (grade 6–8)
constant of variationEnglish
The fixed number k in y = \dfrac{k}{x}. For inverse variation it equals the product xy of any matching pair of values.
Algebra I, Lesson 12.1 (grade 8–9) · Algebra I, Lesson 5.2 (grade 8–9) · Algebra II, Lesson 5.6 (grade 10–11) · +1 more
The fixed number k in y = \dfrac{k}{x}. For inverse variation it equals the product xy of any matching pair of values.
Algebra I, Lesson 12.1 (grade 8–9) · Algebra I, Lesson 5.2 (grade 8–9) · Algebra II, Lesson 5.6 (grade 10–11) · +1 more
constant rate of changeEnglish
A rate that stays the same: the output changes by the same amount for every equal change in the input. This is what makes a situation linear.
Algebra I, Lesson 5.7 (grade 8–9)
A rate that stays the same: the output changes by the same amount for every equal change in the input. This is what makes a situation linear.
Algebra I, Lesson 5.7 (grade 8–9)
constant termEnglish
A number in an expression with no variable attached, such as the 5 in 3x + 5.
Pre-Algebra, Lesson 10.4 (grade 6–8)
A number in an expression with no variable attached, such as the 5 in 3x + 5.
Pre-Algebra, Lesson 10.4 (grade 6–8)
constraintEnglish
A limit in a real situation, such as a budget or the space in a garden, written as an inequality.
Algebra I, Lesson 6.6 (grade 8–9) · Algebra II, Lesson 2.3 (grade 10–11) · Electronics & Microcontrollers, Lesson 10.4 (grade 9–12) · +3 more
A limit in a real situation, such as a budget or the space in a garden, written as an inequality.
Algebra I, Lesson 6.6 (grade 8–9) · Algebra II, Lesson 2.3 (grade 10–11) · Electronics & Microcontrollers, Lesson 10.4 (grade 9–12) · +3 more
Continuity correctionEnglish
An optional refinement: since each bar of the binomial histogram covers half a unit on each side of a whole number, use 40.5 instead of 40 (for example) when finding P(X \le 40) with the normal curve.
Statistics, Lesson 8.3 (grade 11–12)
An optional refinement: since each bar of the binomial histogram covers half a unit on each side of a whole number, use 40.5 instead of 40 (for example) when finding P(X \le 40) with the normal curve.
Statistics, Lesson 8.3 (grade 11–12)
continuous compoundingEnglish
The limit of compounding more and more often; the balance is A = Pe^{rt}.
Algebra II, Lesson 7.2 (grade 10–11)
The limit of compounding more and more often; the balance is A = Pe^{rt}.
Algebra II, Lesson 7.2 (grade 10–11)
Continuous distributionEnglish
A distribution whose values can be any number in an interval (like weights or lengths), described by a density curve. Probabilities are areas under the curve.
Statistics, Lesson 3.4 (grade 11–12)
A distribution whose values can be any number in an interval (like weights or lengths), described by a density curve. Probabilities are areas under the curve.
Statistics, Lesson 3.4 (grade 11–12)
continuous growth rateEnglish
The constant k in y = ae^{kt}; k > 0 means growth and k < 0 means decay.
Algebra II, Lesson 7.3 (grade 10–11)
The constant k in y = ae^{kt}; k > 0 means growth and k < 0 means decay.
Algebra II, Lesson 7.3 (grade 10–11)
Continuous random variableEnglish
A random variable that can take any value in an interval, such as a weight or a time. Its probabilities are areas under a density curve.
Statistics, Lesson 7.1 (grade 11–12) · Statistics, Lesson 7.4 (grade 11–12)
A random variable that can take any value in an interval, such as a weight or a time. Its probabilities are areas under a density curve.
Statistics, Lesson 7.1 (grade 11–12) · Statistics, Lesson 7.4 (grade 11–12)
contradictionEnglish
An equation that is false for every value of the variable, such as 2x + 5 = 2x - 1. It has no solution.
Algebra I, Lesson 2.3 (grade 8–9) · Algebra I, Lesson 6.2 (grade 8–9) · Geometry, Lesson 5.5 (grade 9–10)
An equation that is false for every value of the variable, such as 2x + 5 = 2x - 1. It has no solution.
Algebra I, Lesson 2.3 (grade 8–9) · Algebra I, Lesson 6.2 (grade 8–9) · Geometry, Lesson 5.5 (grade 9–10)
contrapositiveEnglish
The statement formed by switching and negating the hypothesis and conclusion: \sim q \to \sim p.
Geometry, Lesson 1.3 (grade 9–10)
The statement formed by switching and negating the hypothesis and conclusion: \sim q \to \sim p.
Geometry, Lesson 1.3 (grade 9–10)
convenience sampleEnglish
A sample made of the individuals that are easiest to reach. It usually leaves out whole kinds of individuals, so it is usually biased.
Statistics, Lesson 5.1 (grade 11–12)
A sample made of the individuals that are easiest to reach. It usually leaves out whole kinds of individuals, so it is usually biased.
Statistics, Lesson 5.1 (grade 11–12)
convergeEnglish
An infinite series converges if its partial sums get closer and closer to a single number S, as close as you like, as n grows. That number is called the sum of the series.
Algebra II, Lesson 9.4 (grade 10–11)
An infinite series converges if its partial sums get closer and closer to a single number S, as close as you like, as n grows. That number is called the sum of the series.
Algebra II, Lesson 9.4 (grade 10–11)
converseEnglish
The statement formed by switching the hypothesis and conclusion of a conditional: q \to p.
Geometry, Lesson 1.3 (grade 9–10) · Geometry, Lesson 3.3 (grade 9–10) · Geometry, Lesson 6.3 (grade 9–10) · +1 more
The statement formed by switching the hypothesis and conclusion of a conditional: q \to p.
Geometry, Lesson 1.3 (grade 9–10) · Geometry, Lesson 3.3 (grade 9–10) · Geometry, Lesson 6.3 (grade 9–10) · +1 more
Converse of the Corresponding Angles PostulateEnglish
If two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the lines are parallel.
Geometry, Lesson 3.3 (grade 9–10)
If two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the lines are parallel.
Geometry, Lesson 3.3 (grade 9–10)
Converse of the Hinge Theorem (SSS Inequality)English
If two sides of one triangle are congruent to two sides of another, and the third side of the first is longer, then the included angle of the first is larger.
Geometry, Lesson 5.6 (grade 9–10)
If two sides of one triangle are congruent to two sides of another, and the third side of the first is longer, then the included angle of the first is larger.
Geometry, Lesson 5.6 (grade 9–10)
converse of the Pythagorean theoremEnglish
If the sides of a triangle satisfy a^2 + b^2 = c^2, then the triangle is a right triangle, with the right angle across from side c.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 9.2 (grade 9–10)
If the sides of a triangle satisfy a^2 + b^2 = c^2, then the triangle is a right triangle, with the right angle across from side c.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 9.2 (grade 9–10)
Converse of the Triangle Proportionality TheoremEnglish
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Geometry, Lesson 8.5 (grade 9–10)
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Geometry, Lesson 8.5 (grade 9–10)
conversion factorEnglish
A fraction equal to 1 that changes units, such as \dfrac{5280 \text{ ft}}{1 \text{ mi}} or \dfrac{1 \text{ h}}{60 \text{ min}}.
Algebra I, Lesson 12.3 (grade 8–9) · Physics, Lesson 1.2 (grade 11–12) · Pre-Algebra, Lesson 7.5 (grade 6–8) · +1 more
A fraction equal to 1 that changes units, such as \dfrac{5280 \text{ ft}}{1 \text{ mi}} or \dfrac{1 \text{ h}}{60 \text{ min}}.
Algebra I, Lesson 12.3 (grade 8–9) · Physics, Lesson 1.2 (grade 11–12) · Pre-Algebra, Lesson 7.5 (grade 6–8) · +1 more
conversion formulasEnglish
The equations x = r\cos\theta, y = r\sin\theta, r^2 = x^2 + y^2, \tan\theta = \dfrac{y}{x} that translate between polar and rectangular coordinates when the pole is the origin and the polar axis is the positive x-axis.
Trigonometry, Lesson 9.2 (grade 11–12)
The equations x = r\cos\theta, y = r\sin\theta, r^2 = x^2 + y^2, \tan\theta = \dfrac{y}{x} that translate between polar and rectangular coordinates when the pole is the origin and the polar axis is the positive x-axis.
Trigonometry, Lesson 9.2 (grade 11–12)
convex polygonEnglish
A polygon in which no line that contains a side passes through the interior; every interior angle is less than 180^\circ.
Geometry, Lesson 6.1 (grade 9–10)
A polygon in which no line that contains a side passes through the interior; every interior angle is less than 180^\circ.
Geometry, Lesson 6.1 (grade 9–10)
coordinate argumentEnglish
A proof about a figure with given coordinates: compute the needed lengths, slopes or midpoints, then state which definition or theorem the numbers satisfy.
Geometry, Lesson 13.2 (grade 9–10)
A proof about a figure with given coordinates: compute the needed lengths, slopes or midpoints, then state which definition or theorem the numbers satisfy.
Geometry, Lesson 13.2 (grade 9–10)
coordinate planeEnglish
A flat grid made by a horizontal number line (the x-axis) and a vertical number line (the y-axis) that cross at the origin (0, 0).
Algebra I, Lesson 4.1 (grade 8–9) · Pre-Algebra, Lesson 11.1 (grade 6–8)
A flat grid made by a horizontal number line (the x-axis) and a vertical number line (the y-axis) that cross at the origin (0, 0).
Algebra I, Lesson 4.1 (grade 8–9) · Pre-Algebra, Lesson 11.1 (grade 6–8)
coordinate proofEnglish
A proof of a general theorem in which the figure is placed on coordinate axes with variable coordinates, and the conclusion is shown by algebra with the distance, midpoint and slope formulas.
Geometry, Lesson 13.3 (grade 9–10)
A proof of a general theorem in which the figure is placed on coordinate axes with variable coordinates, and the conclusion is shown by algebra with the distance, midpoint and slope formulas.
Geometry, Lesson 13.3 (grade 9–10)
coplanar pointsEnglish
Points that lie in one plane. Points that do not all lie in one plane are noncoplanar.
Geometry, Lesson 2.1 (grade 9–10)
Points that lie in one plane. Points that do not all lie in one plane are noncoplanar.
Geometry, Lesson 2.1 (grade 9–10)
corner-point methodEnglish
Find every vertex of the feasible region, evaluate the objective function at each, and pick the largest or smallest value.
Algebra II, Lesson 2.3 (grade 10–11)
Find every vertex of the feasible region, evaluate the objective function at each, and pick the largest or smallest value.
Algebra II, Lesson 2.3 (grade 10–11)
CorollaryEnglish
A theorem that follows quickly from another theorem that has just been proved.
Geometry, Lesson 4.1 (grade 9–10)
A theorem that follows quickly from another theorem that has just been proved.
Geometry, Lesson 4.1 (grade 9–10)
correction termEnglish
The quantity -2ab\cos C that adjusts the Pythagorean sum a^2 + b^2: negative when C is acute, zero when C is right, positive when C is obtuse.
Trigonometry, Lesson 7.4 (grade 11–12)
The quantity -2ab\cos C that adjusts the Pythagorean sum a^2 + b^2: negative when C is acute, zero when C is right, positive when C is obtuse.
Trigonometry, Lesson 7.4 (grade 11–12)
correlationEnglish
A relationship between two variables in which one tends to change in a regular way as the other changes. It is positive if y tends to rise as x rises, negative if y tends to fall as x rises, and none if there is no clear trend.
Algebra I, Lesson 13.1 (grade 8–9) · Investment Adviser Exam Prep: Series 65, Lesson 3.4 (grade 9–12) · Investment Adviser Exam Prep: Series 65, Lesson 8.1 (grade 9–12) · +3 more
A relationship between two variables in which one tends to change in a regular way as the other changes. It is positive if y tends to rise as x rises, negative if y tends to fall as x rises, and none if there is no clear trend.
Algebra I, Lesson 13.1 (grade 8–9) · Investment Adviser Exam Prep: Series 65, Lesson 3.4 (grade 9–12) · Investment Adviser Exam Prep: Series 65, Lesson 8.1 (grade 9–12) · +3 more
correlation coefficient rEnglish
A number between -1 and 1 that a calculator reports to measure how closely data fit a line. Its sign gives the direction of the correlation, and values near -1 or 1 mean a strong correlation.
Algebra I, Lesson 13.2 (grade 8–9)
A number between -1 and 1 that a calculator reports to measure how closely data fit a line. Its sign gives the direction of the correlation, and values near -1 or 1 mean a strong correlation.
Algebra I, Lesson 13.2 (grade 8–9)
Correlation (r)English
A number between −1 and 1 that measures the direction and strength of the LINEAR relationship between two quantitative variables.
Statistics, Lesson 4.2 (grade 11–12)
A number between −1 and 1 that measures the direction and strength of the LINEAR relationship between two quantitative variables.
Statistics, Lesson 4.2 (grade 11–12)
corresponding anglesEnglish
Two angles formed by a transversal and two lines that sit in the same position at the two intersection points: on the same side of the transversal, and both above or both below their own lines.
Geometry, Lesson 3.1 (grade 9–10)
Two angles formed by a transversal and two lines that sit in the same position at the two intersection points: on the same side of the transversal, and both above or both below their own lines.
Geometry, Lesson 3.1 (grade 9–10)
Corresponding Angles PostulateEnglish
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
Geometry, Lesson 3.2 (grade 9–10)
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
Geometry, Lesson 3.2 (grade 9–10)
Corresponding partsEnglish
Sides or angles that are matched with each other by the pairing of vertices in two polygons.
Geometry, Lesson 4.2 (grade 9–10)
Sides or angles that are matched with each other by the pairing of vertices in two polygons.
Geometry, Lesson 4.2 (grade 9–10)
cosecantEnglish
For an acute angle \theta, \csc\theta = \dfrac{\text{hyp}}{\text{opp}} = \dfrac{1}{\sin\theta}.
Trigonometry, Lesson 1.5 (grade 11–12)
For an acute angle \theta, \csc\theta = \dfrac{\text{hyp}}{\text{opp}} = \dfrac{1}{\sin\theta}.
Trigonometry, Lesson 1.5 (grade 11–12)
CosineEnglish
For an acute angle A of a right triangle, \cos A = \dfrac{\text{adjacent leg}}{\text{hypotenuse}}.
Geometry, Lesson 9.6 (grade 9–10) · Trigonometry, Lesson 1.2 (grade 11–12)
For an acute angle A of a right triangle, \cos A = \dfrac{\text{adjacent leg}}{\text{hypotenuse}}.
Geometry, Lesson 9.6 (grade 9–10) · Trigonometry, Lesson 1.2 (grade 11–12)
cotangentEnglish
For an acute angle \theta, \cot\theta = \dfrac{\text{adj}}{\text{opp}} = \dfrac{1}{\tan\theta}.
Trigonometry, Lesson 1.5 (grade 11–12) · Trigonometry, Lesson 4.7 (grade 11–12)
For an acute angle \theta, \cot\theta = \dfrac{\text{adj}}{\text{opp}} = \dfrac{1}{\tan\theta}.
Trigonometry, Lesson 1.5 (grade 11–12) · Trigonometry, Lesson 4.7 (grade 11–12)
Coterminal anglesEnglish
Angles in standard position with the same terminal side; they differ by a whole number of full turns (360^\circ or 2\pi radians).
Algebra II, Lesson 13.2 (grade 10–11) · Trigonometry, Lesson 3.1 (grade 11–12)
Angles in standard position with the same terminal side; they differ by a whole number of full turns (360^\circ or 2\pi radians).
Algebra II, Lesson 13.2 (grade 10–11) · Trigonometry, Lesson 3.1 (grade 11–12)
counting principleEnglish
If one choice can be made in m ways and a second choice can be made in n ways, the two choices together can be made in m \times n ways.
Pre-Algebra, Lesson 13.4 (grade 6–8)
If one choice can be made in m ways and a second choice can be made in n ways, the two choices together can be made in m \times n ways.
Pre-Algebra, Lesson 13.4 (grade 6–8)
CPCTCEnglish
Short for 'Corresponding Parts of Congruent Triangles are Congruent.' Once two triangles are proved congruent, each pair of corresponding sides and angles is congruent.
Geometry, Lesson 4.5 (grade 9–10)
Short for 'Corresponding Parts of Congruent Triangles are Congruent.' Once two triangles are proved congruent, each pair of corresponding sides and angles is congruent.
Geometry, Lesson 4.5 (grade 9–10)
critical value t^*English
The number such that the middle C% of the t distribution with the given df lies between -t^* and t^*.
Statistics, Lesson 10.3 (grade 11–12)
The number such that the middle C% of the t distribution with the given df lies between -t^* and t^*.
Statistics, Lesson 10.3 (grade 11–12)
critical value z^*English
The number of standard deviations needed so that the middle C% of the standard normal curve lies between -z^* and z^*.
Statistics, Lesson 10.1 (grade 11–12)
The number of standard deviations needed so that the middle C% of the standard normal curve lies between -z^* and z^*.
Statistics, Lesson 10.1 (grade 11–12)
cross productsEnglish
For \dfrac{a}{b} and \dfrac{c}{d}, the products a \times d and b \times c, found by multiplying across diagonally.
Pre-Algebra, Lesson 3.2 (grade 6–8) · Pre-Algebra, Lesson 7.3 (grade 6–8)
For \dfrac{a}{b} and \dfrac{c}{d}, the products a \times d and b \times c, found by multiplying across diagonally.
Pre-Algebra, Lesson 3.2 (grade 6–8) · Pre-Algebra, Lesson 7.3 (grade 6–8)
cross sectionEnglish
The flat shape you get where a plane slices through a solid.
Geometry, Lesson 12.1 (grade 9–10)
The flat shape you get where a plane slices through a solid.
Geometry, Lesson 12.1 (grade 9–10)
crossesEnglish
The graph passes from one side of the x-axis to the other at a zero. This happens at zeros of odd multiplicity.
Algebra II, Lesson 4.7 (grade 10–11)
The graph passes from one side of the x-axis to the other at a zero. This happens at zeros of odd multiplicity.
Algebra II, Lesson 4.7 (grade 10–11)
cube of a binomialEnglish
A product of the form (a + b)^3 or (a - b)^3, a binomial used as a factor three times.
Algebra II, Lesson 4.2 (grade 10–11)
A product of the form (a + b)^3 or (a - b)^3, a binomial used as a factor three times.
Algebra II, Lesson 4.2 (grade 10–11)
cube rootEnglish
A number whose cube is the given number. \sqrt[3]{64} = 4 because 4^3 = 64, and \sqrt[3]{-8} = -2 because (-2)^3 = -8.
Algebra I, Lesson 10.1 (grade 8–9)
A number whose cube is the given number. \sqrt[3]{64} = 4 because 4^3 = 64, and \sqrt[3]{-8} = -2 because (-2)^3 = -8.
Algebra I, Lesson 10.1 (grade 8–9)
cube root functionEnglish
The parent function y = \sqrt[3]{x}, with domain and range all real numbers.
Algebra II, Lesson 6.4 (grade 10–11)
The parent function y = \sqrt[3]{x}, with domain and range all real numbers.
Algebra II, Lesson 6.4 (grade 10–11)
Cumulative probabilityEnglish
The probability that X is at most some value, P(X \le k), found by adding the probabilities of 0, 1, ..., k.
Statistics, Lesson 8.2 (grade 11–12)
The probability that X is at most some value, P(X \le k), found by adding the probabilities of 0, 1, ..., k.
Statistics, Lesson 8.2 (grade 11–12)
Cumulative proportionEnglish
The proportion of values less than a given value: the area under the density curve to its left.
Statistics, Lesson 3.4 (grade 11–12)
The proportion of values less than a given value: the area under the density curve to its left.
Statistics, Lesson 3.4 (grade 11–12)
Cumulative relative frequencyEnglish
For a class in a frequency table, the proportion (or percent) of all values that fall in that class or in any class below it.
Statistics, Lesson 3.1 (grade 11–12)
For a class in a frequency table, the proportion (or percent) of all values that fall in that class or in any class below it.
Statistics, Lesson 3.1 (grade 11–12)
Cumulative relative frequency graphEnglish
A graph that plots cumulative percent against the right endpoint of each class, so you can read the percent of values less than any number on the axis.
Statistics, Lesson 3.1 (grade 11–12)
A graph that plots cumulative percent against the right endpoint of each class, so you can read the percent of values less than any number on the axis.
Statistics, Lesson 3.1 (grade 11–12)
current and windEnglish
A river's current or the wind adds to a boat's or plane's own speed when moving with it and subtracts when moving against it.
Algebra I, Lesson 6.5 (grade 8–9)
A river's current or the wind adds to a boat's or plane's own speed when moving with it and subtracts when moving against it.
Algebra I, Lesson 6.5 (grade 8–9)
customary systemEnglish
The system of units used in everyday life in the United States: inches, feet, yards, miles, ounces, pounds, cups, quarts, gallons.
Pre-Algebra, Lesson 7.5 (grade 6–8)
The system of units used in everyday life in the United States: inches, feet, yards, miles, ounces, pounds, cups, quarts, gallons.
Pre-Algebra, Lesson 7.5 (grade 6–8)
Cutoff valueEnglish
A value that separates a group, such as the height a corn stalk must exceed to be in the tallest 10%.
Statistics, Lesson 3.5 (grade 11–12)
A value that separates a group, such as the height a corn stalk must exceed to be in the tallest 10%.
Statistics, Lesson 3.5 (grade 11–12)
cycleEnglish
One complete pattern of a periodic graph, covering an interval whose length is one period.
Trigonometry, Lesson 4.1 (grade 11–12)
One complete pattern of a periodic graph, covering an interval whose length is one period.
Trigonometry, Lesson 4.1 (grade 11–12)
cylinder, cone and sphereEnglish
Solids with curved surfaces. A cylinder has two congruent parallel circular bases joined by a curved surface; a cone has one circular base and an apex; a sphere is the set of all points in space at a given distance (the radius) from a given point (the center).
Geometry, Lesson 12.1 (grade 9–10)
Solids with curved surfaces. A cylinder has two congruent parallel circular bases joined by a curved surface; a cone has one circular base and an apex; a sphere is the set of all points in space at a given distance (the radius) from a given point (the center).
Geometry, Lesson 12.1 (grade 9–10)
D
decay rateEnglish
The percent by which an amount decreases each time period, written as a decimal r.
Algebra I, Lesson 7.5 (grade 8–9) · Grade 8 Life Science: Heredity, Design and Origins, Lesson 5.2 (grade 8)
The percent by which an amount decreases each time period, written as a decimal r.
Algebra I, Lesson 7.5 (grade 8–9) · Grade 8 Life Science: Heredity, Design and Origins, Lesson 5.2 (grade 8)
decibel (dB)English
The unit of sound level L = 10\log\dfrac{I}{I_0}, where I is the sound's intensity and I_0 = 10^{-12} watts per square meter is the faintest sound a person can hear.
Algebra II, Lesson 8.6 (grade 10–11) · Grade 5 Life Science: The Human Body, Lesson 7.2 (grade 5)
The unit of sound level L = 10\log\dfrac{I}{I_0}, where I is the sound's intensity and I_0 = 10^{-12} watts per square meter is the faintest sound a person can hear.
Algebra II, Lesson 8.6 (grade 10–11) · Grade 5 Life Science: The Human Body, Lesson 7.2 (grade 5)
decimal methodEnglish
Changing the percent to a decimal and then multiplying: 35\% of 60 = 0.35 \times 60.
Pre-Algebra, Lesson 8.2 (grade 6–8)
Changing the percent to a decimal and then multiplying: 35\% of 60 = 0.35 \times 60.
Pre-Algebra, Lesson 8.2 (grade 6–8)
decimal placesEnglish
The number of digits to the right of the decimal point. For example, 2.45 has 2 decimal places.
Pre-Algebra, Lesson 4.3 (grade 6–8)
The number of digits to the right of the decimal point. For example, 2.45 has 2 decimal places.
Pre-Algebra, Lesson 4.3 (grade 6–8)
decimal pointEnglish
The dot that separates the whole-number part (on the left) from the parts smaller than one (on the right).
Pre-Algebra, Lesson 4.1 (grade 6–8)
The dot that separates the whole-number part (on the left) from the parts smaller than one (on the right).
Pre-Algebra, Lesson 4.1 (grade 6–8)
decompositionEnglish
Writing a complicated function as a composition of simpler ones.
Algebra II, Lesson 1.4 (grade 10–11) · Grade 7 Life Science: Cells and Microbes, Lesson 6.2 (grade 7)
Writing a complicated function as a composition of simpler ones.
Algebra II, Lesson 1.4 (grade 10–11) · Grade 7 Life Science: Cells and Microbes, Lesson 6.2 (grade 7)
deductive reasoningEnglish
Reasoning that reaches a conclusion by logic from statements already accepted (given facts, definitions, postulates and proved theorems). If the starting statements are true and the logic is valid, the conclusion must be true.
Geometry, Lesson 1.2 (grade 9–10)
Reasoning that reaches a conclusion by logic from statements already accepted (given facts, definitions, postulates and proved theorems). If the starting statements are true and the logic is valid, the conclusion must be true.
Geometry, Lesson 1.2 (grade 9–10)
Define a variableEnglish
To state in words exactly what a letter stands for, for example "Let w = the number of weeks Samuel saves."
Algebra I, Lesson 1.5 (grade 8–9) · Pre-Algebra, Lesson 10.6 (grade 6–8)
To state in words exactly what a letter stands for, for example "Let w = the number of weeks Samuel saves."
Algebra I, Lesson 1.5 (grade 8–9) · Pre-Algebra, Lesson 10.6 (grade 6–8)
definitionEnglish
A precise statement of the meaning of a new term, using undefined terms and terms already defined. Example: a circle is the set of all points in a plane at a given distance (the radius) from a given point (the center).
Geometry, Lesson 1.1 (grade 9–10)
A precise statement of the meaning of a new term, using undefined terms and terms already defined. Example: a circle is the set of all points in a plane at a given distance (the radius) from a given point (the center).
Geometry, Lesson 1.1 (grade 9–10)
degenerate conicEnglish
What you get when the plane slices through the tip of the double cone: a single point, a line, or a pair of crossing lines. Some equations in general form have no graph at all.
Algebra II, Lesson 11.4 (grade 10–11)
What you get when the plane slices through the tip of the double cone: a single point, a line, or a pair of crossing lines. Some equations in general form have no graph at all.
Algebra II, Lesson 11.4 (grade 10–11)
degreeEnglish
The degree of a monomial is the sum of the exponents of its variables (-6x^2y^3 has degree 5; a nonzero constant has degree 0). The degree of a polynomial is the greatest degree of any of its terms.
Algebra I, Lesson 8.1 (grade 8–9) · Algebra II, Lesson 4.1 (grade 10–11) · Grade 1 Earth Science: Rocks, Water and Weather, Lesson 8.1 (grade 1) · +2 more
The degree of a monomial is the sum of the exponents of its variables (-6x^2y^3 has degree 5; a nonzero constant has degree 0). The degree of a polynomial is the greatest degree of any of its terms.
Algebra I, Lesson 8.1 (grade 8–9) · Algebra II, Lesson 4.1 (grade 10–11) · Grade 1 Earth Science: Rocks, Water and Weather, Lesson 8.1 (grade 1) · +2 more
Degree modeEnglish
The calculator setting in which angles are measured in degrees. Check it by computing \tan 45^\circ, which must equal 1.
Geometry, Lesson 9.5 (grade 9–10) · Trigonometry, Lesson 1.3 (grade 11–12)
The calculator setting in which angles are measured in degrees. Check it by computing \tan 45^\circ, which must equal 1.
Geometry, Lesson 9.5 (grade 9–10) · Trigonometry, Lesson 1.3 (grade 11–12)
Degrees of freedomEnglish
The number of deviations that are free to vary: n − 1, because the deviations must add to 0, so the last one is fixed by the others.
Statistics, Lesson 2.4 (grade 11–12)
The number of deviations that are free to vary: n − 1, because the deviations must add to 0, so the last one is fixed by the others.
Statistics, Lesson 2.4 (grade 11–12)
degrees of freedom (df)English
The number that picks out one t distribution from the family; for one sample, df = n - 1, the number of deviations that are free to vary.
Statistics, Lesson 10.3 (grade 11–12) · Statistics, Lesson 11.3 (grade 11–12)
The number that picks out one t distribution from the family; for one sample, df = n - 1, the number of deviations that are free to vary.
Statistics, Lesson 10.3 (grade 11–12) · Statistics, Lesson 11.3 (grade 11–12)
degrees of freedom (goodness of fit)English
The number of categories minus 1: the number of counts that are free to vary once the total n is fixed.
Statistics, Lesson 13.1 (grade 11–12)
The number of categories minus 1: the number of counts that are free to vary once the total n is fixed.
Statistics, Lesson 13.1 (grade 11–12)
degrees of freedom (two-way table)English
df = (r - 1)(c - 1) for a table with r rows and c columns: the number of cells that can be filled in freely once all the row and column totals are fixed.
Statistics, Lesson 13.2 (grade 11–12)
df = (r - 1)(c - 1) for a table with r rows and c columns: the number of cells that can be filled in freely once all the row and column totals are fixed.
Statistics, Lesson 13.2 (grade 11–12)
denominatorEnglish
The bottom number of a fraction. It tells how many equal parts make one whole. It can never be 0.
Pre-Algebra, Lesson 3.1 (grade 6–8)
The bottom number of a fraction. It tells how many equal parts make one whole. It can never be 0.
Pre-Algebra, Lesson 3.1 (grade 6–8)
Density curveEnglish
A curve that is always on or above the horizontal axis and has total area exactly 1 underneath it. The area under the curve above any interval is the proportion of values in that interval.
Statistics, Lesson 3.2 (grade 11–12)
A curve that is always on or above the horizontal axis and has total area exactly 1 underneath it. The area under the curve above any interval is the proportion of values in that interval.
Statistics, Lesson 3.2 (grade 11–12)
denying the hypothesisEnglish
The invalid argument “p \to q is true and p is false, so q is false.” It treats the inverse as if it were true.
Geometry, Lesson 1.4 (grade 9–10)
The invalid argument “p \to q is true and p is false, so q is false.” It treats the inverse as if it were true.
Geometry, Lesson 1.4 (grade 9–10)
dependent eventsEnglish
Events that are not independent: knowing one has happened changes the probability of the other.
Statistics, Lesson 6.4 (grade 11–12)
Events that are not independent: knowing one has happened changes the probability of the other.
Statistics, Lesson 6.4 (grade 11–12)
dependent systemEnglish
A system whose two equations describe the same line, so every point on the line is a solution (infinitely many solutions).
Algebra I, Lesson 6.1 (grade 8–9) · Algebra II, Lesson 2.1 (grade 10–11)
A system whose two equations describe the same line, so every point on the line is a solution (infinitely many solutions).
Algebra I, Lesson 6.1 (grade 8–9) · Algebra II, Lesson 2.1 (grade 10–11)
dependent variableEnglish
The output quantity whose value depends on the input, usually y.
Algebra I, Lesson 4.1 (grade 8–9) · Food Science, Lesson 1.2 (grade 9–12) · Engineering Design, Robotics & Drones, Lesson 1.4 (grade 9–12) · +3 more
The output quantity whose value depends on the input, usually y.
Algebra I, Lesson 4.1 (grade 8–9) · Food Science, Lesson 1.2 (grade 9–12) · Engineering Design, Robotics & Drones, Lesson 1.4 (grade 9–12) · +3 more
depreciationEnglish
The loss in value of an item, such as a truck or tractor, as it ages.
Algebra I, Lesson 7.5 (grade 8–9) · Algebra II, Lesson 7.3 (grade 10–11) · Accounting, Lesson 3.2 (grade 9–12) · +3 more
The loss in value of an item, such as a truck or tractor, as it ages.
Algebra I, Lesson 7.5 (grade 8–9) · Algebra II, Lesson 7.3 (grade 10–11) · Accounting, Lesson 3.2 (grade 9–12) · +3 more
determinantEnglish
A single number computed from a square matrix, written \det A or with straight bars. For \begin{bmatrix} a & b \\ c & d \end{bmatrix} it is ad - bc.
Algebra II, Lesson 12.3 (grade 10–11)
A single number computed from a square matrix, written \det A or with straight bars. For \begin{bmatrix} a & b \\ c & d \end{bmatrix} it is ad - bc.
Algebra II, Lesson 12.3 (grade 10–11)
DeviationEnglish
How far a value is from the mean, with a sign: x - \bar{x}. Values above the mean have positive deviations; values below have negative deviations.
Statistics, Lesson 2.4 (grade 11–12)
How far a value is from the mean, with a sign: x - \bar{x}. Values above the mean have positive deviations; values below have negative deviations.
Statistics, Lesson 2.4 (grade 11–12)
diagonal of a squareEnglish
The segment joining two opposite corners of a square; it cuts the square into two congruent 45-45-90 triangles.
Trigonometry, Lesson 2.1 (grade 11–12)
The segment joining two opposite corners of a square; it cuts the square into two congruent 45-45-90 triangles.
Trigonometry, Lesson 2.1 (grade 11–12)
differenceEnglish
The result of subtracting one number from another.
Pre-Algebra, Lesson 5.3 (grade 6–8) · Pre-Algebra, Lesson 9.3 (grade 6–8)
The result of subtracting one number from another.
Pre-Algebra, Lesson 5.3 (grade 6–8) · Pre-Algebra, Lesson 9.3 (grade 6–8)
Difference (d)English
For each pair, the first measurement minus the second, d = x_1 - x_2, always subtracted in the same order.
Statistics, Lesson 12.3 (grade 11–12)
For each pair, the first measurement minus the second, d = x_1 - x_2, always subtracted in the same order.
Statistics, Lesson 12.3 (grade 11–12)
difference formulaEnglish
A formula that expresses a function of A - B, such as \cos(A - B), in terms of functions of A and of B.
Trigonometry, Lesson 5.4 (grade 11–12)
A formula that expresses a function of A - B, such as \cos(A - B), in terms of functions of A and of B.
Trigonometry, Lesson 5.4 (grade 11–12)
Difference of meansEnglish
The parameter \mu_1 - \mu_2, the true mean of population (or treatment) 1 minus the true mean of population (or treatment) 2. Its estimate is \bar{x}_1 - \bar{x}_2.
Statistics, Lesson 12.2 (grade 11–12)
The parameter \mu_1 - \mu_2, the true mean of population (or treatment) 1 minus the true mean of population (or treatment) 2. Its estimate is \bar{x}_1 - \bar{x}_2.
Statistics, Lesson 12.2 (grade 11–12)
Difference of proportionsEnglish
The parameter p_1 - p_2, the true proportion of successes in group 1 minus the true proportion in group 2. Its estimate is \hat{p}_1 - \hat{p}_2.
Statistics, Lesson 12.1 (grade 11–12)
The parameter p_1 - p_2, the true proportion of successes in group 1 minus the true proportion in group 2. Its estimate is \hat{p}_1 - \hat{p}_2.
Statistics, Lesson 12.1 (grade 11–12)
Difference of random variablesEnglish
A new random variable X - Y formed by subtracting, such as how much longer one runner takes than another.
Statistics, Lesson 7.3 (grade 11–12)
A new random variable X - Y formed by subtracting, such as how much longer one runner takes than another.
Statistics, Lesson 7.3 (grade 11–12)
difference of two squaresEnglish
An expression of the form a^2 - b^2. It is the product (a + b)(a - b) of a sum and a difference of the same two terms.
Algebra I, Lesson 8.4 (grade 8–9) · Algebra I, Lesson 9.4 (grade 8–9)
An expression of the form a^2 - b^2. It is the product (a + b)(a - b) of a sum and a difference of the same two terms.
Algebra I, Lesson 8.4 (grade 8–9) · Algebra I, Lesson 9.4 (grade 8–9)
digitEnglish
One of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 that we use to write every number.
Pre-Algebra, Lesson 1.1 (grade 6–8)
One of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 that we use to write every number.
Pre-Algebra, Lesson 1.1 (grade 6–8)
digit sumEnglish
The number you get by adding up all the digits of a number. The digit sum of 4,725 is 4 + 7 + 2 + 5 = 18.
Pre-Algebra, Lesson 2.1 (grade 6–8)
The number you get by adding up all the digits of a number. The digit sum of 4,725 is 4 + 7 + 2 + 5 = 18.
Pre-Algebra, Lesson 2.1 (grade 6–8)
dilationEnglish
The dilation with center O and scale factor k \ne 0 maps O to itself and each other point P to the point P' with OP' = |k| \cdot OP, on \overrightarrow{OP} if k > 0 and on the ray opposite \overrightarrow{OP} if k < 0.
Geometry, Lesson 7.5 (grade 9–10)
The dilation with center O and scale factor k \ne 0 maps O to itself and each other point P to the point P' with OP' = |k| \cdot OP, on \overrightarrow{OP} if k > 0 and on the ray opposite \overrightarrow{OP} if k < 0.
Geometry, Lesson 7.5 (grade 9–10)
dimensionsEnglish
The size of a matrix, written rows × columns. A matrix with 2 rows and 3 columns is a 2 × 3 matrix (read "two by three").
Algebra II, Lesson 12.1 (grade 10–11)
The size of a matrix, written rows × columns. A matrix with 2 rows and 3 columns is a 2 × 3 matrix (read "two by three").
Algebra II, Lesson 12.1 (grade 10–11)
direct variationEnglish
Review from Lesson 5.2: a relationship y = kx, where the ratio \dfrac{y}{x} stays constant and the graph is a line through the origin.
Algebra I, Lesson 12.1 (grade 8–9) · Algebra I, Lesson 5.2 (grade 8–9) · Algebra II, Lesson 5.6 (grade 10–11) · +1 more
Review from Lesson 5.2: a relationship y = kx, where the ratio \dfrac{y}{x} stays constant and the graph is a line through the origin.
Algebra I, Lesson 12.1 (grade 8–9) · Algebra I, Lesson 5.2 (grade 8–9) · Algebra II, Lesson 5.6 (grade 10–11) · +1 more
directed distanceEnglish
The signed value r: when r > 0 the point lies on the terminal side of \theta; when r < 0 it lies |r| units out on the opposite ray, in the direction \theta + 180^\circ.
Trigonometry, Lesson 9.1 (grade 11–12)
The signed value r: when r > 0 the point lies on the terminal side of \theta; when r < 0 it lies |r| units out on the opposite ray, in the direction \theta + 180^\circ.
Trigonometry, Lesson 9.1 (grade 11–12)
directed segmentEnglish
A segment with a starting point and an ending point, such as the segment from A to B. The direction matters when we partition it.
Geometry, Lesson 13.1 (grade 9–10)
A segment with a starting point and an ending point, such as the segment from A to B. The direction matters when we partition it.
Geometry, Lesson 13.1 (grade 9–10)
direction angleEnglish
The angle \theta a vector makes with the positive x-axis, measured counterclockwise, usually with 0^\circ \le \theta < 360^\circ.
Trigonometry, Lesson 9.4 (grade 11–12)
The angle \theta a vector makes with the positive x-axis, measured counterclockwise, usually with 0^\circ \le \theta < 360^\circ.
Trigonometry, Lesson 9.4 (grade 11–12)
directrixEnglish
The fixed line in the definition of a parabola. It lies outside the curve, perpendicular to the axis of symmetry.
Algebra II, Lesson 11.1 (grade 10–11)
The fixed line in the definition of a parabola. It lies outside the curve, perpendicular to the axis of symmetry.
Algebra II, Lesson 11.1 (grade 10–11)
discountEnglish
The amount taken off a regular price. A 25% discount takes 25% of the regular price away.
Pre-Algebra, Lesson 8.5 (grade 6–8)
The amount taken off a regular price. A 25% discount takes 25% of the regular price away.
Pre-Algebra, Lesson 8.5 (grade 6–8)
Discrete random variableEnglish
A random variable that takes a list of separate values, often counts such as 0, 1, 2, 3, each with its own probability.
Statistics, Lesson 7.1 (grade 11–12)
A random variable that takes a list of separate values, often counts such as 0, 1, 2, 3, each with its own probability.
Statistics, Lesson 7.1 (grade 11–12)
discriminantEnglish
The expression b^2 - 4ac under the square root in the quadratic formula; its sign tells how many real solutions ax^2 + bx + c = 0 has.
Algebra I, Lesson 11.6 (grade 8–9) · Algebra II, Lesson 3.2 (grade 10–11)
The expression b^2 - 4ac under the square root in the quadratic formula; its sign tells how many real solutions ax^2 + bx + c = 0 has.
Algebra I, Lesson 11.6 (grade 8–9) · Algebra II, Lesson 3.2 (grade 10–11)
distance between parallel linesEnglish
The length of a segment that is perpendicular to both parallel lines and has one endpoint on each.
Geometry, Lesson 3.4 (grade 9–10)
The length of a segment that is perpendicular to both parallel lines and has one endpoint on each.
Geometry, Lesson 3.4 (grade 9–10)
distance between two pointsEnglish
The length of the straight segment joining two points on the coordinate plane.
Pre-Algebra, Lesson 12.7 (grade 6–8)
The length of the straight segment joining two points on the coordinate plane.
Pre-Algebra, Lesson 12.7 (grade 6–8)
distance formulaEnglish
The formula for the length of the segment between two points: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 13.1 (grade 9–10)
The formula for the length of the segment between two points: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 13.1 (grade 9–10)
distance from a point to a lineEnglish
The length of the perpendicular segment from the point to the line. (If the point is on the line, the distance is 0.)
Geometry, Lesson 3.4 (grade 9–10) · Geometry, Lesson 5.1 (grade 9–10)
The length of the perpendicular segment from the point to the line. (If the point is on the line, the distance is 0.)
Geometry, Lesson 3.4 (grade 9–10) · Geometry, Lesson 5.1 (grade 9–10)
Distance from the center to a chordEnglish
The length of the perpendicular segment from the center to the chord.
Geometry, Lesson 10.2 (grade 9–10)
The length of the perpendicular segment from the center to the chord.
Geometry, Lesson 10.2 (grade 9–10)
distance–rate–timeEnglish
The relationship d = rt: distance equals rate (speed) times time.
Algebra I, Lesson 2.6 (grade 8–9)
The relationship d = rt: distance equals rate (speed) times time.
Algebra I, Lesson 2.6 (grade 8–9)
Distributive propertyEnglish
Multiplying a sum by a number is the same as multiplying each part and adding: a(b + c) = ab + ac.
Algebra I, Lesson 1.2 (grade 8–9) · Algebra I, Lesson 2.2 (grade 8–9) · Algebra I, Lesson 8.2 (grade 8–9) · +3 more
Multiplying a sum by a number is the same as multiplying each part and adding: a(b + c) = ab + ac.
Algebra I, Lesson 1.2 (grade 8–9) · Algebra I, Lesson 2.2 (grade 8–9) · Algebra I, Lesson 8.2 (grade 8–9) · +3 more
divergeEnglish
An infinite series diverges if its partial sums do not approach a single number; it has no sum.
Algebra II, Lesson 9.4 (grade 10–11)
An infinite series diverges if its partial sums do not approach a single number; it has no sum.
Algebra II, Lesson 9.4 (grade 10–11)
dividendEnglish
The polynomial being divided, f(x).
Algebra II, Lesson 4.3 (grade 10–11) · Accounting, Lesson 8.4 (grade 9–12) · Entrepreneurship & Sales, Lesson 5.3 (grade 9–12) · +3 more
The polynomial being divided, f(x).
Algebra II, Lesson 4.3 (grade 10–11) · Accounting, Lesson 8.4 (grade 9–12) · Entrepreneurship & Sales, Lesson 5.3 (grade 9–12) · +3 more
dividend, divisor, quotientEnglish
In \dfrac{12x^2 + 8x}{4x} = 3x + 2, the dividend is 12x^2 + 8x (what is divided), the divisor is 4x (what you divide by), and the quotient is 3x + 2 (the result).
Algebra I, Lesson 8.5 (grade 8–9)
In \dfrac{12x^2 + 8x}{4x} = 3x + 2, the dividend is 12x^2 + 8x (what is divided), the divisor is 4x (what you divide by), and the quotient is 3x + 2 (the result).
Algebra I, Lesson 8.5 (grade 8–9)
dividesEnglish
A whole number a divides a whole number N if N = a \cdot m for some whole number m. For example, 3 divides 15 because 15 = 3 \cdot 5.
Algebra II, Lesson 9.6 (grade 10–11)
A whole number a divides a whole number N if N = a \cdot m for some whole number m. For example, 3 divides 15 because 15 = 3 \cdot 5.
Algebra II, Lesson 9.6 (grade 10–11)
divisibleEnglish
A whole number is divisible by another if dividing gives a whole number with no remainder. For example, 18 is divisible by 3 because 18 \div 3 = 6.
Pre-Algebra, Lesson 2.1 (grade 6–8)
A whole number is divisible by another if dividing gives a whole number with no remainder. For example, 18 is divisible by 3 because 18 \div 3 = 6.
Pre-Algebra, Lesson 2.1 (grade 6–8)
division ladderEnglish
A way to factor by dividing a number by primes over and over, writing each quotient underneath, until the quotient is 1 or a prime.
Pre-Algebra, Lesson 2.3 (grade 6–8)
A way to factor by dividing a number by primes over and over, writing each quotient underneath, until the quotient is 1 or a prime.
Pre-Algebra, Lesson 2.3 (grade 6–8)
divisorEnglish
The expression you are dividing by. In \dfrac{a}{b} \div \dfrac{c}{d} the divisor is \dfrac{c}{d}.
Algebra I, Lesson 12.3 (grade 8–9) · Algebra II, Lesson 4.3 (grade 10–11) · Pre-Algebra, Lesson 3.6 (grade 6–8) · +2 more
The expression you are dividing by. In \dfrac{a}{b} \div \dfrac{c}{d} the divisor is \dfrac{c}{d}.
Algebra I, Lesson 12.3 (grade 8–9) · Algebra II, Lesson 4.3 (grade 10–11) · Pre-Algebra, Lesson 3.6 (grade 6–8) · +2 more
domainEnglish
The set of all inputs (x-values) of a relation or function.
Algebra I, Lesson 4.4 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11)
The set of all inputs (x-values) of a relation or function.
Algebra I, Lesson 4.4 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11)
domain checkEnglish
Substituting each candidate into every logarithm of the ORIGINAL equation to confirm each argument is positive.
Algebra II, Lesson 8.5 (grade 10–11)
Substituting each candidate into every logarithm of the ORIGINAL equation to confirm each argument is positive.
Algebra II, Lesson 8.5 (grade 10–11)
dot productEnglish
The number \mathbf{u} \cdot \mathbf{v} = u_1v_1 + u_2v_2 + \cdots + u_nv_n: multiply matching components and add.
Algebra II, Lesson 12.5 (grade 10–11) · Trigonometry, Lesson 9.5 (grade 11–12)
The number \mathbf{u} \cdot \mathbf{v} = u_1v_1 + u_2v_2 + \cdots + u_nv_n: multiply matching components and add.
Algebra II, Lesson 12.5 (grade 10–11) · Trigonometry, Lesson 9.5 (grade 11–12)
DotplotEnglish
A graph with a number line and one dot for each value, stacked when values repeat.
Statistics, Lesson 1.4 (grade 11–12)
A graph with a number line and one dot for each value, stacked when values repeat.
Statistics, Lesson 1.4 (grade 11–12)
double rootEnglish
The single solution of a quadratic equation whose discriminant is 0; the parabola touches the x-axis at its vertex.
Algebra I, Lesson 11.6 (grade 8–9)
The single solution of a quadratic equation whose discriminant is 0; the parabola touches the x-axis at its vertex.
Algebra I, Lesson 11.6 (grade 8–9)
double-angle formulasEnglish
Formulas for \sin 2\theta, \cos 2\theta and \tan 2\theta in terms of functions of \theta.
Trigonometry, Lesson 5.5 (grade 11–12)
Formulas for \sin 2\theta, \cos 2\theta and \tan 2\theta in terms of functions of \theta.
Trigonometry, Lesson 5.5 (grade 11–12)
double-blindEnglish
An experiment in which neither the subjects nor the people who work with them and measure the response know which treatment each subject received. In a single-blind experiment, only one side is kept from knowing.
Statistics, Lesson 5.5 (grade 11–12)
An experiment in which neither the subjects nor the people who work with them and measure the response know which treatment each subject received. In a single-blind experiment, only one side is kept from knowing.
Statistics, Lesson 5.5 (grade 11–12)
doubling timeEnglish
The time it takes a growing quantity to double. For exponential growth it is always the same.
Algebra II, Lesson 7.3 (grade 10–11) · Human Geography, Lesson 10.1 (grade 9–12) · Human Geography, Lesson 2.2 (grade 9–12) · +1 more
The time it takes a growing quantity to double. For exponential growth it is always the same.
Algebra II, Lesson 7.3 (grade 10–11) · Human Geography, Lesson 10.1 (grade 9–12) · Human Geography, Lesson 2.2 (grade 9–12) · +1 more
duality of tests and intervalsEnglish
The fact that a two-sided test at level \alpha rejects H_0: \mu = \mu_0 exactly when \mu_0 falls outside the 100(1 - \alpha)\% confidence interval for \mu.
Statistics, Lesson 11.5 (grade 11–12)
The fact that a two-sided test at level \alpha rejects H_0: \mu = \mu_0 exactly when \mu_0 falls outside the 100(1 - \alpha)\% confidence interval for \mu.
Statistics, Lesson 11.5 (grade 11–12)
E
E notationEnglish
How a calculator shows scientific notation: 3.2E5 means 3.2 \times 10^5.
Algebra I, Lesson 7.3 (grade 8–9)
How a calculator shows scientific notation: 3.2E5 means 3.2 \times 10^5.
Algebra I, Lesson 7.3 (grade 8–9)
effect sizeEnglish
How large the difference between the true parameter and the null value is, in the units of the problem; a confidence interval estimates it.
Statistics, Lesson 11.5 (grade 11–12)
How large the difference between the true parameter and the null value is, in the units of the problem; a confidence interval estimates it.
Statistics, Lesson 11.5 (grade 11–12)
eliminationEnglish
Adding or subtracting multiples of the equations to remove one variable (or one squared variable, such as y^2).
Algebra II, Lesson 11.5 (grade 10–11) · Sports & Games of the World, Lesson 6.1 (grade 8–12) · Grade 7 Geography: Regions of the World, Lesson 9.3 (grade 7)
Adding or subtracting multiples of the equations to remove one variable (or one squared variable, such as y^2).
Algebra II, Lesson 11.5 (grade 10–11) · Sports & Games of the World, Lesson 6.1 (grade 8–12) · Grade 7 Geography: Regions of the World, Lesson 9.3 (grade 7)
elimination methodEnglish
A way to solve a system by adding or subtracting the equations so that one variable drops out, leaving one equation in one variable.
Algebra I, Lesson 6.3 (grade 8–9)
A way to solve a system by adding or subtracting the equations so that one variable drops out, leaving one equation in one variable.
Algebra I, Lesson 6.3 (grade 8–9)
ellipseEnglish
The set of all points in a plane whose distances to two fixed points (the foci) add up to the same constant, called 2a.
Algebra II, Lesson 11.2 (grade 10–11) · Grade 3 Art, Lesson 2.1 (grade 3) · Grade 4 Art, Lesson 2.1 (grade 4) · +3 more
The set of all points in a plane whose distances to two fixed points (the foci) add up to the same constant, called 2a.
Algebra II, Lesson 11.2 (grade 10–11) · Grade 3 Art, Lesson 2.1 (grade 3) · Grade 4 Art, Lesson 2.1 (grade 4) · +3 more
end behaviorEnglish
What the outputs of a function do as x grows without bound to the right (x \to \infty) and to the left (x \to -\infty).
Algebra II, Lesson 1.6 (grade 10–11) · Algebra II, Lesson 4.1 (grade 10–11)
What the outputs of a function do as x grows without bound to the right (x \to \infty) and to the left (x \to -\infty).
Algebra II, Lesson 1.6 (grade 10–11) · Algebra II, Lesson 4.1 (grade 10–11)
enlargement and reductionEnglish
A dilation is an enlargement if |k| > 1 (the image is larger) and a reduction if 0 < |k| < 1 (the image is smaller).
Geometry, Lesson 7.5 (grade 9–10)
A dilation is an enlargement if |k| > 1 (the image is larger) and a reduction if 0 < |k| < 1 (the image is smaller).
Geometry, Lesson 7.5 (grade 9–10)
entryEnglish
One number in a matrix. In matrix A, the entry in row i and column j is written a_{ij}; the row number always comes first.
Algebra II, Lesson 12.1 (grade 10–11) · Grade 2 Business & Finance, Lesson 7.3 (grade 2) · Grade 3 Business & Finance, Lesson 7.2 (grade 3) · +3 more
One number in a matrix. In matrix A, the entry in row i and column j is written a_{ij}; the row number always comes first.
Algebra II, Lesson 12.1 (grade 10–11) · Grade 2 Business & Finance, Lesson 7.3 (grade 2) · Grade 3 Business & Finance, Lesson 7.2 (grade 3) · +3 more
equal coefficientsEnglish
Coefficients that are the same, like 2x and 2x. Subtracting one equation from the other eliminates that variable.
Algebra I, Lesson 6.3 (grade 8–9)
Coefficients that are the same, like 2x and 2x. Subtracting one equation from the other eliminates that variable.
Algebra I, Lesson 6.3 (grade 8–9)
equal matricesEnglish
Two matrices with the same dimensions whose corresponding entries are all equal.
Algebra II, Lesson 12.1 (grade 10–11)
Two matrices with the same dimensions whose corresponding entries are all equal.
Algebra II, Lesson 12.1 (grade 10–11)
EquationEnglish
A statement that two expressions are equal, such as 2n - 5 = 11. It is a complete sentence in mathematics.
Algebra I, Lesson 1.5 (grade 8–9) · Algebra I, Lesson 2.1 (grade 8–9) · Pre-Algebra, Lesson 10.1 (grade 6–8)
A statement that two expressions are equal, such as 2n - 5 = 11. It is a complete sentence in mathematics.
Algebra I, Lesson 1.5 (grade 8–9) · Algebra I, Lesson 2.1 (grade 8–9) · Pre-Algebra, Lesson 10.1 (grade 6–8)
equiangular trianglesEnglish
Euclid's name for triangles whose angles are congruent in pairs; by the AA Postulate, such triangles are similar.
Geometry, Lesson 8.3 (grade 9–10)
Euclid's name for triangles whose angles are congruent in pairs; by the AA Postulate, such triangles are similar.
Geometry, Lesson 8.3 (grade 9–10)
equidistantEnglish
A point is equidistant from two figures when its distance to each of them is the same.
Geometry, Lesson 5.1 (grade 9–10)
A point is equidistant from two figures when its distance to each of them is the same.
Geometry, Lesson 5.1 (grade 9–10)
Equilateral archEnglish
A pointed arch whose two curves are drawn from the two springing points with radius equal to the span, so the apex and the springing points form an equilateral triangle.
Geometry, Lesson 4.6 (grade 9–10)
A pointed arch whose two curves are drawn from the two springing points with radius equal to the span, so the apex and the springing points form an equilateral triangle.
Geometry, Lesson 4.6 (grade 9–10)
equilateral, isosceles, scaleneEnglish
Names for triangles by their sides: an equilateral triangle has all three sides equal, an isosceles triangle has at least two equal sides, and a scalene triangle has no equal sides.
Pre-Algebra, Lesson 12.2 (grade 6–8)
Names for triangles by their sides: an equilateral triangle has all three sides equal, an isosceles triangle has at least two equal sides, and a scalene triangle has no equal sides.
Pre-Algebra, Lesson 12.2 (grade 6–8)
equilateral triangleEnglish
A triangle whose three sides are all congruent.
Geometry, Lesson 2.5 (grade 9–10)
A triangle whose three sides are all congruent.
Geometry, Lesson 2.5 (grade 9–10)
equivalent equationsEnglish
Equations that have exactly the same solution, such as 3x = 21 and x = 7.
Algebra I, Lesson 2.1 (grade 8–9) · Algebra I, Lesson 5.4 (grade 8–9) · Algebra I, Lesson 6.4 (grade 8–9) · +1 more
Equations that have exactly the same solution, such as 3x = 21 and x = 7.
Algebra I, Lesson 2.1 (grade 8–9) · Algebra I, Lesson 5.4 (grade 8–9) · Algebra I, Lesson 6.4 (grade 8–9) · +1 more
equivalent expressionsEnglish
Expressions that have the same value for every allowed value of the variable, such as \dfrac{2}{x} and \dfrac{2(x + 3)}{x(x + 3)} (for x \ne -3).
Algebra I, Lesson 12.4 (grade 8–9) · Algebra II, Lesson 5.2 (grade 10–11)
Expressions that have the same value for every allowed value of the variable, such as \dfrac{2}{x} and \dfrac{2(x + 3)}{x(x + 3)} (for x \ne -3).
Algebra I, Lesson 12.4 (grade 8–9) · Algebra II, Lesson 5.2 (grade 10–11)
equivalent fractionsEnglish
Fractions that look different but name the same amount, like \dfrac{1}{2} and \dfrac{3}{6}.
Pre-Algebra, Lesson 3.1 (grade 6–8)
Fractions that look different but name the same amount, like \dfrac{1}{2} and \dfrac{3}{6}.
Pre-Algebra, Lesson 3.1 (grade 6–8)
equivalent ratiosEnglish
Ratios that make the same comparison, like 2:3 and 4:6. You get one from the other by multiplying or dividing both terms by the same nonzero number.
Pre-Algebra, Lesson 7.1 (grade 6–8)
Ratios that make the same comparison, like 2:3 and 4:6. You get one from the other by multiplying or dividing both terms by the same nonzero number.
Pre-Algebra, Lesson 7.1 (grade 6–8)
Euclidean algorithmEnglish
A method for finding the GCF of two numbers: divide the larger by the smaller, then divide the smaller by the remainder, and keep going until the remainder is 0. The last remainder that is not 0 is the GCF.
Pre-Algebra, Lesson 2.5 (grade 6–8)
A method for finding the GCF of two numbers: divide the larger by the smaller, then divide the smaller by the remainder, and keep going until the remainder is 0. The last remainder that is not 0 is the GCF.
Pre-Algebra, Lesson 2.5 (grade 6–8)
Euclid's fifth postulate (the parallel postulate)English
If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, then the two lines, if extended far enough, meet on that side.
Geometry, Lesson 3.2 (grade 9–10)
If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, then the two lines, if extended far enough, meet on that side.
Geometry, Lesson 3.2 (grade 9–10)
EvaluateEnglish
To find the value of an expression by replacing each variable with a given number and doing the arithmetic.
Algebra I, Lesson 1.3 (grade 8–9) · Pre-Algebra, Lesson 9.2 (grade 6–8)
To find the value of an expression by replacing each variable with a given number and doing the arithmetic.
Algebra I, Lesson 1.3 (grade 8–9) · Pre-Algebra, Lesson 9.2 (grade 6–8)
evaluate a functionEnglish
Find the output for a given input by substituting the input into the rule.
Algebra I, Lesson 4.3 (grade 8–9)
Find the output for a given input by substituting the input into the rule.
Algebra I, Lesson 4.3 (grade 8–9)
even and odd functionsEnglish
f is even if f(-x) = f(x) for every x in its domain, and odd if f(-x) = -f(x).
Algebra II, Lesson 1.6 (grade 10–11)
f is even if f(-x) = f(x) for every x in its domain, and odd if f(-x) = -f(x).
Algebra II, Lesson 1.6 (grade 10–11)
even and odd integersEnglish
An integer is even if it equals 2k for some integer k, and odd if it equals 2k + 1 for some integer k.
Geometry, Lesson 1.2 (grade 9–10)
An integer is even if it equals 2k for some integer k, and odd if it equals 2k + 1 for some integer k.
Geometry, Lesson 1.2 (grade 9–10)
even functionEnglish
A function with f(-x) = f(x) for all x; its graph is symmetric about the y-axis.
Trigonometry, Lesson 4.2 (grade 11–12) · Trigonometry, Lesson 5.1 (grade 11–12)
A function with f(-x) = f(x) for all x; its graph is symmetric about the y-axis.
Trigonometry, Lesson 4.2 (grade 11–12) · Trigonometry, Lesson 5.1 (grade 11–12)
eventEnglish
A set of outcomes from the sample space, such as "the sum is 7."
Algebra II, Lesson 10.4 (grade 10–11) · Grade 3 Composition & Creative Writing: The Fable and the First Story, Lesson 1.3 (grade 3) · Grade 7 Composition & Creative Writing: Commonplace, Encomium and Invective, Lesson 4.4 (grade 7) · +3 more
A set of outcomes from the sample space, such as "the sum is 7."
Algebra II, Lesson 10.4 (grade 10–11) · Grade 3 Composition & Creative Writing: The Fable and the First Story, Lesson 1.3 (grade 3) · Grade 7 Composition & Creative Writing: Commonplace, Encomium and Invective, Lesson 4.4 (grade 7) · +3 more
Exact answerEnglish
An answer written with radicals (such as 5\sqrt{3}) rather than a rounded decimal (such as 8.66).
Geometry, Lesson 9.4 (grade 9–10)
An answer written with radicals (such as 5\sqrt{3}) rather than a rounded decimal (such as 8.66).
Geometry, Lesson 9.4 (grade 9–10)
exact answer in terms of logarithmsEnglish
An answer such as x = \log_3 20 or x = \dfrac{\ln 20}{\ln 3}, kept as an expression with logarithms instead of a rounded decimal.
Algebra II, Lesson 8.4 (grade 10–11)
An answer such as x = \log_3 20 or x = \dfrac{\ln 20}{\ln 3}, kept as an expression with logarithms instead of a rounded decimal.
Algebra II, Lesson 8.4 (grade 10–11)
exact formEnglish
An answer written with integers, fractions and radicals, such as 3 \pm 2\sqrt{5}, with no rounding.
Algebra II, Lesson 3.2 (grade 10–11)
An answer written with integers, fractions and radicals, such as 3 \pm 2\sqrt{5}, with no rounding.
Algebra II, Lesson 3.2 (grade 10–11)
exact valueEnglish
A value written with whole numbers, fractions and radicals, such as \dfrac{\sqrt{2}}{2}, rather than a rounded decimal such as 0.707.
Trigonometry, Lesson 2.1 (grade 11–12) · Trigonometry, Lesson 3.3 (grade 11–12)
A value written with whole numbers, fractions and radicals, such as \dfrac{\sqrt{2}}{2}, rather than a rounded decimal such as 0.707.
Trigonometry, Lesson 2.1 (grade 11–12) · Trigonometry, Lesson 3.3 (grade 11–12)
excluded valueEnglish
A value of the variable that makes the denominator equal to zero. The expression is undefined there, so that value is not allowed.
Algebra I, Lesson 12.2 (grade 8–9) · Algebra II, Lesson 5.1 (grade 10–11)
A value of the variable that makes the denominator equal to zero. The expression is undefined there, so that value is not allowed.
Algebra I, Lesson 12.2 (grade 8–9) · Algebra II, Lesson 5.1 (grade 10–11)
expandEnglish
To rewrite the logarithm of a product, quotient or power as a sum, difference or multiple of simpler logarithms.
Algebra II, Lesson 8.3 (grade 10–11) · Grade 5 Composition & Creative Writing: Narrative and the Chreia, Lesson 7.3 (grade 5) · Grade 6 Composition & Creative Writing: Maxim, Refutation and Confirmation, Lesson 1.2 (grade 6) · +2 more
To rewrite the logarithm of a product, quotient or power as a sum, difference or multiple of simpler logarithms.
Algebra II, Lesson 8.3 (grade 10–11) · Grade 5 Composition & Creative Writing: Narrative and the Chreia, Lesson 7.3 (grade 5) · Grade 6 Composition & Creative Writing: Maxim, Refutation and Confirmation, Lesson 1.2 (grade 6) · +2 more
expanded formEnglish
A number written as a sum showing the value of each digit, such as 4 \times 1{,}000 + 5 \times 10 + 6 \times 1.
Pre-Algebra, Lesson 1.1 (grade 6–8)
A number written as a sum showing the value of each digit, such as 4 \times 1{,}000 + 5 \times 10 + 6 \times 1.
Pre-Algebra, Lesson 1.1 (grade 6–8)
expected count (two-way table)English
The count expected in a cell if H_0 is true: \dfrac{(\text{row total})(\text{column total})}{\text{table total}}.
Statistics, Lesson 13.2 (grade 11–12)
The count expected in a cell if H_0 is true: \dfrac{(\text{row total})(\text{column total})}{\text{table total}}.
Statistics, Lesson 13.2 (grade 11–12)
Expected value (mean) of a random variableEnglish
The long-run average value of X over very many repetitions of the chance process, written \mu_X or E(X). It is found by multiplying each value by its probability and adding.
Statistics, Lesson 7.2 (grade 11–12)
The long-run average value of X over very many repetitions of the chance process, written \mu_X or E(X). It is found by multiplying each value by its probability and adding.
Statistics, Lesson 7.2 (grade 11–12)
Expected z-scoreEnglish
The z-score a value would have, given its position in order, if the data were exactly normal. For 10 values, the smallest is placed at the 5th percentile (z \approx -1.64), the next at the 15th (z \approx -1.04), and so on up to the 95th.
Statistics, Lesson 3.6 (grade 11–12)
The z-score a value would have, given its position in order, if the data were exactly normal. For 10 values, the smallest is placed at the 5th percentile (z \approx -1.64), the next at the 15th (z \approx -1.04), and so on up to the 95th.
Statistics, Lesson 3.6 (grade 11–12)
experimental unitEnglish
The object to which a treatment is applied, such as a plot, a plant, a calf or a loaf of bread. When the units are people, they are called subjects.
Statistics, Lesson 5.4 (grade 11–12)
The object to which a treatment is applied, such as a plot, a plant, a calf or a loaf of bread. When the units are people, they are called subjects.
Statistics, Lesson 5.4 (grade 11–12)
Explanatory variableEnglish
The variable we think helps explain or predict changes in another variable; it goes on the horizontal (x) axis.
Statistics, Lesson 4.1 (grade 11–12)
The variable we think helps explain or predict changes in another variable; it goes on the horizontal (x) axis.
Statistics, Lesson 4.1 (grade 11–12)
explicit formulaEnglish
A rule that finds any term directly from its position n, such as a_n = 4n + 2.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra I, Lesson 7.6 (grade 8–9)
A rule that finds any term directly from its position n, such as a_n = 4n + 2.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra I, Lesson 7.6 (grade 8–9)
explicit ruleEnglish
A formula that gives a_n directly from n, such as a_n = 3n - 1.
Algebra II, Lesson 9.1 (grade 10–11)
A formula that gives a_n directly from n, such as a_n = 3n - 1.
Algebra II, Lesson 9.1 (grade 10–11)
exponentEnglish
The small raised number that tells how many times the base is used as a factor; in 5^3 the exponent is 3.
Algebra I, Lesson 7.1 (grade 8–9) · Pre-Algebra, Lesson 1.4 (grade 6–8) · Pre-Algebra, Lesson 6.1 (grade 6–8)
The small raised number that tells how many times the base is used as a factor; in 5^3 the exponent is 3.
Algebra I, Lesson 7.1 (grade 8–9) · Pre-Algebra, Lesson 1.4 (grade 6–8) · Pre-Algebra, Lesson 6.1 (grade 6–8)
exponent formEnglish
A way of writing repeated factors with exponents. The exponent tells how many times the base is used as a factor: 2 \times 2 \times 2 = 2^3.
Pre-Algebra, Lesson 2.3 (grade 6–8)
A way of writing repeated factors with exponents. The exponent tells how many times the base is used as a factor: 2 \times 2 \times 2 = 2^3.
Pre-Algebra, Lesson 2.3 (grade 6–8)
exponential decayEnglish
A pattern where 0 < b < 1, so the outputs shrink by the same factor at each step, getting closer and closer to 0.
Algebra I, Lesson 7.4 (grade 8–9) · Algebra II, Lesson 7.1 (grade 10–11)
A pattern where 0 < b < 1, so the outputs shrink by the same factor at each step, getting closer and closer to 0.
Algebra I, Lesson 7.4 (grade 8–9) · Algebra II, Lesson 7.1 (grade 10–11)
exponential equationEnglish
An equation with the variable in an exponent, such as 3^x = 20 or e^{0.04t} = 2.
Algebra II, Lesson 8.4 (grade 10–11)
An equation with the variable in an exponent, such as 3^x = 20 or e^{0.04t} = 2.
Algebra II, Lesson 8.4 (grade 10–11)
exponential functionEnglish
A function of the form y = a \cdot b^x with a \ne 0, b > 0 and b \ne 1; the variable is in the exponent.
Algebra I, Lesson 7.4 (grade 8–9) · Algebra II, Lesson 7.1 (grade 10–11)
A function of the form y = a \cdot b^x with a \ne 0, b > 0 and b \ne 1; the variable is in the exponent.
Algebra I, Lesson 7.4 (grade 8–9) · Algebra II, Lesson 7.1 (grade 10–11)
exponential growthEnglish
A pattern where b > 1, so the outputs get larger by the same factor at each step (for a > 0).
Algebra I, Lesson 7.4 (grade 8–9)
A pattern where b > 1, so the outputs get larger by the same factor at each step (for a > 0).
Algebra I, Lesson 7.4 (grade 8–9)
extended ratioEnglish
A comparison of three or more quantities, such as a : b : c, meaning the quantities are ax, bx and cx for some positive number x.
Geometry, Lesson 8.1 (grade 9–10)
A comparison of three or more quantities, such as a : b : c, meaning the quantities are ax, bx and cx for some positive number x.
Geometry, Lesson 8.1 (grade 9–10)
Exterior angleEnglish
An angle formed by one side of a triangle and the extension of an adjacent side. It forms a linear pair with the interior angle at that vertex.
Geometry, Lesson 4.1 (grade 9–10)
An angle formed by one side of a triangle and the extension of an adjacent side. It forms a linear pair with the interior angle at that vertex.
Geometry, Lesson 4.1 (grade 9–10)
exterior angle of a polygonEnglish
The angle formed at a vertex by one side and the extension of the adjacent side; it forms a linear pair with the interior angle at that vertex.
Geometry, Lesson 6.1 (grade 9–10)
The angle formed at a vertex by one side and the extension of the adjacent side; it forms a linear pair with the interior angle at that vertex.
Geometry, Lesson 6.1 (grade 9–10)
External secant segmentEnglish
The part of a secant segment that lies outside the circle, from the outside point to the nearer point where the line meets the circle, such as \overline{PA}.
Geometry, Lesson 10.6 (grade 9–10)
The part of a secant segment that lies outside the circle, from the outside point to the nearer point where the line meets the circle, such as \overline{PA}.
Geometry, Lesson 10.6 (grade 9–10)
extraneous solutionEnglish
A number produced by the solving steps that does not make the original equation true. It must be thrown out.
Algebra I, Lesson 10.4 (grade 8–9) · Algebra I, Lesson 12.5 (grade 8–9) · Algebra II, Lesson 5.5 (grade 10–11) · +3 more
A number produced by the solving steps that does not make the original equation true. It must be thrown out.
Algebra I, Lesson 10.4 (grade 8–9) · Algebra I, Lesson 12.5 (grade 8–9) · Algebra II, Lesson 5.5 (grade 10–11) · +3 more
extrapolationEnglish
Using a model to predict a value outside the range of the data you collected. It is riskier because the pattern may not continue.
Algebra I, Lesson 13.2 (grade 8–9) · Grade 6 Earth Science: The Dynamic Earth, Lesson 1.4 (grade 6) · Grade 6 Earth Science: The Dynamic Earth, Lesson 2.4 (grade 6) · +2 more
Using a model to predict a value outside the range of the data you collected. It is riskier because the pattern may not continue.
Algebra I, Lesson 13.2 (grade 8–9) · Grade 6 Earth Science: The Dynamic Earth, Lesson 1.4 (grade 6) · Grade 6 Earth Science: The Dynamic Earth, Lesson 2.4 (grade 6) · +2 more
extreme and mean ratio (golden ratio)English
A segment is cut in extreme and mean ratio when the whole is to the longer part as the longer part is to the shorter part. That common ratio is \varphi = \dfrac{1+\sqrt{5}}{2} \approx 1.618.
Geometry, Lesson 8.1 (grade 9–10)
A segment is cut in extreme and mean ratio when the whole is to the longer part as the longer part is to the shorter part. That common ratio is \varphi = \dfrac{1+\sqrt{5}}{2} \approx 1.618.
Geometry, Lesson 8.1 (grade 9–10)
F
factorEnglish
Something that is multiplied. In 3(x + 2) the factors are 3 and x + 2; a term, by contrast, is something that is added.
Algebra II, Lesson 5.1 (grade 10–11) · Pre-Algebra, Lesson 1.3 (grade 6–8) · Pre-Algebra, Lesson 2.1 (grade 6–8) · +3 more
Something that is multiplied. In 3(x + 2) the factors are 3 and x + 2; a term, by contrast, is something that is added.
Algebra II, Lesson 5.1 (grade 10–11) · Pre-Algebra, Lesson 1.3 (grade 6–8) · Pre-Algebra, Lesson 2.1 (grade 6–8) · +3 more
factor (an expression)English
To write an expression as a product, often by pulling out a common factor: 6x + 18 = 6(x + 3). Factoring undoes expanding.
Pre-Algebra, Lesson 9.5 (grade 6–8)
To write an expression as a product, often by pulling out a common factor: 6x + 18 = 6(x + 3). Factoring undoes expanding.
Pre-Algebra, Lesson 9.5 (grade 6–8)
factor completelyEnglish
Write a polynomial as a product of factors that cannot be factored further over the integers.
Algebra II, Lesson 4.5 (grade 10–11)
Write a polynomial as a product of factors that cannot be factored further over the integers.
Algebra II, Lesson 4.5 (grade 10–11)
factor (noun)English
One of the expressions being multiplied in a product. In 3(2x + 3), the factors are 3 and 2x + 3.
Algebra I, Lesson 9.1 (grade 8–9)
One of the expressions being multiplied in a product. In 3(2x + 3), the factors are 3 and 2x + 3.
Algebra I, Lesson 9.1 (grade 8–9)
factor pairEnglish
Two integers whose product is a given number. The factor pairs of 12 are 1 \times 12, 2 \times 6, 3 \times 4 and the same pairs with both numbers negative.
Algebra I, Lesson 9.2 (grade 8–9) · Pre-Algebra, Lesson 2.2 (grade 6–8)
Two integers whose product is a given number. The factor pairs of 12 are 1 \times 12, 2 \times 6, 3 \times 4 and the same pairs with both numbers negative.
Algebra I, Lesson 9.2 (grade 8–9) · Pre-Algebra, Lesson 2.2 (grade 6–8)
Factor TheoremEnglish
A polynomial f(x) has x - c as a factor exactly when f(c) = 0.
Algebra II, Lesson 4.5 (grade 10–11)
A polynomial f(x) has x - c as a factor exactly when f(c) = 0.
Algebra II, Lesson 4.5 (grade 10–11)
factor treeEnglish
A diagram that splits a number into two factors, then splits each composite factor again, until every branch ends in a prime.
Pre-Algebra, Lesson 2.3 (grade 6–8)
A diagram that splits a number into two factors, then splits each composite factor again, until every branch ends in a prime.
Pre-Algebra, Lesson 2.3 (grade 6–8)
factor (verb)English
To write an expression as a product. Factoring is the reverse of multiplying out: 6x + 9 factored is 3(2x + 3).
Algebra I, Lesson 9.1 (grade 8–9)
To write an expression as a product. Factoring is the reverse of multiplying out: 6x + 9 factored is 3(2x + 3).
Algebra I, Lesson 9.1 (grade 8–9)
factored completelyEnglish
Written as a product in which no factor (other than a single number) can be factored any further.
Algebra I, Lesson 9.1 (grade 8–9) · Algebra I, Lesson 9.5 (grade 8–9)
Written as a product in which no factor (other than a single number) can be factored any further.
Algebra I, Lesson 9.1 (grade 8–9) · Algebra I, Lesson 9.5 (grade 8–9)
factored (intercept) formEnglish
y = a(x - p)(x - q), which shows the zeros p and q.
Algebra II, Lesson 3.1 (grade 10–11)
y = a(x - p)(x - q), which shows the zeros p and q.
Algebra II, Lesson 3.1 (grade 10–11)
factorialEnglish
For a counting number n, n! = n(n-1)(n-2)\cdots 2 \cdot 1, the number of ways to arrange n different objects in a row; by definition 0! = 1.
Algebra II, Lesson 10.1 (grade 10–11) · Playing the Odds, Lesson 1.2 (grade 8–12) · Statistics, Lesson 6.6 (grade 11–12)
For a counting number n, n! = n(n-1)(n-2)\cdots 2 \cdot 1, the number of ways to arrange n different objects in a row; by definition 0! = 1.
Algebra II, Lesson 10.1 (grade 10–11) · Playing the Odds, Lesson 1.2 (grade 8–12) · Statistics, Lesson 6.6 (grade 11–12)
factoring by groupingEnglish
Factoring the first two terms and the last two terms separately so that a common binomial factor appears, then factoring that binomial out.
Algebra I, Lesson 9.3 (grade 8–9) · Algebra I, Lesson 9.5 (grade 8–9)
Factoring the first two terms and the last two terms separately so that a common binomial factor appears, then factoring that binomial out.
Algebra I, Lesson 9.3 (grade 8–9) · Algebra I, Lesson 9.5 (grade 8–9)
factoring strategyEnglish
An ordered checklist for deciding which factoring method to use, starting with the GCF and then looking at the number of terms.
Algebra I, Lesson 9.5 (grade 8–9)
An ordered checklist for deciding which factoring method to use, starting with the GCF and then looking at the number of terms.
Algebra I, Lesson 9.5 (grade 8–9)
false alarmEnglish
A test result that signals a problem (or a success) that is not really there, such as a viable seed that fails a quick test.
Statistics, Lesson 6.5 (grade 11–12)
A test result that signals a problem (or a success) that is not really there, such as a viable seed that fails a quick test.
Statistics, Lesson 6.5 (grade 11–12)
Family of a tripleEnglish
The whole-number multiples ka, kb, kc of a Pythagorean triple; for example 6, 8, 10 and 9, 12, 15 belong to the 3-4-5 family.
Geometry, Lesson 9.2 (grade 9–10)
The whole-number multiples ka, kb, kc of a Pythagorean triple; for example 6, 8, 10 and 9, 12, 15 belong to the 3-4-5 family.
Geometry, Lesson 9.2 (grade 9–10)
feasible regionEnglish
The solution region of the system of constraints: every point in it is a choice that is actually possible.
Algebra II, Lesson 2.3 (grade 10–11)
The solution region of the system of constraints: every point in it is a choice that is actually possible.
Algebra II, Lesson 2.3 (grade 10–11)
FencesEnglish
The two cutoffs Q1 − 1.5·IQR and Q3 + 1.5·IQR. They are not drawn on the graph; they only decide which values are outliers.
Statistics, Lesson 2.3 (grade 11–12)
The two cutoffs Q1 − 1.5·IQR and Q3 + 1.5·IQR. They are not drawn on the graph; they only decide which values are outliers.
Statistics, Lesson 2.3 (grade 11–12)
first differencesEnglish
The changes in y found by subtracting each y-value from the next one, when the x-values go up by equal steps.
Algebra I, Lesson 13.3 (grade 8–9) · Algebra II, Lesson 3.6 (grade 10–11)
The changes in y found by subtracting each y-value from the next one, when the x-values go up by equal steps.
Algebra I, Lesson 13.3 (grade 8–9) · Algebra II, Lesson 3.6 (grade 10–11)
First quartile (Q1)English
The median of the lower half of the ordered data. About a quarter of the values lie below it.
Statistics, Lesson 2.2 (grade 11–12)
The median of the lower half of the ordered data. About a quarter of the values lie below it.
Statistics, Lesson 2.2 (grade 11–12)
Five-number summaryEnglish
The minimum, Q1, median, Q3 and maximum, written in that order. It splits the data into four parts with about a quarter of the values in each.
Statistics, Lesson 2.2 (grade 11–12)
The minimum, Q1, median, Q3 and maximum, written in that order. It splits the data into four parts with about a quarter of the values in each.
Statistics, Lesson 2.2 (grade 11–12)
fixed feeEnglish
A one-time amount charged no matter how much you use; in a cost equation y = mx + b it is b.
Algebra I, Lesson 5.3 (grade 8–9)
A one-time amount charged no matter how much you use; in a cost equation y = mx + b it is b.
Algebra I, Lesson 5.3 (grade 8–9)
Flow proofEnglish
A proof written as boxes (statements) joined by arrows. Each box has its reason written under it, and arrows show which earlier statements it follows from.
Geometry, Lesson 4.4 (grade 9–10)
A proof written as boxes (statements) joined by arrows. Each box has its reason written under it, and arrows show which earlier statements it follows from.
Geometry, Lesson 4.4 (grade 9–10)
focal widthEnglish
The length of the chord through the focus parallel to the directrix; it equals |4p| and helps you sketch how wide the parabola is.
Algebra II, Lesson 11.1 (grade 10–11)
The length of the chord through the focus parallel to the directrix; it equals |4p| and helps you sketch how wide the parabola is.
Algebra II, Lesson 11.1 (grade 10–11)
fociEnglish
The two fixed points in the definition of an ellipse (singular: focus). They lie on the major axis, c units from the center.
Algebra II, Lesson 11.2 (grade 10–11)
The two fixed points in the definition of an ellipse (singular: focus). They lie on the major axis, c units from the center.
Algebra II, Lesson 11.2 (grade 10–11)
focusEnglish
The fixed point in the definition of a parabola. It lies inside the curve, on its axis of symmetry.
Algebra II, Lesson 11.1 (grade 10–11) · Grade 6 Earth Science: The Dynamic Earth, Lesson 4.1 (grade 6)
The fixed point in the definition of a parabola. It lies inside the curve, on its axis of symmetry.
Algebra II, Lesson 11.1 (grade 10–11) · Grade 6 Earth Science: The Dynamic Earth, Lesson 4.1 (grade 6)
FOILEnglish
A memory aid for multiplying two binomials: multiply the First terms, the Outer terms, the Inner terms and the Last terms, then add. It works only for two binomials.
Algebra I, Lesson 8.3 (grade 8–9) · Explore Horses and Ponies · Expert, Stop 4.2 (Ages 14+)
A memory aid for multiplying two binomials: multiply the First terms, the Outer terms, the Inner terms and the Last terms, then add. It works only for two binomials.
Algebra I, Lesson 8.3 (grade 8–9) · Explore Horses and Ponies · Expert, Stop 4.2 (Ages 14+)
foot of the perpendicularEnglish
The point F where the perpendicular from a point P to a line \ell meets \ell.
Geometry, Lesson 3.4 (grade 9–10)
The point F where the perpendicular from a point P to a line \ell meets \ell.
Geometry, Lesson 3.4 (grade 9–10)
formulaEnglish
A literal equation that states a rule relating quantities, such as A = lw for the area of a rectangle.
Algebra I, Lesson 2.5 (grade 8–9) · Pre-Algebra, Lesson 9.2 (grade 6–8)
A literal equation that states a rule relating quantities, such as A = lw for the area of a rectangle.
Algebra I, Lesson 2.5 (grade 8–9) · Pre-Algebra, Lesson 9.2 (grade 6–8)
fortuneEnglish
An amount you have, shown by a positive number. (Brahmagupta's word.)
Pre-Algebra, Lesson 5.2 (grade 6–8)
An amount you have, shown by a positive number. (Brahmagupta's word.)
Pre-Algebra, Lesson 5.2 (grade 6–8)
four-step processEnglish
State the parameter and confidence level; Plan by naming the procedure and checking conditions; Do the calculations; Conclude in context.
Statistics, Lesson 10.2 (grade 11–12)
State the parameter and confidence level; Plan by naming the procedure and checking conditions; Do the calculations; Conclude in context.
Statistics, Lesson 10.2 (grade 11–12)
fraction methodEnglish
Changing the percent to a fraction and then multiplying: 25\% of 64 = \dfrac{1}{4} \times 64.
Pre-Algebra, Lesson 8.2 (grade 6–8)
Changing the percent to a fraction and then multiplying: 25\% of 64 = \dfrac{1}{4} \times 64.
Pre-Algebra, Lesson 8.2 (grade 6–8)
frequency countEnglish
A way of listing data by giving each value together with how many times it appears, such as "score 8: 5 students".
Pre-Algebra, Lesson 13.2 (grade 6–8)
A way of listing data by giving each value together with how many times it appears, such as "score 8: 5 students".
Pre-Algebra, Lesson 13.2 (grade 6–8)
Frequency tableEnglish
A table that lists each category and the count (frequency) of individuals in it.
Statistics, Lesson 1.2 (grade 11–12)
A table that lists each category and the count (frequency) of individuals in it.
Statistics, Lesson 1.2 (grade 11–12)
front-end estimationEnglish
Estimating by keeping only the first (leftmost) digit of each number and changing the rest to zeros: 4,327 becomes 4,000.
Pre-Algebra, Lesson 1.5 (grade 6–8)
Estimating by keeping only the first (leftmost) digit of each number and changing the rest to zeros: 4,327 becomes 4,000.
Pre-Algebra, Lesson 1.5 (grade 6–8)
frustumEnglish
The part of a pyramid or cone that remains when the top is cut off by a plane parallel to the base, like a lampshade or a flowerpot.
Geometry, Lesson 12.5 (grade 9–10)
The part of a pyramid or cone that remains when the top is cut off by a plane parallel to the base, like a lampshade or a flowerpot.
Geometry, Lesson 12.5 (grade 9–10)
functionEnglish
A relation in which each input is paired with exactly one output.
Algebra I, Lesson 4.2 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11) · Electronics & Microcontrollers, Lesson 7.2 (grade 9–12) · +3 more
A relation in which each input is paired with exactly one output.
Algebra I, Lesson 4.2 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11) · Electronics & Microcontrollers, Lesson 7.2 (grade 9–12) · +3 more
function notationEnglish
A way of naming a function and its output: f(x), read "f of x," means the output of the function f when the input is x.
Algebra I, Lesson 4.3 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11)
A way of naming a function and its output: f(x), read "f of x," means the output of the function f when the input is x.
Algebra I, Lesson 4.3 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11)
function ruleEnglish
An equation, such as f(x) = 3x - 5, that tells how to get the output from the input.
Algebra I, Lesson 4.3 (grade 8–9)
An equation, such as f(x) = 3x - 5, that tells how to get the output from the input.
Algebra I, Lesson 4.3 (grade 8–9)
fundamental counting principleEnglish
If one choice can be made in m ways and, after it, a second choice can be made in n ways, then the two choices together can be made in m \cdot n ways; for more stages, multiply the number of options at every stage.
Algebra II, Lesson 10.1 (grade 10–11)
If one choice can be made in m ways and, after it, a second choice can be made in n ways, then the two choices together can be made in m \cdot n ways; for more stages, multiply the number of options at every stage.
Algebra II, Lesson 10.1 (grade 10–11)
Fundamental Theorem of AlgebraEnglish
Every polynomial of degree n \ge 1 has exactly n complex zeros, counting each zero as many times as its multiplicity.
Algebra II, Lesson 4.6 (grade 10–11)
Every polynomial of degree n \ge 1 has exactly n complex zeros, counting each zero as many times as its multiplicity.
Algebra II, Lesson 4.6 (grade 10–11)
future valueEnglish
The total value of an account at a later date, including all deposits and all the interest they have earned.
Algebra II, Lesson 9.5 (grade 10–11) · Accounting, Lesson 10.4 (grade 9–12) · Grade 8 Business & Finance, Lesson 8.1 (grade 8) · +1 more
The total value of an account at a later date, including all deposits and all the interest they have earned.
Algebra II, Lesson 9.5 (grade 10–11) · Accounting, Lesson 10.4 (grade 9–12) · Grade 8 Business & Finance, Lesson 8.1 (grade 8) · +1 more
G
Gaussian eliminationEnglish
Using row operations to bring an augmented matrix to row-echelon form, then solving by back-substitution from the bottom row up.
Algebra II, Lesson 12.4 (grade 10–11)
Using row operations to bring an augmented matrix to row-echelon form, then solving by back-substitution from the bottom row up.
Algebra II, Lesson 12.4 (grade 10–11)
General formEnglish
The equation of a circle multiplied out and collected on one side, x^2 + y^2 + Dx + Ey + F = 0.
Geometry, Lesson 10.7 (grade 9–10)
The equation of a circle multiplied out and collected on one side, x^2 + y^2 + Dx + Ey + F = 0.
Geometry, Lesson 10.7 (grade 9–10)
general form of a conicEnglish
An equation Ax^2 + Cy^2 + Dx + Ey + F = 0 with A and C not both zero. (Conics turned at an angle also need an xy-term; we leave those to later courses.)
Algebra II, Lesson 11.4 (grade 10–11)
An equation Ax^2 + Cy^2 + Dx + Ey + F = 0 with A and C not both zero. (Conics turned at an angle also need an xy-term; we leave those to later courses.)
Algebra II, Lesson 11.4 (grade 10–11)
general multiplication ruleEnglish
The probability that A and B both happen is the probability of A times the probability of B given that A has happened: P(A \text{ and } B) = P(A) \cdot P(B \mid A).
Statistics, Lesson 6.3 (grade 11–12)
The probability that A and B both happen is the probability of A times the probability of B given that A has happened: P(A \text{ and } B) = P(A) \cdot P(B \mid A).
Statistics, Lesson 6.3 (grade 11–12)
general positionEnglish
A placement whose variable coordinates can describe every figure of the given kind, not just a special one.
Geometry, Lesson 13.3 (grade 9–10)
A placement whose variable coordinates can describe every figure of the given kind, not just a special one.
Geometry, Lesson 13.3 (grade 9–10)
general solutionEnglish
A formula that lists every solution, such as x = \dfrac{\pi}{6} + 2k\pi, where k is any integer.
Trigonometry, Lesson 6.4 (grade 11–12)
A formula that lists every solution, such as x = \dfrac{\pi}{6} + 2k\pi, where k is any integer.
Trigonometry, Lesson 6.4 (grade 11–12)
geometric mean (mean proportional)English
For positive numbers a and b, the positive number x with \dfrac{a}{x} = \dfrac{x}{b}. Then x^2 = ab, so x = \sqrt{ab}.
Geometry, Lesson 8.1 (grade 9–10)
For positive numbers a and b, the positive number x with \dfrac{a}{x} = \dfrac{x}{b}. Then x^2 = ab, so x = \sqrt{ab}.
Geometry, Lesson 8.1 (grade 9–10)
geometric meansEnglish
The terms that fill in between two given terms so that all of them together form a geometric sequence. The single geometric mean of two positive numbers a and b is \sqrt{ab}.
Algebra II, Lesson 9.3 (grade 10–11)
The terms that fill in between two given terms so that all of them together form a geometric sequence. The single geometric mean of two positive numbers a and b is \sqrt{ab}.
Algebra II, Lesson 9.3 (grade 10–11)
geometric probabilityEnglish
When a point is chosen at random so that it is equally likely to land anywhere in a region, the probability that it lands in a smaller part of the region is \dfrac{\text{area of the part}}{\text{area of the whole region}}.
Geometry, Lesson 11.6 (grade 9–10)
When a point is chosen at random so that it is equally likely to land anywhere in a region, the probability that it lands in a smaller part of the region is \dfrac{\text{area of the part}}{\text{area of the whole region}}.
Geometry, Lesson 11.6 (grade 9–10)
Geometric random variableEnglish
X = the number of the trial on which the first success occurs. Its possible values are 1, 2, 3, ..., with no upper limit.
Statistics, Lesson 8.4 (grade 11–12)
X = the number of the trial on which the first success occurs. Its possible values are 1, 2, 3, ..., with no upper limit.
Statistics, Lesson 8.4 (grade 11–12)
geometric sequenceEnglish
A sequence in which each term after the first is found by multiplying the previous term by the same nonzero number.
Algebra I, Lesson 7.6 (grade 8–9) · Algebra II, Lesson 9.3 (grade 10–11)
A sequence in which each term after the first is found by multiplying the previous term by the same nonzero number.
Algebra I, Lesson 7.6 (grade 8–9) · Algebra II, Lesson 9.3 (grade 10–11)
geometric seriesEnglish
The sum of the terms of a geometric sequence. S_n stands for the sum of the first n terms.
Algebra II, Lesson 9.3 (grade 10–11)
The sum of the terms of a geometric sequence. S_n stands for the sum of the first n terms.
Algebra II, Lesson 9.3 (grade 10–11)
Geometric settingEnglish
Independent trials, each a success or failure with the same probability p of success, repeated until the first success occurs. The number of trials is not fixed in advance.
Statistics, Lesson 8.4 (grade 11–12)
Independent trials, each a success or failure with the same probability p of success, repeated until the first success occurs. The number of trials is not fixed in advance.
Statistics, Lesson 8.4 (grade 11–12)
givenEnglish
The information you are told to accept at the start of a proof; usually the hypothesis of the conditional being proved.
Geometry, Lesson 2.6 (grade 9–10) · Statistics, Lesson 6.3 (grade 11–12)
The information you are told to accept at the start of a proof; usually the hypothesis of the conditional being proved.
Geometry, Lesson 2.6 (grade 9–10) · Statistics, Lesson 6.3 (grade 11–12)
given pointEnglish
A specific point (x_1, y_1) that the line is known to pass through; its coordinates are numbers, while x and y stay as variables.
Algebra I, Lesson 5.4 (grade 8–9)
A specific point (x_1, y_1) that the line is known to pass through; its coordinates are numbers, while x and y stay as variables.
Algebra I, Lesson 5.4 (grade 8–9)
given sideEnglish
A side whose length is known at the start of the problem.
Trigonometry, Lesson 1.3 (grade 11–12)
A side whose length is known at the start of the problem.
Trigonometry, Lesson 1.3 (grade 11–12)
glide reflectionEnglish
A translation along a line \ell (by a vector parallel to \ell) followed by the reflection in \ell.
Geometry, Lesson 7.4 (grade 9–10)
A translation along a line \ell (by a vector parallel to \ell) followed by the reflection in \ell.
Geometry, Lesson 7.4 (grade 9–10)
goodness-of-fit testEnglish
A significance test of whether the distribution of one categorical variable in a population matches a claimed (hypothesized) distribution.
Statistics, Lesson 13.1 (grade 11–12)
A significance test of whether the distribution of one categorical variable in a population matches a claimed (hypothesized) distribution.
Statistics, Lesson 13.1 (grade 11–12)
graph of an equationEnglish
The picture made by plotting every solution of the equation. For a linear equation the picture is a line.
Pre-Algebra, Lesson 11.3 (grade 6–8)
The picture made by plotting every solution of the equation. For a linear equation the picture is a line.
Pre-Algebra, Lesson 11.3 (grade 6–8)
greatest common factor (GCF)English
The largest number that is a factor of each of the given numbers. The GCF of 12 and 18 is 6.
Pre-Algebra, Lesson 2.4 (grade 6–8) · Pre-Algebra, Lesson 3.2 (grade 6–8) · Pre-Algebra, Lesson 9.5 (grade 6–8)
The largest number that is a factor of each of the given numbers. The GCF of 12 and 18 is 6.
Pre-Algebra, Lesson 2.4 (grade 6–8) · Pre-Algebra, Lesson 3.2 (grade 6–8) · Pre-Algebra, Lesson 9.5 (grade 6–8)
greatest common factor (GCF) of monomialsEnglish
The largest monomial that divides every one of the monomials evenly: the GCF of the coefficients times each shared variable raised to its smallest exponent.
Algebra I, Lesson 9.1 (grade 8–9)
The largest monomial that divides every one of the monomials evenly: the GCF of the coefficients times each shared variable raised to its smallest exponent.
Algebra I, Lesson 9.1 (grade 8–9)
greatest integer functionEnglish
\lfloor x \rfloor is the greatest integer that is less than or equal to x. For example, \lfloor 2.7 \rfloor = 2 and \lfloor -2.3 \rfloor = -3.
Algebra II, Lesson 1.3 (grade 10–11)
\lfloor x \rfloor is the greatest integer that is less than or equal to x. For example, \lfloor 2.7 \rfloor = 2 and \lfloor -2.3 \rfloor = -3.
Algebra II, Lesson 1.3 (grade 10–11)
Grouping symbolsEnglish
Symbols that say "do this part first": parentheses ( ), brackets [ ], absolute value bars and the fraction bar.
Algebra I, Lesson 1.3 (grade 8–9) · Pre-Algebra, Lesson 1.4 (grade 6–8)
Symbols that say "do this part first": parentheses ( ), brackets [ ], absolute value bars and the fraction bar.
Algebra I, Lesson 1.3 (grade 8–9) · Pre-Algebra, Lesson 1.4 (grade 6–8)
growth factorEnglish
The base b: the number the output is multiplied by each time x increases by 1. If b > 1 the function shows growth; if 0 < b < 1 it shows decay.
Algebra II, Lesson 7.1 (grade 10–11)
The base b: the number the output is multiplied by each time x increases by 1. If b > 1 the function shows growth; if 0 < b < 1 it shows decay.
Algebra II, Lesson 7.1 (grade 10–11)
growth factor (base)English
The number b that each output is multiplied by when x goes up by 1.
Algebra I, Lesson 7.4 (grade 8–9)
The number b that each output is multiplied by when x goes up by 1.
Algebra I, Lesson 7.4 (grade 8–9)
growth rateEnglish
The percent by which an amount increases each time period, written as a decimal r (5% means r = 0.05).
Algebra I, Lesson 7.5 (grade 8–9) · Algebra II, Lesson 7.1 (grade 10–11)
The percent by which an amount increases each time period, written as a decimal r (5% means r = 0.05).
Algebra I, Lesson 7.5 (grade 8–9) · Algebra II, Lesson 7.1 (grade 10–11)
guide graphEnglish
The sine or cosine curve drawn lightly first, from which the cosecant or secant graph is sketched.
Trigonometry, Lesson 4.7 (grade 11–12)
The sine or cosine curve drawn lightly first, from which the cosecant or secant graph is sketched.
Trigonometry, Lesson 4.7 (grade 11–12)
H
half-angle formulasEnglish
Formulas for \sin\dfrac{\theta}{2}, \cos\dfrac{\theta}{2} and \tan\dfrac{\theta}{2} in terms of functions of \theta.
Trigonometry, Lesson 5.5 (grade 11–12)
Formulas for \sin\dfrac{\theta}{2}, \cos\dfrac{\theta}{2} and \tan\dfrac{\theta}{2} in terms of functions of \theta.
Trigonometry, Lesson 5.5 (grade 11–12)
half-lifeEnglish
The time it takes for half of a radioactive substance to decay, so that half the amount remains.
Algebra I, Lesson 7.5 (grade 8–9) · Algebra II, Lesson 7.3 (grade 10–11) · Grade 6 Earth Science: The Dynamic Earth, Lesson 1.4 (grade 6) · +3 more
The time it takes for half of a radioactive substance to decay, so that half the amount remains.
Algebra I, Lesson 7.5 (grade 8–9) · Algebra II, Lesson 7.3 (grade 10–11) · Grade 6 Earth Science: The Dynamic Earth, Lesson 1.4 (grade 6) · +3 more
half-periodEnglish
The horizontal distance from a maximum to the next minimum (or minimum to the next maximum). It is half of the period.
Trigonometry, Lesson 4.5 (grade 11–12)
The horizontal distance from a maximum to the next minimum (or minimum to the next maximum). It is half of the period.
Trigonometry, Lesson 4.5 (grade 11–12)
half-planeEnglish
All the points on one side of a line in the coordinate plane.
Algebra I, Lesson 6.6 (grade 8–9) · Algebra II, Lesson 2.2 (grade 10–11)
All the points on one side of a line in the coordinate plane.
Algebra I, Lesson 6.6 (grade 8–9) · Algebra II, Lesson 2.2 (grade 10–11)
harmonic meanEnglish
For two positive numbers a and b, the number \dfrac{2ab}{a + b}. It is the true average speed of a round trip driven at a and b.
Algebra II, Lesson 5.6 (grade 10–11) · Architecture & Civil Engineering, Lesson 3.3 (grade 9–12)
For two positive numbers a and b, the number \dfrac{2ab}{a + b}. It is the true average speed of a round trip driven at a and b.
Algebra II, Lesson 5.6 (grade 10–11) · Architecture & Civil Engineering, Lesson 3.3 (grade 9–12)
heading and courseEnglish
The heading is the direction a boat or plane is pointed; the course (or track) is the direction it actually travels over the ground once the current or wind is added.
Trigonometry, Lesson 9.5 (grade 11–12)
The heading is the direction a boat or plane is pointed; the course (or track) is the direction it actually travels over the ground once the current or wind is added.
Trigonometry, Lesson 9.5 (grade 11–12)
heavier tailsEnglish
More area far from the center than the normal curve has, so a larger critical value is needed to hold the middle 95%.
Statistics, Lesson 10.3 (grade 11–12)
More area far from the center than the normal curve has, so a larger critical value is needed to hold the middle 95%.
Statistics, Lesson 10.3 (grade 11–12)
height (altitude) of a prism or cylinderEnglish
The perpendicular distance between the planes of the two bases.
Geometry, Lesson 12.2 (grade 9–10)
The perpendicular distance between the planes of the two bases.
Geometry, Lesson 12.2 (grade 9–10)
height hEnglish
For SSA data A, a, b, the length h = b\sin A: the shortest distance from vertex C to the line along which side c lies.
Trigonometry, Lesson 7.3 (grade 11–12)
For SSA data A, a, b, the length h = b\sin A: the shortest distance from vertex C to the line along which side c lies.
Trigonometry, Lesson 7.3 (grade 11–12)
height of a pyramid or coneEnglish
The perpendicular distance from the apex to the plane of the base.
Geometry, Lesson 12.3 (grade 9–10) · Geometry, Lesson 12.5 (grade 9–10)
The perpendicular distance from the apex to the plane of the base.
Geometry, Lesson 12.3 (grade 9–10) · Geometry, Lesson 12.5 (grade 9–10)
height of a trapezoidEnglish
The perpendicular distance between the lines containing the two bases.
Geometry, Lesson 11.2 (grade 9–10)
The perpendicular distance between the lines containing the two bases.
Geometry, Lesson 11.2 (grade 9–10)
Heron's formulaEnglish
The area of a triangle with sides a, b, c is \sqrt{s(s-a)(s-b)(s-c)}, where s is the semiperimeter.
Trigonometry, Lesson 7.1 (grade 11–12)
The area of a triangle with sides a, b, c is \sqrt{s(s-a)(s-b)(s-c)}, where s is the semiperimeter.
Trigonometry, Lesson 7.1 (grade 11–12)
Hinge Theorem (SAS Inequality)English
If two sides of one triangle are congruent to two sides of another, and the included angle of the first is larger, then the third side of the first is longer.
Geometry, Lesson 5.6 (grade 9–10)
If two sides of one triangle are congruent to two sides of another, and the included angle of the first is larger, then the third side of the first is longer.
Geometry, Lesson 5.6 (grade 9–10)
HistogramEnglish
A graph of a quantitative variable that groups values into classes of equal width and draws touching bars whose heights show the count (or percent) of values in each class.
Statistics, Lesson 1.4 (grade 11–12)
A graph of a quantitative variable that groups values into classes of equal width and draws touching bars whose heights show the count (or percent) of values in each class.
Statistics, Lesson 1.4 (grade 11–12)
hole (removable discontinuity)English
A single missing point on a graph, at an x-value where a common factor of the numerator and denominator is 0. It is drawn as an open circle.
Algebra II, Lesson 5.4 (grade 10–11)
A single missing point on a graph, at an x-value where a common factor of the numerator and denominator is 0. It is drawn as an open circle.
Algebra II, Lesson 5.4 (grade 10–11)
horizontal asymptoteEnglish
A horizontal line y = k that the graph approaches as x goes far to the right or far to the left. It describes end behavior; the graph may cross it at some middle point.
Algebra II, Lesson 5.3 (grade 10–11) · Algebra II, Lesson 7.1 (grade 10–11) · Trigonometry, Lesson 6.2 (grade 11–12)
A horizontal line y = k that the graph approaches as x goes far to the right or far to the left. It describes end behavior; the graph may cross it at some middle point.
Algebra II, Lesson 5.3 (grade 10–11) · Algebra II, Lesson 7.1 (grade 10–11) · Trigonometry, Lesson 6.2 (grade 11–12)
horizontal compressionEnglish
Multiplying the input by a constant b with |b| > 1, which squeezes the graph toward the y-axis; |b| < 1 stretches it.
Trigonometry, Lesson 4.3 (grade 11–12)
Multiplying the input by a constant b with |b| > 1, which squeezes the graph toward the y-axis; |b| < 1 stretches it.
Trigonometry, Lesson 4.3 (grade 11–12)
horizontal lineEnglish
A flat line y = k; every point on it has the same y-coordinate k, and its slope is 0.
Algebra I, Lesson 5.5 (grade 8–9) · Grade 1 Art, Lesson 1.2 (grade 1)
A flat line y = k; every point on it has the same y-coordinate k, and its slope is 0.
Algebra I, Lesson 5.5 (grade 8–9) · Grade 1 Art, Lesson 1.2 (grade 1)
horizontal line testEnglish
A function is one-to-one exactly when no horizontal line crosses its graph more than once.
Algebra II, Lesson 1.5 (grade 10–11)
A function is one-to-one exactly when no horizontal line crosses its graph more than once.
Algebra II, Lesson 1.5 (grade 10–11)
horizontal shiftEnglish
Sliding a graph left or right without changing its shape. The graph of y = f(x + c) with c > 0 is the graph of y = f(x) moved c units to the left.
Trigonometry, Lesson 4.2 (grade 11–12)
Sliding a graph left or right without changing its shape. The graph of y = f(x + c) with c > 0 is the graph of y = f(x) moved c units to the left.
Trigonometry, Lesson 4.2 (grade 11–12)
horizontal stretch or compressionEnglish
Replacing x with bx (b > 0): a compression toward the y-axis by the factor \dfrac{1}{b} if b > 1, a stretch if 0 < b < 1.
Algebra II, Lesson 1.2 (grade 10–11)
Replacing x with bx (b > 0): a compression toward the y-axis by the factor \dfrac{1}{b} if b > 1, a stretch if 0 < b < 1.
Algebra II, Lesson 1.2 (grade 10–11)
hundredthsEnglish
The second place to the right of the decimal point. One hundredth is one of 100 equal parts: 0.01 = \dfrac{1}{100}.
Pre-Algebra, Lesson 4.1 (grade 6–8)
The second place to the right of the decimal point. One hundredth is one of 100 equal parts: 0.01 = \dfrac{1}{100}.
Pre-Algebra, Lesson 4.1 (grade 6–8)
hyperbolaEnglish
The shape of the graph of y = \dfrac{k}{x}: two separate curved pieces, called branches, that get closer and closer to the axes without ever touching them.
Algebra I, Lesson 12.1 (grade 8–9) · Algebra II, Lesson 11.3 (grade 10–11)
The shape of the graph of y = \dfrac{k}{x}: two separate curved pieces, called branches, that get closer and closer to the axes without ever touching them.
Algebra I, Lesson 12.1 (grade 8–9) · Algebra II, Lesson 11.3 (grade 10–11)
hypotenuseEnglish
The longest side of a right triangle, the side across from the right angle. The other two sides are the legs.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 4.7 (grade 9–10) · Geometry, Lesson 9.1 (grade 9–10) · +2 more
The longest side of a right triangle, the side across from the right angle. The other two sides are the legs.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 4.7 (grade 9–10) · Geometry, Lesson 9.1 (grade 9–10) · +2 more
Hypotenuse-Leg (HL) TheoremEnglish
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Geometry, Lesson 4.7 (grade 9–10)
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Geometry, Lesson 4.7 (grade 9–10)
I
IdentityEnglish
A number that leaves others unchanged: 0 is the additive identity (a + 0 = a) and 1 is the multiplicative identity (a \cdot 1 = a).
Algebra I, Lesson 1.2 (grade 8–9) · Algebra I, Lesson 2.3 (grade 8–9) · Algebra I, Lesson 6.2 (grade 8–9) · +1 more
A number that leaves others unchanged: 0 is the additive identity (a + 0 = a) and 1 is the multiplicative identity (a \cdot 1 = a).
Algebra I, Lesson 1.2 (grade 8–9) · Algebra I, Lesson 2.3 (grade 8–9) · Algebra I, Lesson 6.2 (grade 8–9) · +1 more
identity matrixEnglish
The square matrix I with 1s on the main diagonal (top left to bottom right) and 0s everywhere else. For any matrix A of the right size, AI = A and IA = A.
Algebra II, Lesson 12.2 (grade 10–11)
The square matrix I with 1s on the main diagonal (top left to bottom right) and 0s everywhere else. For any matrix A of the right size, AI = A and IA = A.
Algebra II, Lesson 12.2 (grade 10–11)
identity propertyEnglish
Adding 0 or multiplying by 1 leaves a number unchanged. 0 is the identity for addition, and 1 is the identity for multiplication.
Pre-Algebra, Lesson 1.2 (grade 6–8)
Adding 0 or multiplying by 1 leaves a number unchanged. 0 is the identity for addition, and 1 is the identity for multiplication.
Pre-Algebra, Lesson 1.2 (grade 6–8)
identity transformationEnglish
The transformation that leaves every point where it is, such as a rotation of 360^\circ or a translation by \langle 0, 0 \rangle.
Geometry, Lesson 7.4 (grade 9–10)
The transformation that leaves every point where it is, such as a rotation of 360^\circ or a translation by \langle 0, 0 \rangle.
Geometry, Lesson 7.4 (grade 9–10)
imageEnglish
The point (or figure) that a transformation produces from a given point (or figure).
Algebra II, Lesson 12.6 (grade 10–11) · Kindergarten Business & Finance, Lesson 2.3 (grade K)
The point (or figure) that a transformation produces from a given point (or figure).
Algebra II, Lesson 12.6 (grade 10–11) · Kindergarten Business & Finance, Lesson 2.3 (grade K)
improper fractionEnglish
A fraction whose numerator is equal to or larger than its denominator, like \dfrac{7}{4}. It is 1 or more.
Pre-Algebra, Lesson 3.4 (grade 6–8)
A fraction whose numerator is equal to or larger than its denominator, like \dfrac{7}{4}. It is 1 or more.
Pre-Algebra, Lesson 3.4 (grade 6–8)
inaccessible distanceEnglish
A distance that cannot be measured directly, for example across a river, a canyon or a lake.
Trigonometry, Lesson 8.3 (grade 11–12)
A distance that cannot be measured directly, for example across a river, a canyon or a lake.
Trigonometry, Lesson 8.3 (grade 11–12)
incenterEnglish
The point where the three angle bisectors of a triangle meet. It is equidistant from the three sides.
Geometry, Lesson 5.2 (grade 9–10)
The point where the three angle bisectors of a triangle meet. It is equidistant from the three sides.
Geometry, Lesson 5.2 (grade 9–10)
Included angleEnglish
The angle formed by two sides of a triangle; for sides \overline{AB} and \overline{AC} it is \angle A, the angle at their common endpoint.
Geometry, Lesson 4.3 (grade 9–10) · Geometry, Lesson 5.6 (grade 9–10) · Geometry, Lesson 8.4 (grade 9–10) · +1 more
The angle formed by two sides of a triangle; for sides \overline{AB} and \overline{AC} it is \angle A, the angle at their common endpoint.
Geometry, Lesson 4.3 (grade 9–10) · Geometry, Lesson 5.6 (grade 9–10) · Geometry, Lesson 8.4 (grade 9–10) · +1 more
Included sideEnglish
The side of a triangle that lies between two angles; for \angle A and \angle B it is \overline{AB}.
Geometry, Lesson 4.3 (grade 9–10)
The side of a triangle that lies between two angles; for \angle A and \angle B it is \overline{AB}.
Geometry, Lesson 4.3 (grade 9–10)
inconsistent systemEnglish
A system with no solution; for two lines this means the lines are parallel.
Algebra II, Lesson 2.1 (grade 10–11)
A system with no solution; for two lines this means the lines are parallel.
Algebra II, Lesson 2.1 (grade 10–11)
increasing, decreasingEnglish
f is increasing on an interval if its graph rises from left to right there (larger inputs give larger outputs), and decreasing if it falls.
Algebra II, Lesson 1.6 (grade 10–11)
f is increasing on an interval if its graph rises from left to right there (larger inputs give larger outputs), and decreasing if it falls.
Algebra II, Lesson 1.6 (grade 10–11)
increasing, decreasing, constantEnglish
Reading a graph from left to right, it is increasing where it rises, decreasing where it falls and constant where it stays level.
Algebra I, Lesson 4.4 (grade 8–9)
Reading a graph from left to right, it is increasing where it rises, decreasing where it falls and constant where it stays level.
Algebra I, Lesson 4.4 (grade 8–9)
independent eventsEnglish
Events where one happening does not change the probability of the other, such as two separate free throws.
Algebra II, Lesson 10.4 (grade 10–11) · Playing the Odds, Lesson 1.3 (grade 8–12) · Tactics & Strategy, Lesson 1.4 (grade 8–12) · +2 more
Events where one happening does not change the probability of the other, such as two separate free throws.
Algebra II, Lesson 10.4 (grade 10–11) · Playing the Odds, Lesson 1.3 (grade 8–12) · Tactics & Strategy, Lesson 1.4 (grade 8–12) · +2 more
Independent random variablesEnglish
Random variables for which knowing the value of one does not change the probabilities for the other.
Statistics, Lesson 7.3 (grade 11–12)
Random variables for which knowing the value of one does not change the probabilities for the other.
Statistics, Lesson 7.3 (grade 11–12)
Independent samplesEnglish
Two groups in which the individuals in one group have no link to particular individuals in the other group.
Statistics, Lesson 12.4 (grade 11–12)
Two groups in which the individuals in one group have no link to particular individuals in the other group.
Statistics, Lesson 12.4 (grade 11–12)
independent variableEnglish
The input quantity that you choose or that changes on its own, usually x.
Algebra I, Lesson 4.1 (grade 8–9) · Food Science, Lesson 1.2 (grade 9–12) · Engineering Design, Robotics & Drones, Lesson 1.4 (grade 9–12) · +3 more
The input quantity that you choose or that changes on its own, usually x.
Algebra I, Lesson 4.1 (grade 8–9) · Food Science, Lesson 1.2 (grade 9–12) · Engineering Design, Robotics & Drones, Lesson 1.4 (grade 9–12) · +3 more
indexEnglish
The small number n in \sqrt[n]{a} that tells which root to take. A square root has index 2, which is usually not written.
Algebra II, Lesson 6.1 (grade 10–11) · Grade 7 Composition & Creative Writing: Commonplace, Encomium and Invective, Lesson 1.4 (grade 7)
The small number n in \sqrt[n]{a} that tells which root to take. A square root has index 2, which is usually not written.
Algebra II, Lesson 6.1 (grade 10–11) · Grade 7 Composition & Creative Writing: Commonplace, Encomium and Invective, Lesson 1.4 (grade 7)
Indirect measurementEnglish
Finding a distance that cannot be measured directly by measuring an equal distance that can be reached, using congruent (or, later, similar) triangles.
Geometry, Lesson 4.5 (grade 9–10) · Geometry, Lesson 8.3 (grade 9–10)
Finding a distance that cannot be measured directly by measuring an equal distance that can be reached, using congruent (or, later, similar) triangles.
Geometry, Lesson 4.5 (grade 9–10) · Geometry, Lesson 8.3 (grade 9–10)
indirect proofEnglish
A proof that assumes temporarily that the conclusion is false and shows that this assumption leads to a contradiction; also called proof by contradiction (Latin reductio ad absurdum).
Geometry, Lesson 5.5 (grade 9–10)
A proof that assumes temporarily that the conclusion is false and shows that this assumption leads to a contradiction; also called proof by contradiction (Latin reductio ad absurdum).
Geometry, Lesson 5.5 (grade 9–10)
Individuals and variablesEnglish
The individuals are the objects a data set describes (people, animals, fields, days, boards). A variable is any characteristic of an individual that can take different values from one individual to the next.
Statistics, Lesson 1.1 (grade 11–12)
The individuals are the objects a data set describes (people, animals, fields, days, boards). A variable is any characteristic of an individual that can take different values from one individual to the next.
Statistics, Lesson 1.1 (grade 11–12)
inductive hypothesisEnglish
The assumption, made only inside the inductive step, that the statement is true for some particular counting number k.
Algebra II, Lesson 9.6 (grade 10–11)
The assumption, made only inside the inductive step, that the statement is true for some particular counting number k.
Algebra II, Lesson 9.6 (grade 10–11)
inductive reasoningEnglish
Reasoning that looks at several examples, notices a pattern and guesses that the pattern always continues.
Geometry, Lesson 1.2 (grade 9–10)
Reasoning that looks at several examples, notices a pattern and guesses that the pattern always continues.
Geometry, Lesson 1.2 (grade 9–10)
inductive stepEnglish
The proof that if the statement is true for k, then it must also be true for k + 1.
Algebra II, Lesson 9.6 (grade 10–11)
The proof that if the statement is true for k, then it must also be true for k + 1.
Algebra II, Lesson 9.6 (grade 10–11)
inequalityEnglish
A statement that two quantities are not equal, using one of the symbols < (less than), > (greater than), \le (less than or equal to) or \ge (greater than or equal to).
Algebra I, Lesson 3.1 (grade 8–9) · Pre-Algebra, Lesson 10.7 (grade 6–8)
A statement that two quantities are not equal, using one of the symbols < (less than), > (greater than), \le (less than or equal to) or \ge (greater than or equal to).
Algebra I, Lesson 3.1 (grade 8–9) · Pre-Algebra, Lesson 10.7 (grade 6–8)
inequality symbolsEnglish
< means "is less than," > means "is greater than," \le means "is less than or equal to" (at most), and \ge means "is greater than or equal to" (at least).
Pre-Algebra, Lesson 10.7 (grade 6–8)
< means "is less than," > means "is greater than," \le means "is less than or equal to" (at most), and \ge means "is greater than or equal to" (at least).
Pre-Algebra, Lesson 10.7 (grade 6–8)
Inference procedureEnglish
A method for drawing a conclusion about a parameter from sample data: a confidence interval (to estimate) or a significance test (to weigh evidence for a claim).
Statistics, Lesson 12.4 (grade 11–12)
A method for drawing a conclusion about a parameter from sample data: a confidence interval (to estimate) or a significance test (to weigh evidence for a claim).
Statistics, Lesson 12.4 (grade 11–12)
infinite seriesEnglish
A sum with infinitely many terms, such as \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \cdots.
Algebra II, Lesson 9.4 (grade 10–11)
A sum with infinitely many terms, such as \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \cdots.
Algebra II, Lesson 9.4 (grade 10–11)
infinity (\infty)English
A symbol meaning "without end." It is not a number, so it always gets a parenthesis: [4, \infty) means x \ge 4.
Algebra I, Lesson 3.3 (grade 8–9)
A symbol meaning "without end." It is not a number, so it always gets a parenthesis: [4, \infty) means x \ge 4.
Algebra I, Lesson 3.3 (grade 8–9)
Inflection pointEnglish
A point where a curve changes from bending downward (like an upside-down bowl) to bending upward (like a bowl). On a normal curve these points are exactly one standard deviation on each side of the mean.
Statistics, Lesson 3.3 (grade 11–12)
A point where a curve changes from bending downward (like an upside-down bowl) to bending upward (like a bowl). On a normal curve these points are exactly one standard deviation on each side of the mean.
Statistics, Lesson 3.3 (grade 11–12)
Influential pointEnglish
A point that, if removed, would change the regression line (or r) a great deal. Points far out in the x direction are often influential.
Statistics, Lesson 4.5 (grade 11–12)
A point that, if removed, would change the regression line (or r) a great deal. Points far out in the x direction are often influential.
Statistics, Lesson 4.5 (grade 11–12)
initial sideEnglish
The ray where the rotation that forms an angle begins.
Trigonometry, Lesson 3.1 (grade 11–12)
The ray where the rotation that forms an angle begins.
Trigonometry, Lesson 3.1 (grade 11–12)
Initial side and terminal sideEnglish
The ray where the turning starts (the positive x-axis) and the ray where it stops. Counterclockwise turning gives a positive angle; clockwise gives a negative angle.
Algebra II, Lesson 13.2 (grade 10–11)
The ray where the turning starts (the positive x-axis) and the ray where it stops. Counterclockwise turning gives a positive angle; clockwise gives a negative angle.
Algebra II, Lesson 13.2 (grade 10–11)
initial valueEnglish
The value of the output when the input is 0; in y = mx + b it is b.
Algebra I, Lesson 5.7 (grade 8–9)
The value of the output when the input is 0; in y = mx + b it is b.
Algebra I, Lesson 5.7 (grade 8–9)
inner and outer functionEnglish
In f(g(x)), g is the inner function (it acts first) and f is the outer function (it acts second).
Algebra II, Lesson 1.4 (grade 10–11)
In f(g(x)), g is the inner function (it acts first) and f is the outer function (it acts second).
Algebra II, Lesson 1.4 (grade 10–11)
inputEnglish
A value of the independent variable, usually the x-value of an ordered pair.
Algebra I, Lesson 4.2 (grade 8–9) · Grade 6 Engineering & Physics, Lesson 4.4 (grade 6) · Pre-Algebra, Lesson 11.2 (grade 6–8)
A value of the independent variable, usually the x-value of an ordered pair.
Algebra I, Lesson 4.2 (grade 8–9) · Grade 6 Engineering & Physics, Lesson 4.4 (grade 6) · Pre-Algebra, Lesson 11.2 (grade 6–8)
input-output tableEnglish
A table that lists inputs and their matching outputs side by side.
Pre-Algebra, Lesson 11.2 (grade 6–8)
A table that lists inputs and their matching outputs side by side.
Pre-Algebra, Lesson 11.2 (grade 6–8)
Inscribed angleEnglish
An angle whose vertex is on a circle and whose sides contain chords of the circle.
Geometry, Lesson 10.4 (grade 9–10)
An angle whose vertex is on a circle and whose sides contain chords of the circle.
Geometry, Lesson 10.4 (grade 9–10)
inscribed circleEnglish
The circle inside a triangle that touches each side at exactly one point (its incircle). Its center is the incenter and its radius, the inradius, is the distance from the incenter to each side.
Geometry, Lesson 5.2 (grade 9–10)
The circle inside a triangle that touches each side at exactly one point (its incircle). Its center is the incenter and its radius, the inradius, is the distance from the incenter to each side.
Geometry, Lesson 5.2 (grade 9–10)
Inscribed polygon and circumscribed circleEnglish
A polygon is inscribed in a circle when all of its vertices lie on the circle; the circle is then circumscribed about the polygon.
Geometry, Lesson 10.4 (grade 9–10)
A polygon is inscribed in a circle when all of its vertices lie on the circle; the circle is then circumscribed about the polygon.
Geometry, Lesson 10.4 (grade 9–10)
integerEnglish
Any whole number, its opposite, or zero: \ldots, -3, -2, -1, 0, 1, 2, 3, \ldots
Pre-Algebra, Lesson 5.1 (grade 6–8)
Any whole number, its opposite, or zero: \ldots, -3, -2, -1, 0, 1, 2, 3, \ldots
Pre-Algebra, Lesson 5.1 (grade 6–8)
IntegersEnglish
The whole numbers and their opposites: ..., −3, −2, −1, 0, 1, 2, 3, ...
Algebra I, Lesson 1.1 (grade 8–9) · Pre-Algebra, Lesson 6.5 (grade 6–8)
The whole numbers and their opposites: ..., −3, −2, −1, 0, 1, 2, 3, ...
Algebra I, Lesson 1.1 (grade 8–9) · Pre-Algebra, Lesson 6.5 (grade 6–8)
Intercepted arcEnglish
The arc that lies in the interior of an angle and has its endpoints on the sides of the angle. An inscribed angle \angle ABC intercepts the arc \overset{\frown}{AC} that does not contain B.
Geometry, Lesson 10.4 (grade 9–10)
The arc that lies in the interior of an angle and has its endpoints on the sides of the angle. An inscribed angle \angle ABC intercepts the arc \overset{\frown}{AC} that does not contain B.
Geometry, Lesson 10.4 (grade 9–10)
interior angleEnglish
An angle inside a polygon, formed where two of its sides meet.
Pre-Algebra, Lesson 12.2 (grade 6–8)
An angle inside a polygon, formed where two of its sides meet.
Pre-Algebra, Lesson 12.2 (grade 6–8)
interior of an angleEnglish
The region between the sides of an angle (less than a straight angle): the points on the same side of \overleftrightarrow{BA} as C and on the same side of \overleftrightarrow{BC} as A.
Geometry, Lesson 2.3 (grade 9–10)
The region between the sides of an angle (less than a straight angle): the points on the same side of \overleftrightarrow{BA} as C and on the same side of \overleftrightarrow{BC} as A.
Geometry, Lesson 2.3 (grade 9–10)
interpolationEnglish
Using a model to predict a value inside the range of the data you collected.
Algebra I, Lesson 13.2 (grade 8–9)
Using a model to predict a value inside the range of the data you collected.
Algebra I, Lesson 13.2 (grade 8–9)
Interquartile range (IQR)English
IQR = Q3 − Q1, the spread of the middle half of the data.
Statistics, Lesson 2.2 (grade 11–12)
IQR = Q3 − Q1, the spread of the middle half of the data.
Statistics, Lesson 2.2 (grade 11–12)
intersectionEnglish
The intersection of two figures is the set of all points that lie in both of them.
Geometry, Lesson 2.1 (grade 9–10)
The intersection of two figures is the set of all points that lie in both of them.
Geometry, Lesson 2.1 (grade 9–10)
intersection ("and")English
The numbers that make BOTH inequalities true. Its graph is the overlap of the two graphs, often a piece between two numbers.
Algebra I, Lesson 3.3 (grade 8–9)
The numbers that make BOTH inequalities true. Its graph is the overlap of the two graphs, often a piece between two numbers.
Algebra I, Lesson 3.3 (grade 8–9)
interval notationEnglish
A short way to write a set of numbers using its endpoints: a bracket [ or ] means the endpoint is included, a parenthesis ( or ) means it is not. Example: [-2, 5) means -2 \le x < 5.
Algebra I, Lesson 3.3 (grade 8–9) · Algebra I, Lesson 4.4 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11)
A short way to write a set of numbers using its endpoints: a bracket [ or ] means the endpoint is included, a parenthesis ( or ) means it is not. Example: [-2, 5) means -2 \le x < 5.
Algebra I, Lesson 3.3 (grade 8–9) · Algebra I, Lesson 4.4 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11)
InverseEnglish
The additive inverse (opposite) of a is -a, because a + (-a) = 0. The multiplicative inverse (reciprocal) of a nonzero a is \dfrac{1}{a}, because a \cdot \dfrac{1}{a} = 1.
Algebra I, Lesson 1.2 (grade 8–9) · Geometry, Lesson 1.3 (grade 9–10)
The additive inverse (opposite) of a is -a, because a + (-a) = 0. The multiplicative inverse (reciprocal) of a nonzero a is \dfrac{1}{a}, because a \cdot \dfrac{1}{a} = 1.
Algebra I, Lesson 1.2 (grade 8–9) · Geometry, Lesson 1.3 (grade 9–10)
inverse cosineEnglish
\cos^{-1} x (also written \arccos x) is the acute angle whose cosine is x, for 0 < x < 1.
Trigonometry, Lesson 1.4 (grade 11–12) · Trigonometry, Lesson 6.2 (grade 11–12)
\cos^{-1} x (also written \arccos x) is the acute angle whose cosine is x, for 0 < x < 1.
Trigonometry, Lesson 1.4 (grade 11–12) · Trigonometry, Lesson 6.2 (grade 11–12)
inverse functionEnglish
The function f^{-1} that undoes f: if f(a) = b, then f^{-1}(b) = a. Read "f inverse."
Algebra II, Lesson 1.5 (grade 10–11)
The function f^{-1} that undoes f: if f(a) = b, then f^{-1}(b) = a. Read "f inverse."
Algebra II, Lesson 1.5 (grade 10–11)
inverse matrixEnglish
For a square matrix A, the matrix A^{-1} (if it exists) with AA^{-1} = I and A^{-1}A = I. It undoes multiplication by A, just as \dfrac{1}{5} undoes multiplication by 5.
Algebra II, Lesson 12.3 (grade 10–11)
For a square matrix A, the matrix A^{-1} (if it exists) with AA^{-1} = I and A^{-1}A = I. It undoes multiplication by A, just as \dfrac{1}{5} undoes multiplication by 5.
Algebra II, Lesson 12.3 (grade 10–11)
Inverse normal calculationEnglish
Starting from an area (a proportion) and finding the value that cuts off that area: the reverse of Lesson 3.4.
Statistics, Lesson 3.5 (grade 11–12)
Starting from an area (a proportion) and finding the value that cuts off that area: the reverse of Lesson 3.4.
Statistics, Lesson 3.5 (grade 11–12)
inverse operationEnglish
The operation that undoes another one. Subtracting undoes adding, and adding undoes subtracting.
Pre-Algebra, Lesson 10.2 (grade 6–8) · Pre-Algebra, Lesson 10.3 (grade 6–8) · Pre-Algebra, Lesson 6.4 (grade 6–8)
The operation that undoes another one. Subtracting undoes adding, and adding undoes subtracting.
Pre-Algebra, Lesson 10.2 (grade 6–8) · Pre-Algebra, Lesson 10.3 (grade 6–8) · Pre-Algebra, Lesson 6.4 (grade 6–8)
inverse operationsEnglish
Operations that undo each other: addition and subtraction undo each other, and so do multiplication and division.
Algebra I, Lesson 2.1 (grade 8–9) · Pre-Algebra, Lesson 10.1 (grade 6–8)
Operations that undo each other: addition and subtraction undo each other, and so do multiplication and division.
Algebra I, Lesson 2.1 (grade 8–9) · Pre-Algebra, Lesson 10.1 (grade 6–8)
Inverse ratioEnglish
\sin^{-1} x, \cos^{-1} x and \tan^{-1} x give the acute angle whose sine, cosine or tangent is x. For example, \sin^{-1}(0.5) = 30^\circ.
Geometry, Lesson 9.6 (grade 9–10)
\sin^{-1} x, \cos^{-1} x and \tan^{-1} x give the acute angle whose sine, cosine or tangent is x. For example, \sin^{-1}(0.5) = 30^\circ.
Geometry, Lesson 9.6 (grade 9–10)
inverse sineEnglish
\sin^{-1} x (also written \arcsin x) is the acute angle whose sine is x, for 0 < x < 1.
Trigonometry, Lesson 1.4 (grade 11–12) · Trigonometry, Lesson 6.1 (grade 11–12)
\sin^{-1} x (also written \arcsin x) is the acute angle whose sine is x, for 0 < x < 1.
Trigonometry, Lesson 1.4 (grade 11–12) · Trigonometry, Lesson 6.1 (grade 11–12)
Inverse sine, cosine and tangentEnglish
\sin^{-1} x is the acute angle whose sine is x (and likewise \cos^{-1} x and \tan^{-1} x). They undo sine, cosine and tangent, the way any inverse function undoes its function.
Algebra II, Lesson 13.1 (grade 10–11)
\sin^{-1} x is the acute angle whose sine is x (and likewise \cos^{-1} x and \tan^{-1} x). They undo sine, cosine and tangent, the way any inverse function undoes its function.
Algebra II, Lesson 13.1 (grade 10–11)
inverse tangentEnglish
\tan^{-1} x (also written \arctan x) is the acute angle whose tangent is x, for x > 0.
Trigonometry, Lesson 1.4 (grade 11–12) · Trigonometry, Lesson 6.2 (grade 11–12)
\tan^{-1} x (also written \arctan x) is the acute angle whose tangent is x, for x > 0.
Trigonometry, Lesson 1.4 (grade 11–12) · Trigonometry, Lesson 6.2 (grade 11–12)
inverse variationEnglish
A relationship between two quantities that can be written y = \dfrac{k}{x} with k \ne 0. When one quantity is multiplied by a number, the other is divided by that same number.
Algebra I, Lesson 12.1 (grade 8–9) · Algebra II, Lesson 5.6 (grade 10–11)
A relationship between two quantities that can be written y = \dfrac{k}{x} with k \ne 0. When one quantity is multiplied by a number, the other is divided by that same number.
Algebra I, Lesson 12.1 (grade 8–9) · Algebra II, Lesson 5.6 (grade 10–11)
invertibleEnglish
Having an inverse. A square matrix is invertible exactly when its determinant is not 0; a matrix with determinant 0 is called singular.
Algebra II, Lesson 12.3 (grade 10–11)
Having an inverse. A square matrix is invertible exactly when its determinant is not 0; a matrix with determinant 0 is called singular.
Algebra II, Lesson 12.3 (grade 10–11)
Irrational numberEnglish
A real number that cannot be written as a fraction of integers. Its decimal goes on forever without ending and without repeating, like \sqrt{2} = 1.41421356... or \pi = 3.14159265...
Algebra I, Lesson 1.1 (grade 8–9) · Pre-Algebra, Lesson 6.5 (grade 6–8)
A real number that cannot be written as a fraction of integers. Its decimal goes on forever without ending and without repeating, like \sqrt{2} = 1.41421356... or \pi = 3.14159265...
Algebra I, Lesson 1.1 (grade 8–9) · Pre-Algebra, Lesson 6.5 (grade 6–8)
isolate a radicalEnglish
Use inverse operations so that a radical stands alone on one side of the equation before you raise both sides to a power.
Algebra II, Lesson 6.5 (grade 10–11)
Use inverse operations so that a radical stands alone on one side of the equation before you raise both sides to a power.
Algebra II, Lesson 6.5 (grade 10–11)
isolate the absolute valueEnglish
Use inverse operations to get the absolute value expression alone on one side, as in |x - 1| = 5, before splitting into cases.
Algebra I, Lesson 3.4 (grade 8–9)
Use inverse operations to get the absolute value expression alone on one side, as in |x - 1| = 5, before splitting into cases.
Algebra I, Lesson 3.4 (grade 8–9)
isolate the variableEnglish
To get the variable all by itself on one side of the equation, such as x = 14.
Pre-Algebra, Lesson 10.2 (grade 6–8)
To get the variable all by itself on one side of the equation, such as x = 14.
Pre-Algebra, Lesson 10.2 (grade 6–8)
Isosceles Triangle TheoremEnglish
If two sides of a triangle are congruent, then the angles opposite them are congruent (Euclid I.5).
Geometry, Lesson 4.6 (grade 9–10)
If two sides of a triangle are congruent, then the angles opposite them are congruent (Euclid I.5).
Geometry, Lesson 4.6 (grade 9–10)
J
joint variationEnglish
y = kxz: y varies directly as the product of two or more variables.
Algebra II, Lesson 5.6 (grade 10–11)
y = kxz: y varies directly as the product of two or more variables.
Algebra II, Lesson 5.6 (grade 10–11)
K
key pointsEnglish
For y = \log_b x, the points \left(\dfrac{1}{b}, -1\right), (1, 0) and (b, 1), where the argument is a simple power of the base.
Algebra II, Lesson 8.2 (grade 10–11) · Trigonometry, Lesson 4.2 (grade 11–12)
For y = \log_b x, the points \left(\dfrac{1}{b}, -1\right), (1, 0) and (b, 1), where the argument is a simple power of the base.
Algebra II, Lesson 8.2 (grade 10–11) · Trigonometry, Lesson 4.2 (grade 11–12)
L
Large Counts conditionEnglish
The sample has at least 10 successes and at least 10 failures (n\hat{p} \ge 10 and n(1 - \hat{p}) \ge 10), so the sampling distribution of \hat{p} is approximately normal.
Statistics, Lesson 10.2 (grade 11–12) · Statistics, Lesson 8.3 (grade 11–12) · Statistics, Lesson 9.2 (grade 11–12)
The sample has at least 10 successes and at least 10 failures (n\hat{p} \ge 10 and n(1 - \hat{p}) \ge 10), so the sampling distribution of \hat{p} is approximately normal.
Statistics, Lesson 10.2 (grade 11–12) · Statistics, Lesson 8.3 (grade 11–12) · Statistics, Lesson 9.2 (grade 11–12)
Large Counts condition (for a test)English
The check that np_0 \ge 10 and n(1 - p_0) \ge 10, so that the sampling distribution of \hat{p} is approximately normal when H_0 is true.
Statistics, Lesson 11.2 (grade 11–12)
The check that np_0 \ge 10 and n(1 - p_0) \ge 10, so that the sampling distribution of \hat{p} is approximately normal when H_0 is true.
Statistics, Lesson 11.2 (grade 11–12)
Large sample rule of thumbEnglish
In this course, n \ge 30 is usually large enough for the CLT, even for a strongly skewed population. Extremely skewed populations or populations with extreme outliers may need more.
Statistics, Lesson 9.4 (grade 11–12)
In this course, n \ge 30 is usually large enough for the CLT, even for a strongly skewed population. Extremely skewed populations or populations with extreme outliers may need more.
Statistics, Lesson 9.4 (grade 11–12)
lateral areaEnglish
The total area of the lateral faces of a prism, or of the curved surface of a cylinder (not counting the bases).
Geometry, Lesson 12.2 (grade 9–10) · Pre-Algebra, Lesson 12.5 (grade 6–8)
The total area of the lateral faces of a prism, or of the curved surface of a cylinder (not counting the bases).
Geometry, Lesson 12.2 (grade 9–10) · Pre-Algebra, Lesson 12.5 (grade 6–8)
lateral edgeEnglish
An edge of a pyramid that joins the apex to a vertex of the base. It is longer than the slant height.
Geometry, Lesson 12.3 (grade 9–10)
An edge of a pyramid that joins the apex to a vertex of the base. It is longer than the slant height.
Geometry, Lesson 12.3 (grade 9–10)
lateral faces and lateral edgesEnglish
In a prism, the faces that are not bases are the lateral faces; the edges where two lateral faces meet are the lateral edges.
Geometry, Lesson 12.2 (grade 9–10)
In a prism, the faces that are not bases are the lateral faces; the edges where two lateral faces meet are the lateral edges.
Geometry, Lesson 12.2 (grade 9–10)
Law of CosinesEnglish
In any triangle, c^2 = a^2 + b^2 - 2ab\cos C, and likewise for the other two sides.
Trigonometry, Lesson 7.4 (grade 11–12)
In any triangle, c^2 = a^2 + b^2 - 2ab\cos C, and likewise for the other two sides.
Trigonometry, Lesson 7.4 (grade 11–12)
Law of DetachmentEnglish
If p \to q is true and p is true, then q is true. (Also called modus ponens.)
Geometry, Lesson 1.4 (grade 9–10)
If p \to q is true and p is true, then q is true. (Also called modus ponens.)
Geometry, Lesson 1.4 (grade 9–10)
Law of SyllogismEnglish
If p \to q and q \to r are both true, then p \to r is true.
Geometry, Lesson 1.4 (grade 9–10)
If p \to q and q \to r are both true, then p \to r is true.
Geometry, Lesson 1.4 (grade 9–10)
leading coefficientEnglish
The coefficient of the first term when a polynomial is written in standard form. In -3x^2 + 7x + 4 it is -3.
Algebra I, Lesson 8.1 (grade 8–9) · Algebra I, Lesson 9.3 (grade 8–9) · Algebra II, Lesson 4.1 (grade 10–11)
The coefficient of the first term when a polynomial is written in standard form. In -3x^2 + 7x + 4 it is -3.
Algebra I, Lesson 8.1 (grade 8–9) · Algebra I, Lesson 9.3 (grade 8–9) · Algebra II, Lesson 4.1 (grade 10–11)
least common denominator (LCD)English
The simplest expression that every denominator divides into. Build it from each different factor, using each factor the greatest number of times it appears in any one denominator.
Algebra I, Lesson 12.4 (grade 8–9) · Algebra I, Lesson 2.4 (grade 8–9) · Algebra II, Lesson 5.2 (grade 10–11) · +1 more
The simplest expression that every denominator divides into. Build it from each different factor, using each factor the greatest number of times it appears in any one denominator.
Algebra I, Lesson 12.4 (grade 8–9) · Algebra I, Lesson 2.4 (grade 8–9) · Algebra II, Lesson 5.2 (grade 10–11) · +1 more
least common multiple (LCM)English
The smallest positive number that two numbers both divide into evenly; used to pick multipliers, e.g. the LCM of 2 and 3 is 6.
Algebra I, Lesson 6.4 (grade 8–9) · Pre-Algebra, Lesson 2.6 (grade 6–8) · Pre-Algebra, Lesson 3.3 (grade 6–8)
The smallest positive number that two numbers both divide into evenly; used to pick multipliers, e.g. the LCM of 2 and 3 is 6.
Algebra I, Lesson 6.4 (grade 8–9) · Pre-Algebra, Lesson 2.6 (grade 6–8) · Pre-Algebra, Lesson 3.3 (grade 6–8)
Least-squares regression lineEnglish
The one line that makes the sum of the squared residuals as small as possible.
Statistics, Lesson 4.3 (grade 11–12)
The one line that makes the sum of the squared residuals as small as possible.
Statistics, Lesson 4.3 (grade 11–12)
LegsEnglish
The two sides of a right triangle that form the right angle.
Geometry, Lesson 9.1 (grade 9–10) · Pre-Algebra, Lesson 12.6 (grade 6–8) · Trigonometry, Lesson 1.1 (grade 11–12)
The two sides of a right triangle that form the right angle.
Geometry, Lesson 9.1 (grade 9–10) · Pre-Algebra, Lesson 12.6 (grade 6–8) · Trigonometry, Lesson 1.1 (grade 11–12)
Legs and base of an isosceles triangleEnglish
The two congruent sides are the legs; the third side is the base.
Geometry, Lesson 4.6 (grade 9–10)
The two congruent sides are the legs; the third side is the base.
Geometry, Lesson 4.6 (grade 9–10)
Legs of a right triangleEnglish
The two sides that form the right angle.
Geometry, Lesson 4.7 (grade 9–10)
The two sides that form the right angle.
Geometry, Lesson 4.7 (grade 9–10)
level lineEnglish
The set of points where the objective function equals a fixed number c, such as 3x + 4y = 24. Every point on it gives the same value.
Algebra II, Lesson 2.3 (grade 10–11)
The set of points where the objective function equals a fixed number c, such as 3x + 4y = 24. Every point on it gives the same value.
Algebra II, Lesson 2.3 (grade 10–11)
like denominatorsEnglish
Denominators that are exactly the same, as in \dfrac{3}{x + 1} and \dfrac{5}{x + 1}.
Algebra I, Lesson 12.4 (grade 8–9)
Denominators that are exactly the same, as in \dfrac{3}{x + 1} and \dfrac{5}{x + 1}.
Algebra I, Lesson 12.4 (grade 8–9)
like fractionsEnglish
Fractions with the same denominator, like \dfrac{2}{7} and \dfrac{3}{7}.
Pre-Algebra, Lesson 3.3 (grade 6–8)
Fractions with the same denominator, like \dfrac{2}{7} and \dfrac{3}{7}.
Pre-Algebra, Lesson 3.3 (grade 6–8)
like radicalsEnglish
Radicals with the same index and the same radicand, such as 3\sqrt{2} and -7\sqrt{2}. Only like radicals can be combined by adding or subtracting.
Algebra I, Lesson 10.3 (grade 8–9) · Algebra II, Lesson 6.3 (grade 10–11)
Radicals with the same index and the same radicand, such as 3\sqrt{2} and -7\sqrt{2}. Only like radicals can be combined by adding or subtracting.
Algebra I, Lesson 10.3 (grade 8–9) · Algebra II, Lesson 6.3 (grade 10–11)
Like termsEnglish
Terms with exactly the same variables raised to exactly the same powers, such as 3x^2 and -5x^2. Constants are like terms with one another.
Algebra I, Lesson 1.4 (grade 8–9) · Algebra I, Lesson 2.2 (grade 8–9) · Algebra II, Lesson 4.2 (grade 10–11) · +2 more
Terms with exactly the same variables raised to exactly the same powers, such as 3x^2 and -5x^2. Constants are like terms with one another.
Algebra I, Lesson 1.4 (grade 8–9) · Algebra I, Lesson 2.2 (grade 8–9) · Algebra II, Lesson 4.2 (grade 10–11) · +2 more
limaçonEnglish
The graph of r = a + b\cos\theta or r = a + b\sin\theta (a, b > 0); it has an inner loop if a < b, is a cardioid if a = b, has a dimple if b < a < 2b, and is convex if a \ge 2b. The name comes from the French word for snail.
Trigonometry, Lesson 9.3 (grade 11–12)
The graph of r = a + b\cos\theta or r = a + b\sin\theta (a, b > 0); it has an inner loop if a < b, is a cardioid if a = b, has a dimple if b < a < 2b, and is convex if a \ge 2b. The name comes from the French word for snail.
Trigonometry, Lesson 9.3 (grade 11–12)
line of best fitEnglish
The line that fits the data best by a definite rule. The usual rule is least squares: the line that makes the sum of the squared residuals as small as possible.
Algebra I, Lesson 13.2 (grade 8–9)
The line that fits the data best by a definite rule. The usual rule is least squares: the line that makes the sum of the squared residuals as small as possible.
Algebra I, Lesson 13.2 (grade 8–9)
line of fitEnglish
A line drawn through the middle of the points of a scatter plot that shows the trend of the data. It does not have to pass through any of the data points.
Algebra I, Lesson 13.2 (grade 8–9)
A line drawn through the middle of the points of a scatter plot that shows the trend of the data. It does not have to pass through any of the data points.
Algebra I, Lesson 13.2 (grade 8–9)
line of greatest slopeEnglish
On a sloping plane, the steepest line, perpendicular to the horizontal lines in that plane.
Trigonometry, Lesson 8.4 (grade 11–12)
On a sloping plane, the steepest line, perpendicular to the horizontal lines in that plane.
Trigonometry, Lesson 8.4 (grade 11–12)
line of reflection (mirror line)English
The line m in which a figure is reflected.
Geometry, Lesson 7.2 (grade 9–10)
The line m in which a figure is reflected.
Geometry, Lesson 7.2 (grade 9–10)
Line of sightEnglish
The straight line from an observer's eye to the object being observed.
Geometry, Lesson 9.7 (grade 9–10) · Trigonometry, Lesson 8.1 (grade 11–12)
The straight line from an observer's eye to the object being observed.
Geometry, Lesson 9.7 (grade 9–10) · Trigonometry, Lesson 8.1 (grade 11–12)
line symmetryEnglish
A figure has line symmetry if a reflection in some line maps the figure onto itself; that line is a line of symmetry.
Geometry, Lesson 7.2 (grade 9–10)
A figure has line symmetry if a reflection in some line maps the figure onto itself; that line is a line of symmetry.
Geometry, Lesson 7.2 (grade 9–10)
line up the decimal pointsEnglish
Write the numbers in a column so the decimal points are directly under each other; then every digit sits under a digit of the same place value.
Pre-Algebra, Lesson 4.2 (grade 6–8)
Write the numbers in a column so the decimal points are directly under each other; then every digit sits under a digit of the same place value.
Pre-Algebra, Lesson 4.2 (grade 6–8)
linear equationEnglish
An equation whose graph is a straight line, such as y = 2x - 3.
Algebra I, Lesson 5.3 (grade 8–9) · Pre-Algebra, Lesson 11.3 (grade 6–8)
An equation whose graph is a straight line, such as y = 2x - 3.
Algebra I, Lesson 5.3 (grade 8–9) · Pre-Algebra, Lesson 11.3 (grade 6–8)
linear equation in three variablesEnglish
An equation that can be written ax + by + cz = d, where a, b, c are not all zero. Its graph in space is a flat plane.
Algebra II, Lesson 2.4 (grade 10–11)
An equation that can be written ax + by + cz = d, where a, b, c are not all zero. Its graph in space is a flat plane.
Algebra II, Lesson 2.4 (grade 10–11)
linear inequality in two variablesEnglish
An inequality such as y < 2x - 1 or 3x + 2y \ge 6. Its solutions are all ordered pairs that make it true.
Algebra I, Lesson 6.6 (grade 8–9)
An inequality such as y < 2x - 1 or 3x + 2y \ge 6. Its solutions are all ordered pairs that make it true.
Algebra I, Lesson 6.6 (grade 8–9)
linear modelEnglish
A linear equation or function, such as y = mx + b, used to describe a real situation and make predictions.
Algebra I, Lesson 5.7 (grade 8–9)
A linear equation or function, such as y = mx + b, used to describe a real situation and make predictions.
Algebra I, Lesson 5.7 (grade 8–9)
linear pairEnglish
Two adjacent angles whose noncommon sides are opposite rays. If B is between A and C and D is not on \overleftrightarrow{AC}, then \angle ABD and \angle DBC form a linear pair.
Geometry, Lesson 2.4 (grade 9–10)
Two adjacent angles whose noncommon sides are opposite rays. If B is between A and C and D is not on \overleftrightarrow{AC}, then \angle ABD and \angle DBC form a linear pair.
Geometry, Lesson 2.4 (grade 9–10)
linear programmingEnglish
A method for finding the best (largest or smallest) value of a linear expression when the variables must satisfy a system of linear inequalities.
Algebra II, Lesson 2.3 (grade 10–11)
A method for finding the best (largest or smallest) value of a linear expression when the variables must satisfy a system of linear inequalities.
Algebra II, Lesson 2.3 (grade 10–11)
linear speedEnglish
The distance traveled along the circular path per unit of time, v = \dfrac{s}{t}.
Trigonometry, Lesson 3.5 (grade 11–12)
The distance traveled along the circular path per unit of time, v = \dfrac{s}{t}.
Trigonometry, Lesson 3.5 (grade 11–12)
linear transformationEnglish
A rule that sends each point (x, y) to a new point by multiplying the column \begin{bmatrix} x \\ y \end{bmatrix} by a fixed 2 × 2 matrix. It always sends the origin to itself.
Algebra II, Lesson 12.6 (grade 10–11) · Statistics, Lesson 2.6 (grade 11–12) · Statistics, Lesson 7.3 (grade 11–12)
A rule that sends each point (x, y) to a new point by multiplying the column \begin{bmatrix} x \\ y \end{bmatrix} by a fixed 2 × 2 matrix. It always sends the origin to itself.
Algebra II, Lesson 12.6 (grade 10–11) · Statistics, Lesson 2.6 (grade 11–12) · Statistics, Lesson 7.3 (grade 11–12)
literal equationEnglish
An equation with two or more variables (letters), such as d = rt or 2x + 3y = 6.
Algebra I, Lesson 2.5 (grade 8–9)
An equation with two or more variables (letters), such as d = rt or 2x + 3y = 6.
Algebra I, Lesson 2.5 (grade 8–9)
LL, HA and LAEnglish
Leg-Leg, Hypotenuse-Angle and Leg-Angle: shortcut names for SAS, AAS and ASA (or AAS) when the triangles are right triangles.
Geometry, Lesson 4.7 (grade 9–10)
Leg-Leg, Hypotenuse-Angle and Leg-Angle: shortcut names for SAS, AAS and ASA (or AAS) when the triangles are right triangles.
Geometry, Lesson 4.7 (grade 9–10)
locusEnglish
The set of all points that satisfy a given condition (plural: loci). For example, the locus of points 3 cm from a point O is the circle with center O and radius 3 cm.
Geometry, Lesson 5.1 (grade 9–10)
The set of all points that satisfy a given condition (plural: loci). For example, the locus of points 3 cm from a point O is the circle with center O and radius 3 cm.
Geometry, Lesson 5.1 (grade 9–10)
logarithmEnglish
For b > 0, b \ne 1 and x > 0, \log_b x is the exponent you put on b to get x: \log_b x = y means b^y = x.
Algebra II, Lesson 8.1 (grade 10–11)
For b > 0, b \ne 1 and x > 0, \log_b x is the exponent you put on b to get x: \log_b x = y means b^y = x.
Algebra II, Lesson 8.1 (grade 10–11)
logarithmic equationEnglish
An equation in which the variable appears inside a logarithm, such as \log_2(x + 3) = 5.
Algebra II, Lesson 8.5 (grade 10–11)
An equation in which the variable appears inside a logarithm, such as \log_2(x + 3) = 5.
Algebra II, Lesson 8.5 (grade 10–11)
logarithmic functionEnglish
A function f(x) = \log_b x with b > 0 and b \ne 1; it is the inverse of g(x) = b^x.
Algebra II, Lesson 8.2 (grade 10–11)
A function f(x) = \log_b x with b > 0 and b \ne 1; it is the inverse of g(x) = b^x.
Algebra II, Lesson 8.2 (grade 10–11)
logarithmic scaleEnglish
A scale that records the logarithm of a quantity instead of the quantity itself, so that each step of 1 means multiplying by the base (usually 10).
Algebra II, Lesson 8.6 (grade 10–11) · Grade 6 Earth Science: The Dynamic Earth, Lesson 4.2 (grade 6)
A scale that records the logarithm of a quantity instead of the quantity itself, so that each step of 1 means multiplying by the base (usually 10).
Algebra II, Lesson 8.6 (grade 10–11) · Grade 6 Earth Science: The Dynamic Earth, Lesson 4.2 (grade 6)
logically equivalent statementsEnglish
Statements that are always both true or both false.
Geometry, Lesson 1.3 (grade 9–10)
Statements that are always both true or both false.
Geometry, Lesson 1.3 (grade 9–10)
logistic functionEnglish
A function of the form f(t) = \dfrac{L}{1 + Ae^{-kt}} with L > 0, A > 0 and k > 0; it grows almost exponentially at first and then levels off.
Algebra II, Lesson 7.4 (grade 10–11)
A function of the form f(t) = \dfrac{L}{1 + Ae^{-kt}} with L > 0, A > 0 and k > 0; it grows almost exponentially at first and then levels off.
Algebra II, Lesson 7.4 (grade 10–11)
Long legEnglish
In a 30^\circ-60^\circ-90^\circ triangle, the leg opposite the 60^\circ angle.
Geometry, Lesson 9.4 (grade 9–10) · Trigonometry, Lesson 2.2 (grade 11–12)
In a 30^\circ-60^\circ-90^\circ triangle, the leg opposite the 60^\circ angle.
Geometry, Lesson 9.4 (grade 9–10) · Trigonometry, Lesson 2.2 (grade 11–12)
lowest termsEnglish
A fraction is in lowest terms (simplest form) when the numerator and denominator have no common factor except 1, like \dfrac{3}{4}.
Pre-Algebra, Lesson 3.2 (grade 6–8)
A fraction is in lowest terms (simplest form) when the numerator and denominator have no common factor except 1, like \dfrac{3}{4}.
Pre-Algebra, Lesson 3.2 (grade 6–8)
lurking variableEnglish
A hidden third quantity that affects both variables and can make them look related even though neither one causes the other.
Algebra I, Lesson 13.1 (grade 8–9) · Statistics, Lesson 4.1 (grade 11–12) · Statistics, Lesson 4.5 (grade 11–12)
A hidden third quantity that affects both variables and can make them look related even though neither one causes the other.
Algebra I, Lesson 13.1 (grade 8–9) · Statistics, Lesson 4.1 (grade 11–12) · Statistics, Lesson 4.5 (grade 11–12)
M
magnitudeEnglish
The length of a vector, written |\mathbf{u}|. For \langle a, b \rangle it is \sqrt{a^2 + b^2}.
Algebra II, Lesson 12.5 (grade 10–11) · Grade 6 Earth Science: The Dynamic Earth, Lesson 4.2 (grade 6) · Grade 6 Geography: Physical Geography: The Earth’s Systems, Lesson 3.3 (grade 6) · +1 more
The length of a vector, written |\mathbf{u}|. For \langle a, b \rangle it is \sqrt{a^2 + b^2}.
Algebra II, Lesson 12.5 (grade 10–11) · Grade 6 Earth Science: The Dynamic Earth, Lesson 4.2 (grade 6) · Grade 6 Geography: Physical Geography: The Earth’s Systems, Lesson 3.3 (grade 6) · +1 more
magnitude (of a star)English
A measure of how bright a star looks; smaller numbers are brighter, and a difference of 5 magnitudes is a factor of 100 in brightness.
Algebra II, Lesson 8.6 (grade 10–11)
A measure of how bright a star looks; smaller numbers are brighter, and a difference of 5 magnitudes is a factor of 100 in brightness.
Algebra II, Lesson 8.6 (grade 10–11)
major axisEnglish
The longest chord of an ellipse, through both foci; its length is 2a and its endpoints are the vertices.
Algebra II, Lesson 11.2 (grade 10–11) · Grade 5 Earth Science: The Sky: Sun, Moon and Stars, Lesson 5.2 (grade 5)
The longest chord of an ellipse, through both foci; its length is 2a and its endpoints are the vertices.
Algebra II, Lesson 11.2 (grade 10–11) · Grade 5 Earth Science: The Sky: Sun, Moon and Stars, Lesson 5.2 (grade 5)
Marginal distributionEnglish
The distribution of one variable by itself, found from the row totals or the column totals in the margins of a two-way table, usually as percents of the grand total.
Statistics, Lesson 1.3 (grade 11–12)
The distribution of one variable by itself, found from the row totals or the column totals in the margins of a two-way table, usually as percents of the grand total.
Statistics, Lesson 1.3 (grade 11–12)
matched pairs designEnglish
A randomized block design with blocks of two: either each subject receives both treatments in a random order, or two very similar units are paired and the treatments are randomly assigned within each pair.
Statistics, Lesson 5.6 (grade 11–12)
A randomized block design with blocks of two: either each subject receives both treatments in a random order, or two very similar units are paired and the treatments are randomly assigned within each pair.
Statistics, Lesson 5.6 (grade 11–12)
mathematical inductionEnglish
A method of proving that a statement P(n) is true for every counting number n by proving a base case and an inductive step.
Algebra II, Lesson 9.6 (grade 10–11)
A method of proving that a statement P(n) is true for every counting number n by proving a base case and an inductive step.
Algebra II, Lesson 9.6 (grade 10–11)
matrixEnglish
A rectangular table of numbers arranged in rows and columns and enclosed in brackets. The plural is matrices.
Algebra II, Lesson 12.1 (grade 10–11)
A rectangular table of numbers arranged in rows and columns and enclosed in brackets. The plural is matrices.
Algebra II, Lesson 12.1 (grade 10–11)
matrix equationEnglish
A system written as AX = B, where X is the column of variables and B is the column of constants.
Algebra II, Lesson 12.4 (grade 10–11)
A system written as AX = B, where X is the column of variables and B is the column of constants.
Algebra II, Lesson 12.4 (grade 10–11)
matrix productEnglish
For A (m × n) and B (n × p), the m × p matrix AB whose entry in row i, column j is found by multiplying row i of A by column j of B entry by entry and adding.
Algebra II, Lesson 12.2 (grade 10–11)
For A (m × n) and B (n × p), the m × p matrix AB whose entry in row i, column j is found by multiplying row i of A by column j of B entry by entry and adding.
Algebra II, Lesson 12.2 (grade 10–11)
maximum and minimum valuesEnglish
For a sinusoid with amplitude |a| and midline y = d, the maximum is d + |a| and the minimum is d - |a|.
Trigonometry, Lesson 4.4 (grade 11–12)
For a sinusoid with amplitude |a| and midline y = d, the maximum is d + |a| and the minimum is d - |a|.
Trigonometry, Lesson 4.4 (grade 11–12)
Mean difference \mu_dEnglish
The true mean of the differences for all pairs in the population (or for all pairs that could receive the treatments). It is the parameter of a paired analysis.
Statistics, Lesson 12.3 (grade 11–12)
The true mean of the differences for all pairs in the population (or for all pairs that could receive the treatments). It is the parameter of a paired analysis.
Statistics, Lesson 12.3 (grade 11–12)
Mean of a density curveEnglish
The balance point: the place where the curve would balance if it were cut out of solid material. It is written \mu.
Statistics, Lesson 3.2 (grade 11–12)
The balance point: the place where the curve would balance if it were cut out of solid material. It is written \mu.
Statistics, Lesson 3.2 (grade 11–12)
Mean of a geometric random variableEnglish
\mu = 1/p, the average number of trials needed to get the first success, over many repetitions.
Statistics, Lesson 8.4 (grade 11–12)
\mu = 1/p, the average number of trials needed to get the first success, over many repetitions.
Statistics, Lesson 8.4 (grade 11–12)
Mean of \bar{x}English
\mu_{\bar{x}} = \mu: over all possible samples, the sample means average out to the population mean.
Statistics, Lesson 9.3 (grade 11–12)
\mu_{\bar{x}} = \mu: over all possible samples, the sample means average out to the population mean.
Statistics, Lesson 9.3 (grade 11–12)
Mean proportionalEnglish
Euclid's name for the geometric mean: a length x with a : x = x : b.
Geometry, Lesson 9.3 (grade 9–10)
Euclid's name for the geometric mean: a length x with a : x = x : b.
Geometry, Lesson 9.3 (grade 9–10)
measure of centerEnglish
A single number that describes a typical value of a data set. The mean, median and mode are measures of center.
Pre-Algebra, Lesson 13.2 (grade 6–8) · Statistics, Lesson 2.1 (grade 11–12)
A single number that describes a typical value of a data set. The mean, median and mode are measures of center.
Pre-Algebra, Lesson 13.2 (grade 6–8) · Statistics, Lesson 2.1 (grade 11–12)
Measures of center and positionEnglish
Numbers that locate values on the number line: the mean, the median, the quartiles, the minimum and the maximum. Adding a constant moves all of them.
Statistics, Lesson 2.6 (grade 11–12)
Numbers that locate values on the number line: the mean, the median, the quartiles, the minimum and the maximum. Adding a constant moves all of them.
Statistics, Lesson 2.6 (grade 11–12)
Measures of spreadEnglish
Numbers that measure how far apart the values are: the range, the IQR and the standard deviation. Adding a constant does not change them.
Statistics, Lesson 2.6 (grade 11–12)
Numbers that measure how far apart the values are: the range, the IQR and the standard deviation. Adding a constant does not change them.
Statistics, Lesson 2.6 (grade 11–12)
Median of a density curveEnglish
The equal-areas point: the value with half the area under the curve to its left and half to its right.
Statistics, Lesson 3.2 (grade 11–12)
The equal-areas point: the value with half the area under the curve to its left and half to its right.
Statistics, Lesson 3.2 (grade 11–12)
median of a triangleEnglish
A segment from a vertex to the midpoint of the opposite side. Every triangle has three medians.
Geometry, Lesson 5.3 (grade 9–10)
A segment from a vertex to the midpoint of the opposite side. Every triangle has three medians.
Geometry, Lesson 5.3 (grade 9–10)
method of exhaustionEnglish
The ancient Greek method, credited to Eudoxus, of proving an area or volume by trapping it between figures whose sizes come as close to it as desired; an early form of the limits used in calculus.
Geometry, Lesson 12.5 (grade 9–10)
The ancient Greek method, credited to Eudoxus, of proving an area or volume by trapping it between figures whose sizes come as close to it as desired; an early form of the limits used in calculus.
Geometry, Lesson 12.5 (grade 9–10)
metric systemEnglish
The system of units based on powers of 10: millimeters, centimeters, meters, kilometers, grams, kilograms, milliliters, liters.
Pre-Algebra, Lesson 7.5 (grade 6–8)
The system of units based on powers of 10: millimeters, centimeters, meters, kilometers, grams, kilograms, milliliters, liters.
Pre-Algebra, Lesson 7.5 (grade 6–8)
midlineEnglish
The horizontal line y = d halfway between the maximum and minimum values of a sinusoid.
Trigonometry, Lesson 4.4 (grade 11–12) · Trigonometry, Lesson 8.5 (grade 11–12)
The horizontal line y = d halfway between the maximum and minimum values of a sinusoid.
Trigonometry, Lesson 4.4 (grade 11–12) · Trigonometry, Lesson 8.5 (grade 11–12)
midline valueEnglish
The average of the maximum and minimum values, d = \dfrac{M + m}{2}.
Trigonometry, Lesson 4.5 (grade 11–12)
The average of the maximum and minimum values, d = \dfrac{M + m}{2}.
Trigonometry, Lesson 4.5 (grade 11–12)
midpointEnglish
The point exactly halfway between two points, dividing the segment into two equal parts.
Algebra I, Lesson 10.5 (grade 8–9) · Grade 4 Art, Lesson 2.3 (grade 4) · Geometry, Lesson 2.2 (grade 9–10)
The point exactly halfway between two points, dividing the segment into two equal parts.
Algebra I, Lesson 10.5 (grade 8–9) · Grade 4 Art, Lesson 2.3 (grade 4) · Geometry, Lesson 2.2 (grade 9–10)
Midpoint FormulaEnglish
The midpoint of the segment joining (x_1, y_1) and (x_2, y_2) is \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right).
Geometry, Lesson 13.1 (grade 9–10)
The midpoint of the segment joining (x_1, y_1) and (x_2, y_2) is \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right).
Geometry, Lesson 13.1 (grade 9–10)
midpoint (inflection point)English
The point on a logistic graph where f = \frac{L}{2}; there the curve is rising fastest and changes from bending upward to bending downward.
Algebra II, Lesson 7.4 (grade 10–11)
The point on a logistic graph where f = \frac{L}{2}; there the curve is rising fastest and changes from bending upward to bending downward.
Algebra II, Lesson 7.4 (grade 10–11)
midsegment of a trapezoidEnglish
The segment that joins the midpoints of the legs of a trapezoid.
Geometry, Lesson 6.5 (grade 9–10)
The segment that joins the midpoints of the legs of a trapezoid.
Geometry, Lesson 6.5 (grade 9–10)
midsegment of a triangleEnglish
A segment that joins the midpoints of two sides of a triangle. Every triangle has three midsegments.
Geometry, Lesson 5.4 (grade 9–10)
A segment that joins the midpoints of two sides of a triangle. Every triangle has three midsegments.
Geometry, Lesson 5.4 (grade 9–10)
midsegment triangleEnglish
The triangle whose sides are the three midsegments of a triangle.
Geometry, Lesson 5.4 (grade 9–10)
The triangle whose sides are the three midsegments of a triangle.
Geometry, Lesson 5.4 (grade 9–10)
minimum value / maximum valueEnglish
The smallest (or largest) y-value a function ever reaches; for a parabola it is the y-coordinate of the vertex.
Algebra I, Lesson 11.1 (grade 8–9)
The smallest (or largest) y-value a function ever reaches; for a parabola it is the y-coordinate of the vertex.
Algebra I, Lesson 11.1 (grade 8–9)
minorEnglish
The determinant of the smaller matrix left when you cross out one row and one column of a larger matrix.
Algebra II, Lesson 12.3 (grade 10–11)
The determinant of the smaller matrix left when you cross out one row and one column of a larger matrix.
Algebra II, Lesson 12.3 (grade 10–11)
Minor arc, major arc, semicircleEnglish
A minor arc is the part of the circle inside a central angle; its measure is the measure of the central angle. The major arc is the rest of the circle, with measure 360^\circ minus the minor arc. If the endpoints are the ends of a diameter, each arc is a semicircle and measures 180^\circ.
Geometry, Lesson 10.1 (grade 9–10)
A minor arc is the part of the circle inside a central angle; its measure is the measure of the central angle. The major arc is the rest of the circle, with measure 360^\circ minus the minor arc. If the endpoints are the ends of a diameter, each arc is a semicircle and measures 180^\circ.
Geometry, Lesson 10.1 (grade 9–10)
minor axisEnglish
The chord through the center perpendicular to the major axis; its length is 2b and its endpoints are the co-vertices.
Algebra II, Lesson 11.2 (grade 10–11)
The chord through the center perpendicular to the major axis; its length is 2b and its endpoints are the co-vertices.
Algebra II, Lesson 11.2 (grade 10–11)
minute (of angle)English
One sixtieth of a degree: 1^\circ = 60'. A second is one sixtieth of a minute: 1' = 60''.
Geometry, Lesson 2.3 (grade 9–10)
One sixtieth of a degree: 1^\circ = 60'. A second is one sixtieth of a minute: 1' = 60''.
Geometry, Lesson 2.3 (grade 9–10)
minute of arcEnglish
One sixtieth of a degree, written 1'; one second of arc (1'') is one sixtieth of a minute.
Trigonometry, Lesson 3.3 (grade 11–12)
One sixtieth of a degree, written 1'; one second of arc (1'') is one sixtieth of a minute.
Trigonometry, Lesson 3.3 (grade 11–12)
mirror pointEnglish
The point on the other side of the axis of symmetry at the same height as a given point and the same distance from the axis.
Algebra I, Lesson 11.2 (grade 8–9)
The point on the other side of the axis of symmetry at the same height as a given point and the same distance from the axis.
Algebra I, Lesson 11.2 (grade 8–9)
missing legEnglish
An unknown side that forms the right angle. Find it with a^2 = c^2 - b^2.
Pre-Algebra, Lesson 12.7 (grade 6–8)
An unknown side that forms the right angle. Find it with a^2 = c^2 - b^2.
Pre-Algebra, Lesson 12.7 (grade 6–8)
missing termEnglish
The one unknown number in a proportion, shown in this lesson by a box \square.
Pre-Algebra, Lesson 7.3 (grade 6–8)
The one unknown number in a proportion, shown in this lesson by a box \square.
Pre-Algebra, Lesson 7.3 (grade 6–8)
mixed numberEnglish
A whole number and a proper fraction written together, like 2\tfrac{1}{3}, which means 2 + \dfrac{1}{3}.
Pre-Algebra, Lesson 3.4 (grade 6–8)
A whole number and a proper fraction written together, like 2\tfrac{1}{3}, which means 2 + \dfrac{1}{3}.
Pre-Algebra, Lesson 3.4 (grade 6–8)
mixture problemEnglish
A problem where two ingredients are combined, and the amount of something (value, or a pure substance) in the parts adds up to the amount in the whole.
Algebra I, Lesson 2.6 (grade 8–9) · Algebra I, Lesson 6.5 (grade 8–9)
A problem where two ingredients are combined, and the amount of something (value, or a pure substance) in the parts adds up to the amount in the whole.
Algebra I, Lesson 2.6 (grade 8–9) · Algebra I, Lesson 6.5 (grade 8–9)
modelEnglish
A function, such as a line, an exponential function or a parabola, chosen to describe a real situation so that we can understand it and make predictions.
Algebra I, Lesson 13.3 (grade 8–9) · Grade 1 Business & Finance, Lesson 6.2 (grade 1) · Grade 2 Earth Science: The Earth's Surface, Lesson 2.2 (grade 2) · +3 more
A function, such as a line, an exponential function or a parabola, chosen to describe a real situation so that we can understand it and make predictions.
Algebra I, Lesson 13.3 (grade 8–9) · Grade 1 Business & Finance, Lesson 6.2 (grade 1) · Grade 2 Earth Science: The Earth's Surface, Lesson 2.2 (grade 2) · +3 more
Modified boxplotEnglish
A boxplot in which outliers are drawn as separate dots and the whiskers reach only to the most extreme values that are not outliers.
Statistics, Lesson 2.3 (grade 11–12)
A boxplot in which outliers are drawn as separate dots and the whiskers reach only to the most extreme values that are not outliers.
Statistics, Lesson 2.3 (grade 11–12)
monomialEnglish
A number, a variable, or a product of a number and variables with whole-number exponents, such as 7, x, or -4a^2b^5.
Algebra I, Lesson 7.1 (grade 8–9) · Algebra I, Lesson 8.1 (grade 8–9)
A number, a variable, or a product of a number and variables with whole-number exponents, such as 7, x, or -4a^2b^5.
Algebra I, Lesson 7.1 (grade 8–9) · Algebra I, Lesson 8.1 (grade 8–9)
\mu and \sigmaEnglish
The Greek letters mu and sigma name the mean and standard deviation of a density curve (an idealized population), to tell them apart from \bar{x} and s of actual data.
Statistics, Lesson 3.2 (grade 11–12)
The Greek letters mu and sigma name the mean and standard deviation of a density curve (an idealized population), to tell them apart from \bar{x} and s of actual data.
Statistics, Lesson 3.2 (grade 11–12)
multiple testingEnglish
Running many significance tests on the same study or data. Even when every null hypothesis is true, some tests will be "significant" by chance alone.
Statistics, Lesson 11.5 (grade 11–12) · Statistics, Lesson 13.3 (grade 11–12)
Running many significance tests on the same study or data. Even when every null hypothesis is true, some tests will be "significant" by chance alone.
Statistics, Lesson 11.5 (grade 11–12) · Statistics, Lesson 13.3 (grade 11–12)
multiple-angle equationEnglish
An equation in which the variable appears as bx inside a trigonometric function, such as \sin 2x or \tan 3x.
Trigonometry, Lesson 6.5 (grade 11–12)
An equation in which the variable appears as bx inside a trigonometric function, such as \sin 2x or \tan 3x.
Trigonometry, Lesson 6.5 (grade 11–12)
multiplication counting principleEnglish
If one choice can be made in m ways and, for each of them, a second choice can be made in n ways, then the two choices together can be made in m \times n ways (and so on for more choices).
Statistics, Lesson 6.6 (grade 11–12)
If one choice can be made in m ways and, for each of them, a second choice can be made in n ways, then the two choices together can be made in m \times n ways (and so on for more choices).
Statistics, Lesson 6.6 (grade 11–12)
multiplication property of equalityEnglish
Multiplying both sides of an equation by the same nonzero number keeps it true and does not change its solutions.
Algebra I, Lesson 6.4 (grade 8–9)
Multiplying both sides of an equation by the same nonzero number keeps it true and does not change its solutions.
Algebra I, Lesson 6.4 (grade 8–9)
multiplication rule for independent eventsEnglish
If A and B are independent, the probability that both happen is P(A \text{ and } B) = P(A) \cdot P(B).
Statistics, Lesson 6.4 (grade 11–12)
If A and B are independent, the probability that both happen is P(A \text{ and } B) = P(A) \cdot P(B).
Statistics, Lesson 6.4 (grade 11–12)
multiplicityEnglish
The number of times a factor x - c appears in the factored form. In (x - 2)^3(x + 1), the zero 2 has multiplicity 3.
Algebra II, Lesson 4.6 (grade 10–11) · Algebra II, Lesson 4.7 (grade 10–11)
The number of times a factor x - c appears in the factored form. In (x - 2)^3(x + 1), the zero 2 has multiplicity 3.
Algebra II, Lesson 4.6 (grade 10–11) · Algebra II, Lesson 4.7 (grade 10–11)
multistage sampleEnglish
A sample chosen in stages, for example an SRS of counties, then an SRS of farms in each chosen county, then an SRS of animals on each chosen farm.
Statistics, Lesson 5.2 (grade 11–12)
A sample chosen in stages, for example an SRS of counties, then an SRS of farms in each chosen county, then an SRS of animals on each chosen farm.
Statistics, Lesson 5.2 (grade 11–12)
multi-step equationEnglish
An equation that needs more than two steps to solve, often because one side must be simplified first.
Algebra I, Lesson 2.2 (grade 8–9) · Pre-Algebra, Lesson 10.5 (grade 6–8)
An equation that needs more than two steps to solve, often because one side must be simplified first.
Algebra I, Lesson 2.2 (grade 8–9) · Pre-Algebra, Lesson 10.5 (grade 6–8)
multi-step problemEnglish
A word problem that needs two or more calculations, where the answer to one step is used in the next.
Pre-Algebra, Lesson 3.7 (grade 6–8)
A word problem that needs two or more calculations, where the answer to one step is used in the next.
Pre-Algebra, Lesson 3.7 (grade 6–8)
mutually exclusiveEnglish
Two events are mutually exclusive (or disjoint) if they have no outcomes in common, so they cannot both happen at once.
Statistics, Lesson 6.2 (grade 11–12)
Two events are mutually exclusive (or disjoint) if they have no outcomes in common, so they cannot both happen at once.
Statistics, Lesson 6.2 (grade 11–12)
N
natural exponential functionEnglish
The function y = e^x, the exponential function whose base is e.
Algebra II, Lesson 7.2 (grade 10–11)
The function y = e^x, the exponential function whose base is e.
Algebra II, Lesson 7.2 (grade 10–11)
natural logarithmEnglish
The logarithm with base e \approx 2.71828, written \ln x, so \ln x = \log_e x.
Algebra II, Lesson 8.1 (grade 10–11)
The logarithm with base e \approx 2.71828, written \ln x, so \ln x = \log_e x.
Algebra II, Lesson 8.1 (grade 10–11)
Near arc and far arcEnglish
For an angle whose vertex is outside a circle, the two intercepted arcs: the near arc is the one closer to the vertex, the far arc the one farther away.
Geometry, Lesson 10.5 (grade 9–10)
For an angle whose vertex is outside a circle, the two intercepted arcs: the near arc is the one closer to the vertex, the far arc the one farther away.
Geometry, Lesson 10.5 (grade 9–10)
negationEnglish
The opposite of a statement, written \sim p and read “not p.” The negation of “the angle is acute” is “the angle is not acute.”
Geometry, Lesson 1.3 (grade 9–10)
The opposite of a statement, written \sim p and read “not p.” The negation of “the angle is acute” is “the angle is not acute.”
Geometry, Lesson 1.3 (grade 9–10)
Negative associationEnglish
Larger values of one variable tend to go with smaller values of the other, so the points slope downhill from left to right.
Statistics, Lesson 4.1 (grade 11–12)
Larger values of one variable tend to go with smaller values of the other, so the points slope downhill from left to right.
Statistics, Lesson 4.1 (grade 11–12)
negative exponentEnglish
For any nonzero number a and whole number n, a^{-n} = \dfrac{1}{a^n}; a negative exponent means "one over" the positive power.
Algebra I, Lesson 7.2 (grade 8–9) · Pre-Algebra, Lesson 6.3 (grade 6–8)
For any nonzero number a and whole number n, a^{-n} = \dfrac{1}{a^n}; a negative exponent means "one over" the positive power.
Algebra I, Lesson 7.2 (grade 8–9) · Pre-Algebra, Lesson 6.3 (grade 6–8)
negative fractionEnglish
A fraction less than zero, such as -\dfrac{3}{4}. It can be written three ways: -\dfrac{3}{4} = \dfrac{-3}{4} = \dfrac{3}{-4}.
Pre-Algebra, Lesson 5.6 (grade 6–8)
A fraction less than zero, such as -\dfrac{3}{4}. It can be written three ways: -\dfrac{3}{4} = \dfrac{-3}{4} = \dfrac{3}{-4}.
Pre-Algebra, Lesson 5.6 (grade 6–8)
negative numberEnglish
A number less than zero. It is written with a minus sign in front, like -5, and sits to the left of 0 on the number line.
Pre-Algebra, Lesson 5.1 (grade 6–8)
A number less than zero. It is written with a minus sign in front, like -5, and sits to the left of 0 on the number line.
Pre-Algebra, Lesson 5.1 (grade 6–8)
netEnglish
A flat pattern of polygons (and, for curved solids, circles and other shapes) that can be folded up to cover the surface of a solid exactly, with no gaps or overlaps.
Geometry, Lesson 12.1 (grade 9–10) · Grade 2 Life Science: Animal Families, Lesson 5.4 (grade 2) · Pre-Algebra, Lesson 12.5 (grade 6–8)
A flat pattern of polygons (and, for curved solids, circles and other shapes) that can be folded up to cover the surface of a solid exactly, with no gaps or overlaps.
Geometry, Lesson 12.1 (grade 9–10) · Grade 2 Life Science: Animal Families, Lesson 5.4 (grade 2) · Pre-Algebra, Lesson 12.5 (grade 6–8)
Net gainEnglish
What a player receives minus what the player pays. A loss is a negative net gain.
Statistics, Lesson 7.2 (grade 11–12)
What a player receives minus what the player pays. A loss is a negative net gain.
Statistics, Lesson 7.2 (grade 11–12)
Newton's law of coolingEnglish
A model saying that the difference between an object's temperature and the room's temperature shrinks exponentially: T = T_s + (T_0 - T_s)e^{-kt}.
Algebra II, Lesson 7.3 (grade 10–11)
A model saying that the difference between an object's temperature and the room's temperature shrinks exponentially: T = T_s + (T_0 - T_s)e^{-kt}.
Algebra II, Lesson 7.3 (grade 10–11)
no solutionEnglish
The answer when an inequality is false for every number, such as 2x + 1 > 2x + 5.
Algebra I, Lesson 3.2 (grade 8–9)
The answer when an inequality is false for every number, such as 2x + 1 > 2x + 5.
Algebra I, Lesson 3.2 (grade 8–9)
non-Euclidean geometryEnglish
A consistent geometry in which the parallel postulate is replaced by a different assumption about parallels. It shows that the parallel postulate cannot be proved from Euclid's other postulates.
Geometry, Lesson 3.2 (grade 9–10)
A consistent geometry in which the parallel postulate is replaced by a different assumption about parallels. It shows that the parallel postulate cannot be proved from Euclid's other postulates.
Geometry, Lesson 3.2 (grade 9–10)
Non-included sideEnglish
A side of a triangle that is not between two given angles; it lies opposite one of them.
Geometry, Lesson 4.4 (grade 9–10)
A side of a triangle that is not between two given angles; it lies opposite one of them.
Geometry, Lesson 4.4 (grade 9–10)
nonlinear systemEnglish
A system of equations in which at least one equation is not linear, such as a line and a circle.
Algebra II, Lesson 11.5 (grade 10–11)
A system of equations in which at least one equation is not linear, such as a line and a circle.
Algebra II, Lesson 11.5 (grade 10–11)
non-real solutionEnglish
A solution p + qi with q \ne 0. It is a complex number that is not a real number.
Algebra II, Lesson 3.4 (grade 10–11)
A solution p + qi with q \ne 0. It is a complex number that is not a real number.
Algebra II, Lesson 3.4 (grade 10–11)
Nonresistant summaryEnglish
A summary that outliers and skewness can pull strongly: the mean, the standard deviation and the range.
Statistics, Lesson 2.5 (grade 11–12)
A summary that outliers and skewness can pull strongly: the mean, the standard deviation and the range.
Statistics, Lesson 2.5 (grade 11–12)
nonresponseEnglish
When individuals chosen for the sample cannot be contacted or refuse to answer. The response rate is the percent of the chosen sample that actually responds.
Statistics, Lesson 5.3 (grade 11–12)
When individuals chosen for the sample cannot be contacted or refuse to answer. The response rate is the percent of the chosen sample that actually responds.
Statistics, Lesson 5.3 (grade 11–12)
nonsampling errorEnglish
Error from the way the data were gathered, such as undercoverage, nonresponse, voluntary response or misleading question wording; the margin of error does not include it.
Statistics, Lesson 10.5 (grade 11–12) · Statistics, Lesson 5.3 (grade 11–12)
Error from the way the data were gathered, such as undercoverage, nonresponse, voluntary response or misleading question wording; the margin of error does not include it.
Statistics, Lesson 10.5 (grade 11–12) · Statistics, Lesson 5.3 (grade 11–12)
Normal approximation to the binomialEnglish
Using the normal distribution N(np, \sqrt{np(1 - p)}) in place of the exact binomial distribution B(n, p) to find probabilities when n is large.
Statistics, Lesson 8.3 (grade 11–12)
Using the normal distribution N(np, \sqrt{np(1 - p)}) in place of the exact binomial distribution B(n, p) to find probabilities when n is large.
Statistics, Lesson 8.3 (grade 11–12)
Normal curveEnglish
The bell-shaped density curve of a normal distribution. Its peak, mean and median are all at \mu.
Statistics, Lesson 3.3 (grade 11–12)
The bell-shaped density curve of a normal distribution. Its peak, mean and median are all at \mu.
Statistics, Lesson 3.3 (grade 11–12)
Normal probability plotEnglish
A graph that plots each data value against the z-score it would be expected to have if the data came from a normal distribution. A roughly straight line of points means the data are roughly normal.
Statistics, Lesson 3.6 (grade 11–12)
A graph that plots each data value against the z-score it would be expected to have if the data came from a normal distribution. A roughly straight line of points means the data are roughly normal.
Statistics, Lesson 3.6 (grade 11–12)
Normal random variableEnglish
A continuous random variable whose distribution is a normal curve N(\mu, \sigma).
Statistics, Lesson 7.4 (grade 11–12)
A continuous random variable whose distribution is a normal curve N(\mu, \sigma).
Statistics, Lesson 7.4 (grade 11–12)
Normal/Large Sample conditionEnglish
The population is normal, or n \ge 30, or (for a small sample) a dotplot, stemplot or boxplot of the data shows no strong skewness and no outliers.
Statistics, Lesson 10.4 (grade 11–12) · Statistics, Lesson 9.4 (grade 11–12)
The population is normal, or n \ge 30, or (for a small sample) a dotplot, stemplot or boxplot of the data shows no strong skewness and no outliers.
Statistics, Lesson 10.4 (grade 11–12) · Statistics, Lesson 9.4 (grade 11–12)
nth rootEnglish
A number b is an nth root of a if b^n = a. For example, -2 is a cube root of -8 because (-2)^3 = -8.
Algebra II, Lesson 6.1 (grade 10–11)
A number b is an nth root of a if b^n = a. For example, -2 is a cube root of -8 because (-2)^3 = -8.
Algebra II, Lesson 6.1 (grade 10–11)
null hypothesis (H_0)English
The claim being tested, usually a statement of "no effect," "no difference" or "nothing has changed." It gives the parameter one specific value, such as H_0: p = 0.5.
Statistics, Lesson 11.1 (grade 11–12)
The claim being tested, usually a statement of "no effect," "no difference" or "nothing has changed." It gives the parameter one specific value, such as H_0: p = 0.5.
Statistics, Lesson 11.1 (grade 11–12)
null value (p_0)English
The specific value of the proportion stated in the null hypothesis, such as 0.90 in H_0: p = 0.90.
Statistics, Lesson 11.2 (grade 11–12)
The specific value of the proportion stated in the null hypothesis, such as 0.90 in H_0: p = 0.90.
Statistics, Lesson 11.2 (grade 11–12)
numeratorEnglish
The top number of a fraction. It tells how many of the equal parts you have.
Pre-Algebra, Lesson 3.1 (grade 6–8)
The top number of a fraction. It tells how many of the equal parts you have.
Pre-Algebra, Lesson 3.1 (grade 6–8)
O
objective functionEnglish
The linear expression, such as profit P = 150x + 100y or cost C = 0.30x + 0.20y, that you want to maximize or minimize.
Algebra II, Lesson 2.3 (grade 10–11)
The linear expression, such as profit P = 150x + 100y or cost C = 0.30x + 0.20y, that you want to maximize or minimize.
Algebra II, Lesson 2.3 (grade 10–11)
oblique prism or cylinderEnglish
A prism or cylinder that leans: its lateral edges (or its axis) are not perpendicular to the bases. Its height is still the perpendicular distance between the bases.
Geometry, Lesson 12.4 (grade 9–10)
A prism or cylinder that leans: its lateral edges (or its axis) are not perpendicular to the bases. Its height is still the perpendicular distance between the bases.
Geometry, Lesson 12.4 (grade 9–10)
oblique triangleEnglish
A triangle with no right angle. All three of its angles are acute, or one is obtuse.
Trigonometry, Lesson 7.1 (grade 11–12)
A triangle with no right angle. All three of its angles are acute, or one is obtuse.
Trigonometry, Lesson 7.1 (grade 11–12)
observational studyEnglish
A study that observes individuals and measures variables without trying to influence the responses. The researchers do not decide who gets which treatment.
Statistics, Lesson 5.4 (grade 11–12)
A study that observes individuals and measures variables without trying to influence the responses. The researchers do not decide who gets which treatment.
Statistics, Lesson 5.4 (grade 11–12)
Obtuse triangleEnglish
A triangle with one obtuse angle (greater than 90^\circ and less than 180^\circ).
Geometry, Lesson 9.2 (grade 9–10)
A triangle with one obtuse angle (greater than 90^\circ and less than 180^\circ).
Geometry, Lesson 9.2 (grade 9–10)
odd functionEnglish
A function with f(-x) = -f(x) for all x; its graph is symmetric about the origin.
Trigonometry, Lesson 4.1 (grade 11–12) · Trigonometry, Lesson 5.1 (grade 11–12)
A function with f(-x) = -f(x) for all x; its graph is symmetric about the origin.
Trigonometry, Lesson 4.1 (grade 11–12) · Trigonometry, Lesson 5.1 (grade 11–12)
"of"English
In fraction problems, "of" means multiply: \dfrac{1}{2} of 10 means \dfrac{1}{2} \times 10 = 5.
Pre-Algebra, Lesson 3.5 (grade 6–8)
In fraction problems, "of" means multiply: \dfrac{1}{2} of 10 means \dfrac{1}{2} \times 10 = 5.
Pre-Algebra, Lesson 3.5 (grade 6–8)
one-sample t intervalEnglish
The confidence interval \bar{x} \pm t^* \dfrac{s}{\sqrt{n}} for a population mean \mu, with t^* from the t distribution with n - 1 degrees of freedom.
Statistics, Lesson 10.4 (grade 11–12)
The confidence interval \bar{x} \pm t^* \dfrac{s}{\sqrt{n}} for a population mean \mu, with t^* from the t distribution with n - 1 degrees of freedom.
Statistics, Lesson 10.4 (grade 11–12)
one-sample t testEnglish
A significance test of H_0: \mu = \mu_0 that compares a sample mean with the null value and finds the P-value from a t distribution.
Statistics, Lesson 11.3 (grade 11–12)
A significance test of H_0: \mu = \mu_0 that compares a sample mean with the null value and finds the P-value from a t distribution.
Statistics, Lesson 11.3 (grade 11–12)
one-sample z test for a proportionEnglish
A significance test of H_0: p = p_0 that uses the standard normal distribution to find the P-value for an observed sample proportion \hat{p}.
Statistics, Lesson 11.2 (grade 11–12)
A significance test of H_0: p = p_0 that uses the standard normal distribution to find the P-value for an observed sample proportion \hat{p}.
Statistics, Lesson 11.2 (grade 11–12)
one-to-one functionEnglish
A function in which different inputs always give different outputs. Only one-to-one functions have inverse functions.
Algebra II, Lesson 1.5 (grade 10–11) · Trigonometry, Lesson 6.1 (grade 11–12)
A function in which different inputs always give different outputs. Only one-to-one functions have inverse functions.
Algebra II, Lesson 1.5 (grade 10–11) · Trigonometry, Lesson 6.1 (grade 11–12)
open circleEnglish
A hollow dot on a number line graph showing that the endpoint is NOT a solution (used with < and >).
Algebra I, Lesson 3.1 (grade 8–9)
A hollow dot on a number line graph showing that the endpoint is NOT a solution (used with < and >).
Algebra I, Lesson 3.1 (grade 8–9)
open circle / closed circleEnglish
On a number-line graph, an open (hollow) circle means the endpoint is not included (< or >); a closed (filled) circle means it is included (\le or \ge).
Pre-Algebra, Lesson 10.7 (grade 6–8)
On a number-line graph, an open (hollow) circle means the endpoint is not included (< or >); a closed (filled) circle means it is included (\le or \ge).
Pre-Algebra, Lesson 10.7 (grade 6–8)
opposite coefficientsEnglish
Coefficients that add to zero, like 3y and -3y. Adding the equations eliminates that variable.
Algebra I, Lesson 6.3 (grade 8–9)
Coefficients that add to zero, like 3y and -3y. Adding the equations eliminates that variable.
Algebra I, Lesson 6.3 (grade 8–9)
Opposite legEnglish
For an acute angle of a right triangle, the leg that does not touch the angle.
Geometry, Lesson 9.5 (grade 9–10)
For an acute angle of a right triangle, the leg that does not touch the angle.
Geometry, Lesson 9.5 (grade 9–10)
opposite raysEnglish
If B is between A and C, then \overrightarrow{BA} and \overrightarrow{BC} are opposite rays: they share the endpoint B and together make up the whole line.
Geometry, Lesson 2.1 (grade 9–10)
If B is between A and C, then \overrightarrow{BA} and \overrightarrow{BC} are opposite rays: they share the endpoint B and together make up the whole line.
Geometry, Lesson 2.1 (grade 9–10)
opposite reciprocalEnglish
The number you get by flipping a fraction and changing its sign. The opposite reciprocal of \dfrac{2}{5} is -\dfrac{5}{2}; of 3 it is -\dfrac{1}{3}.
Algebra I, Lesson 5.6 (grade 8–9)
The number you get by flipping a fraction and changing its sign. The opposite reciprocal of \dfrac{2}{5} is -\dfrac{5}{2}; of 3 it is -\dfrac{1}{3}.
Algebra I, Lesson 5.6 (grade 8–9)
opposite reciprocalsEnglish
Two numbers whose product is -1, such as \dfrac{2}{3} and -\dfrac{3}{2}. The slope of a line perpendicular to a line of slope m \ne 0 is -\dfrac{1}{m}.
Geometry, Lesson 3.5 (grade 9–10)
Two numbers whose product is -1, such as \dfrac{2}{3} and -\dfrac{3}{2}. The slope of a line perpendicular to a line of slope m \ne 0 is -\dfrac{1}{m}.
Geometry, Lesson 3.5 (grade 9–10)
opposite sideEnglish
For an acute angle of a right triangle, the leg that does not touch the angle.
Trigonometry, Lesson 1.2 (grade 11–12)
For an acute angle of a right triangle, the leg that does not touch the angle.
Trigonometry, Lesson 1.2 (grade 11–12)
opposite sides and opposite anglesEnglish
In quadrilateral ABCD, sides that do not share a vertex (\overline{AB} and \overline{CD}; \overline{BC} and \overline{DA}) and angles at vertices that are not next to each other (\angle A and \angle C; \angle B and \angle D).
Geometry, Lesson 6.2 (grade 9–10)
In quadrilateral ABCD, sides that do not share a vertex (\overline{AB} and \overline{CD}; \overline{BC} and \overline{DA}) and angles at vertices that are not next to each other (\angle A and \angle C; \angle B and \angle D).
Geometry, Lesson 6.2 (grade 9–10)
oppositesEnglish
Two expressions whose sum is zero, such as x - 5 and 5 - x. Each one equals -1 times the other.
Algebra I, Lesson 12.2 (grade 8–9) · Algebra II, Lesson 5.1 (grade 10–11) · Pre-Algebra, Lesson 5.1 (grade 6–8)
Two expressions whose sum is zero, such as x - 5 and 5 - x. Each one equals -1 times the other.
Algebra I, Lesson 12.2 (grade 8–9) · Algebra II, Lesson 5.1 (grade 10–11) · Pre-Algebra, Lesson 5.1 (grade 6–8)
optimizeEnglish
To find the greatest or least possible value of a quantity, such as the largest area or the highest profit.
Algebra I, Lesson 11.2 (grade 8–9)
To find the greatest or least possible value of a quantity, such as the largest area or the highest profit.
Algebra I, Lesson 11.2 (grade 8–9)
Order of operationsEnglish
The agreed order for doing operations: grouping symbols first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
Algebra I, Lesson 1.3 (grade 8–9) · Pre-Algebra, Lesson 1.4 (grade 6–8) · Pre-Algebra, Lesson 5.6 (grade 6–8)
The agreed order for doing operations: grouping symbols first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
Algebra I, Lesson 1.3 (grade 8–9) · Pre-Algebra, Lesson 1.4 (grade 6–8) · Pre-Algebra, Lesson 5.6 (grade 6–8)
order of rotational symmetryEnglish
The number of different positions in one full turn in which the figure fits onto itself. If the order is n, the smallest angle of rotational symmetry is \dfrac{360^\circ}{n}.
Geometry, Lesson 7.3 (grade 9–10)
The number of different positions in one full turn in which the figure fits onto itself. If the order is n, the smallest angle of rotational symmetry is \dfrac{360^\circ}{n}.
Geometry, Lesson 7.3 (grade 9–10)
ordered pairEnglish
A pair of numbers (x, y) written in a set order: first the horizontal position x, then the vertical position y.
Algebra I, Lesson 4.1 (grade 8–9) · Pre-Algebra, Lesson 11.1 (grade 6–8)
A pair of numbers (x, y) written in a set order: first the horizontal position x, then the vertical position y.
Algebra I, Lesson 4.1 (grade 8–9) · Pre-Algebra, Lesson 11.1 (grade 6–8)
ordered tripleEnglish
A point (x, y, z) in space, written in the order x, y, z. A solution of a three-variable system is an ordered triple.
Algebra II, Lesson 2.4 (grade 10–11)
A point (x, y, z) in space, written in the order x, y, z. A solution of a three-variable system is an ordered triple.
Algebra II, Lesson 2.4 (grade 10–11)
originEnglish
The point (0, 0), where the x-axis and y-axis cross.
Algebra I, Lesson 5.2 (grade 8–9) · Grade 7 Composition & Creative Writing: Commonplace, Encomium and Invective, Lesson 2.1 (grade 7) · Pre-Algebra, Lesson 11.1 (grade 6–8)
The point (0, 0), where the x-axis and y-axis cross.
Algebra I, Lesson 5.2 (grade 8–9) · Grade 7 Composition & Creative Writing: Commonplace, Encomium and Invective, Lesson 2.1 (grade 7) · Pre-Algebra, Lesson 11.1 (grade 6–8)
original amountEnglish
The starting amount, before the change. It is the whole (100%) in a percent change problem.
Pre-Algebra, Lesson 8.4 (grade 6–8)
The starting amount, before the change. It is the whole (100%) in a percent change problem.
Pre-Algebra, Lesson 8.4 (grade 6–8)
orthocenterEnglish
The point where the three lines containing the altitudes of a triangle meet.
Geometry, Lesson 5.3 (grade 9–10)
The point where the three lines containing the altitudes of a triangle meet.
Geometry, Lesson 5.3 (grade 9–10)
orthogonalEnglish
Another word for perpendicular. Two nonzero vectors are orthogonal when they meet at a right angle.
Algebra II, Lesson 12.5 (grade 10–11) · Grade 6 Art, Lesson 6.1 (grade 6) · Graphic Design & Illustration, Lesson 1.4 (grade 9–12) · +1 more
Another word for perpendicular. Two nonzero vectors are orthogonal when they meet at a right angle.
Algebra II, Lesson 12.5 (grade 10–11) · Grade 6 Art, Lesson 6.1 (grade 6) · Graphic Design & Illustration, Lesson 1.4 (grade 9–12) · +1 more
outlierEnglish
A data point that lies far away from the pattern formed by the other points.
Algebra I, Lesson 13.1 (grade 8–9) · Pre-Algebra, Lesson 13.2 (grade 6–8) · Statistics, Lesson 1.5 (grade 11–12)
A data point that lies far away from the pattern formed by the other points.
Algebra I, Lesson 13.1 (grade 8–9) · Pre-Algebra, Lesson 13.2 (grade 6–8) · Statistics, Lesson 1.5 (grade 11–12)
Outlier (1.5 × IQR rule)English
A value below Q1 − 1.5·IQR or above Q3 + 1.5·IQR. It is unusually far from the middle half of the data.
Statistics, Lesson 2.3 (grade 11–12)
A value below Q1 − 1.5·IQR or above Q3 + 1.5·IQR. It is unusually far from the middle half of the data.
Statistics, Lesson 2.3 (grade 11–12)
Outlier (in regression)English
A point that lies far from the overall pattern of the scatterplot; a point with a large residual is an outlier in the y direction.
Statistics, Lesson 4.5 (grade 11–12)
A point that lies far from the overall pattern of the scatterplot; a point with a large residual is an outlier in the y direction.
Statistics, Lesson 4.5 (grade 11–12)
outputEnglish
A value of the dependent variable, usually the y-value of an ordered pair.
Algebra I, Lesson 4.2 (grade 8–9) · Grade 6 Engineering & Physics, Lesson 4.4 (grade 6) · Pre-Algebra, Lesson 11.2 (grade 6–8)
A value of the dependent variable, usually the y-value of an ordered pair.
Algebra I, Lesson 4.2 (grade 8–9) · Grade 6 Engineering & Physics, Lesson 4.4 (grade 6) · Pre-Algebra, Lesson 11.2 (grade 6–8)
Overlapping trianglesEnglish
Triangles that share part of their interiors, and often a side or an angle, in a figure.
Geometry, Lesson 4.5 (grade 9–10)
Triangles that share part of their interiors, and often a side or an angle, in a figure.
Geometry, Lesson 4.5 (grade 9–10)
P
paired dataEnglish
Data that come in pairs of numbers measured on the same thing, such as the hours a student studied and that student's quiz score. Each pair becomes an ordered pair (x, y).
Algebra I, Lesson 13.1 (grade 8–9) · Statistics, Lesson 12.3 (grade 11–12)
Data that come in pairs of numbers measured on the same thing, such as the hours a student studied and that student's quiz score. Each pair becomes an ordered pair (x, y).
Algebra I, Lesson 13.1 (grade 8–9) · Statistics, Lesson 12.3 (grade 11–12)
Paired t proceduresEnglish
One-sample t procedures (interval and test) applied to the list of differences, with df = n − 1 where n is the number of pairs.
Statistics, Lesson 12.3 (grade 11–12)
One-sample t procedures (interval and test) applied to the list of differences, with df = n − 1 where n is the number of pairs.
Statistics, Lesson 12.3 (grade 11–12)
parabolaEnglish
The U-shaped curve that is the graph of a quadratic function. It opens up or down.
Algebra I, Lesson 11.1 (grade 8–9) · Algebra II, Lesson 11.1 (grade 10–11) · Architecture & Civil Engineering, Lesson 4.4 (grade 9–12) · +1 more
The U-shaped curve that is the graph of a quadratic function. It opens up or down.
Algebra I, Lesson 11.1 (grade 8–9) · Algebra II, Lesson 11.1 (grade 10–11) · Architecture & Civil Engineering, Lesson 4.4 (grade 9–12) · +1 more
paragraph proofEnglish
A proof written in sentences, in which each statement is still supported by a stated reason.
Geometry, Lesson 2.6 (grade 9–10)
A proof written in sentences, in which each statement is still supported by a stated reason.
Geometry, Lesson 2.6 (grade 9–10)
Parallel boxplotsEnglish
Two or more boxplots drawn on the same scale so that groups can be compared.
Statistics, Lesson 2.3 (grade 11–12)
Two or more boxplots drawn on the same scale so that groups can be compared.
Statistics, Lesson 2.3 (grade 11–12)
Parallel graphsEnglish
Graphs of several groups drawn on the same scale, such as parallel boxplots, back-to-back stemplots or stacked histograms, so that the groups can be compared by eye.
Statistics, Lesson 2.5 (grade 11–12)
Graphs of several groups drawn on the same scale, such as parallel boxplots, back-to-back stemplots or stacked histograms, so that the groups can be compared by eye.
Statistics, Lesson 2.5 (grade 11–12)
parallel linesEnglish
Lines in the same plane that never meet. Non-vertical parallel lines have equal slopes and different y-intercepts.
Algebra I, Lesson 5.6 (grade 8–9) · Grade 2 Art, Lesson 1.2 (grade 2) · Geometry, Lesson 3.1 (grade 9–10)
Lines in the same plane that never meet. Non-vertical parallel lines have equal slopes and different y-intercepts.
Algebra I, Lesson 5.6 (grade 8–9) · Grade 2 Art, Lesson 1.2 (grade 2) · Geometry, Lesson 3.1 (grade 9–10)
parallel ruleEnglish
A drafting and navigation tool made of two straightedges joined by two equal crossbars that pivot at their ends, so that the straightedges always stay parallel.
Geometry, Lesson 6.3 (grade 9–10)
A drafting and navigation tool made of two straightedges joined by two equal crossbars that pivot at their ends, so that the straightedges always stay parallel.
Geometry, Lesson 6.3 (grade 9–10)
parallelogramEnglish
A quadrilateral with both pairs of opposite sides parallel. Parallelogram ABCD has \overline{AB} \parallel \overline{DC} and \overline{AD} \parallel \overline{BC}.
Geometry, Lesson 6.2 (grade 9–10) · Pre-Algebra, Lesson 12.3 (grade 6–8)
A quadrilateral with both pairs of opposite sides parallel. Parallelogram ABCD has \overline{AB} \parallel \overline{DC} and \overline{AD} \parallel \overline{BC}.
Geometry, Lesson 6.2 (grade 9–10) · Pre-Algebra, Lesson 12.3 (grade 6–8)
parallelogram lawEnglish
To add \mathbf{u} and \mathbf{v} drawn from a common point, complete the parallelogram; the diagonal from that point is \mathbf{u} + \mathbf{v}. Equivalently, place the tail of \mathbf{v} at the tip of \mathbf{u} (tip-to-tail).
Trigonometry, Lesson 9.5 (grade 11–12)
To add \mathbf{u} and \mathbf{v} drawn from a common point, complete the parallelogram; the diagonal from that point is \mathbf{u} + \mathbf{v}. Equivalently, place the tail of \mathbf{v} at the tip of \mathbf{u} (tip-to-tail).
Trigonometry, Lesson 9.5 (grade 11–12)
ParameterEnglish
A number that describes a whole population, such as the population proportion p, mean \mu or standard deviation \sigma. It is fixed, but usually unknown.
Statistics, Lesson 9.1 (grade 11–12)
A number that describes a whole population, such as the population proportion p, mean \mu or standard deviation \sigma. It is fixed, but usually unknown.
Statistics, Lesson 9.1 (grade 11–12)
Parameter and statisticEnglish
A parameter is a number that describes the population (usually unknown). A statistic is a number computed from a sample; we use statistics to estimate parameters.
Statistics, Lesson 1.1 (grade 11–12)
A parameter is a number that describes the population (usually unknown). A statistic is a number computed from a sample; we use statistics to estimate parameters.
Statistics, Lesson 1.1 (grade 11–12)
Parameter of interestEnglish
The single number about the population or treatments that the question is really asking about, such as p, p_1 - p_2, \mu, \mu_d or \mu_1 - \mu_2. Always define it in words.
Statistics, Lesson 12.4 (grade 11–12)
The single number about the population or treatments that the question is really asking about, such as p, p_1 - p_2, \mu, \mu_d or \mu_1 - \mu_2. Always define it in words.
Statistics, Lesson 12.4 (grade 11–12)
parent functionEnglish
The simplest function of a family, such as y = x^2 for all parabolas. Every other member is a transformation of it.
Algebra II, Lesson 1.2 (grade 10–11)
The simplest function of a family, such as y = x^2 for all parabolas. Every other member is a transformation of it.
Algebra II, Lesson 1.2 (grade 10–11)
partEnglish
The piece of the whole being described. It usually comes next to the word "is" in a percent question.
Pre-Algebra, Lesson 8.3 (grade 6–8)
The piece of the whole being described. It usually comes next to the word "is" in a percent question.
Pre-Algebra, Lesson 8.3 (grade 6–8)
partial productsEnglish
The smaller products you add together when you split a factor into parts, such as 70 and 21 in 7 \times 13 = 7 \times 10 + 7 \times 3 = 70 + 21.
Pre-Algebra, Lesson 1.3 (grade 6–8)
The smaller products you add together when you split a factor into parts, such as 70 and 21 in 7 \times 13 = 7 \times 10 + 7 \times 3 = 70 + 21.
Pre-Algebra, Lesson 1.3 (grade 6–8)
partial sumEnglish
The sum S_n of the first n terms of an infinite series.
Algebra II, Lesson 9.4 (grade 10–11)
The sum S_n of the first n terms of an infinite series.
Algebra II, Lesson 9.4 (grade 10–11)
part-to-part ratioEnglish
A ratio that compares one part of a group to another part, such as boys to girls.
Pre-Algebra, Lesson 7.1 (grade 6–8)
A ratio that compares one part of a group to another part, such as boys to girls.
Pre-Algebra, Lesson 7.1 (grade 6–8)
part-to-whole ratioEnglish
A ratio that compares one part of a group to the whole group, such as boys to all students.
Pre-Algebra, Lesson 7.1 (grade 6–8)
A ratio that compares one part of a group to the whole group, such as boys to all students.
Pre-Algebra, Lesson 7.1 (grade 6–8)
Pascal's ruleEnglish
The fact C(n, r) = C(n-1, r-1) + C(n-1, r), which is the adding rule that builds Pascal's triangle.
Algebra II, Lesson 10.3 (grade 10–11)
The fact C(n, r) = C(n-1, r-1) + C(n-1, r), which is the adding rule that builds Pascal's triangle.
Algebra II, Lesson 10.3 (grade 10–11)
Pascal's triangleEnglish
A triangle of numbers whose rows begin and end with 1, where each entry between the two 1s is the sum of the two entries just above it. Rows and positions are numbered starting from 0.
Algebra II, Lesson 10.3 (grade 10–11) · Statistics, Lesson 6.6 (grade 11–12)
A triangle of numbers whose rows begin and end with 1, where each entry between the two 1s is the sum of the two entries just above it. Rows and positions are numbered starting from 0.
Algebra II, Lesson 10.3 (grade 10–11) · Statistics, Lesson 6.6 (grade 11–12)
PeaksEnglish
A distribution is single-peaked if its graph has one clear high point, and has two (or more) peaks if there are separate high points, which often means two different groups are mixed together.
Statistics, Lesson 1.5 (grade 11–12)
A distribution is single-peaked if its graph has one clear high point, and has two (or more) peaks if there are separate high points, which often means two different groups are mixed together.
Statistics, Lesson 1.5 (grade 11–12)
per hundredEnglish
For every hundred. The word percent comes from the Latin per centum, "by the hundred."
Pre-Algebra, Lesson 8.1 (grade 6–8)
For every hundred. The word percent comes from the Latin per centum, "by the hundred."
Pre-Algebra, Lesson 8.1 (grade 6–8)
percentEnglish
A ratio that compares a number to 100. The symbol % means "out of 100" or "per hundred," so 23% means 23 out of 100.
Pre-Algebra, Lesson 8.1 (grade 6–8)
A ratio that compares a number to 100. The symbol % means "out of 100" or "per hundred," so 23% means 23 out of 100.
Pre-Algebra, Lesson 8.1 (grade 6–8)
percent equationEnglish
The rule \text{part} = \text{percent} \times \text{whole}, with the percent written as a decimal or fraction.
Pre-Algebra, Lesson 8.3 (grade 6–8)
The rule \text{part} = \text{percent} \times \text{whole}, with the percent written as a decimal or fraction.
Pre-Algebra, Lesson 8.3 (grade 6–8)
percent of a numberEnglish
A part of a number found by multiplying the number by the percent written as a decimal or fraction. "30% of 80" means 0.30 \times 80.
Pre-Algebra, Lesson 8.2 (grade 6–8)
A part of a number found by multiplying the number by the percent written as a decimal or fraction. "30% of 80" means 0.30 \times 80.
Pre-Algebra, Lesson 8.2 (grade 6–8)
percent of decreaseEnglish
The amount of decrease as a percent of the original amount.
Pre-Algebra, Lesson 8.4 (grade 6–8)
The amount of decrease as a percent of the original amount.
Pre-Algebra, Lesson 8.4 (grade 6–8)
percent of increaseEnglish
The amount of increase as a percent of the original amount.
Pre-Algebra, Lesson 8.4 (grade 6–8)
The amount of increase as a percent of the original amount.
Pre-Algebra, Lesson 8.4 (grade 6–8)
percent proportionEnglish
The proportion \dfrac{\text{part}}{\text{whole}} = \dfrac{\text{percent}}{100}.
Pre-Algebra, Lesson 8.3 (grade 6–8)
The proportion \dfrac{\text{part}}{\text{whole}} = \dfrac{\text{percent}}{100}.
Pre-Algebra, Lesson 8.3 (grade 6–8)
PercentileEnglish
The percentile of a value is the percent of values in the data set that are less than that value. A value at the 80th percentile is greater than 80% of the data.
Statistics, Lesson 3.1 (grade 11–12)
The percentile of a value is the percent of values in the data set that are less than that value. A value at the 80th percentile is greater than 80% of the data.
Statistics, Lesson 3.1 (grade 11–12)
Percentile of a normal distributionEnglish
The value with the given percent of the distribution below it. The 90th percentile has area 0.90 to its left.
Statistics, Lesson 3.5 (grade 11–12)
The value with the given percent of the distribution below it. The 90th percentile has area 0.90 to its left.
Statistics, Lesson 3.5 (grade 11–12)
Perfect correlationEnglish
r = 1 or r = −1: every point lies exactly on a straight line with positive or negative slope.
Statistics, Lesson 4.2 (grade 11–12)
r = 1 or r = −1: every point lies exactly on a straight line with positive or negative slope.
Statistics, Lesson 4.2 (grade 11–12)
perfect nth powerEnglish
A number or expression that equals something raised to the nth power, such as 27 = 3^3 (a perfect cube) or x^8 = (x^2)^4 (a perfect fourth power).
Algebra II, Lesson 6.2 (grade 10–11)
A number or expression that equals something raised to the nth power, such as 27 = 3^3 (a perfect cube) or x^8 = (x^2)^4 (a perfect fourth power).
Algebra II, Lesson 6.2 (grade 10–11)
perfect squareEnglish
A number that is the square of a whole number (1, 4, 9, 16, 25, ...), or a monomial such as x^6 that is the square of another monomial (x^6 = (x^3)^2).
Algebra I, Lesson 10.1 (grade 8–9) · Algebra I, Lesson 9.4 (grade 8–9) · Pre-Algebra, Lesson 6.4 (grade 6–8)
A number that is the square of a whole number (1, 4, 9, 16, 25, ...), or a monomial such as x^6 that is the square of another monomial (x^6 = (x^3)^2).
Algebra I, Lesson 10.1 (grade 8–9) · Algebra I, Lesson 9.4 (grade 8–9) · Pre-Algebra, Lesson 6.4 (grade 6–8)
perfect-square trinomialEnglish
A trinomial that equals the square of a binomial, such as x^2 + 6x + 9 = (x + 3)^2.
Algebra I, Lesson 11.4 (grade 8–9) · Algebra I, Lesson 8.4 (grade 8–9) · Algebra I, Lesson 9.4 (grade 8–9)
A trinomial that equals the square of a binomial, such as x^2 + 6x + 9 = (x + 3)^2.
Algebra I, Lesson 11.4 (grade 8–9) · Algebra I, Lesson 8.4 (grade 8–9) · Algebra I, Lesson 9.4 (grade 8–9)
PeriodicEnglish
Repeating its values at regular intervals; sine and cosine repeat every 360^\circ (every 2\pi radians).
Algebra II, Lesson 13.2 (grade 10–11)
Repeating its values at regular intervals; sine and cosine repeat every 360^\circ (every 2\pi radians).
Algebra II, Lesson 13.2 (grade 10–11)
periodic functionEnglish
A function f for which some positive number p satisfies f(x + p) = f(x) for every x in its domain.
Trigonometry, Lesson 4.1 (grade 11–12)
A function f for which some positive number p satisfies f(x + p) = f(x) for every x in its domain.
Trigonometry, Lesson 4.1 (grade 11–12)
periodic motionEnglish
Motion that repeats itself exactly after a fixed interval of time, the period.
Trigonometry, Lesson 8.5 (grade 11–12)
Motion that repeats itself exactly after a fixed interval of time, the period.
Trigonometry, Lesson 8.5 (grade 11–12)
periodic rate iEnglish
The interest rate for one period: the annual rate divided by the number of periods per year. At 6% compounded monthly, i = \dfrac{0.06}{12} = 0.005.
Algebra II, Lesson 9.5 (grade 10–11)
The interest rate for one period: the annual rate divided by the number of periods per year. At 6% compounded monthly, i = \dfrac{0.06}{12} = 0.005.
Algebra II, Lesson 9.5 (grade 10–11)
permutationEnglish
An arrangement of objects in which order matters. P(n, r) is the number of ways to choose and arrange r of n different objects.
Algebra II, Lesson 10.1 (grade 10–11) · Algebra II, Lesson 10.2 (grade 10–11) · Playing the Odds, Lesson 1.2 (grade 8–12) · +1 more
An arrangement of objects in which order matters. P(n, r) is the number of ways to choose and arrange r of n different objects.
Algebra II, Lesson 10.1 (grade 10–11) · Algebra II, Lesson 10.2 (grade 10–11) · Playing the Odds, Lesson 1.2 (grade 8–12) · +1 more
perpendicular bisectorEnglish
A line (or ray or segment) that is perpendicular to a segment at its midpoint.
Geometry, Lesson 2.5 (grade 9–10) · Geometry, Lesson 5.1 (grade 9–10)
A line (or ray or segment) that is perpendicular to a segment at its midpoint.
Geometry, Lesson 2.5 (grade 9–10) · Geometry, Lesson 5.1 (grade 9–10)
Perpendicular bisector of a chordEnglish
The line that is perpendicular to the chord at its midpoint.
Geometry, Lesson 10.2 (grade 9–10)
The line that is perpendicular to the chord at its midpoint.
Geometry, Lesson 10.2 (grade 9–10)
perpendicular linesEnglish
Lines that meet at a right angle (90°).
Algebra I, Lesson 5.6 (grade 8–9) · Geometry, Lesson 2.5 (grade 9–10) · Geometry, Lesson 3.4 (grade 9–10)
Lines that meet at a right angle (90°).
Algebra I, Lesson 5.6 (grade 8–9) · Geometry, Lesson 2.5 (grade 9–10) · Geometry, Lesson 3.4 (grade 9–10)
pHEnglish
A measure of acidity: \text{pH} = -\log[\text{H}^+], where [\text{H}^+] is the concentration of hydrogen ions in moles per liter. Lower pH means more acidic; 7 is neutral.
Algebra II, Lesson 8.6 (grade 10–11) · Culinary Arts & Meal Planning, Lesson 5.2 (grade 9–12) · Food Science, Lesson 4.3 (grade 9–12) · +3 more
A measure of acidity: \text{pH} = -\log[\text{H}^+], where [\text{H}^+] is the concentration of hydrogen ions in moles per liter. Lower pH means more acidic; 7 is neutral.
Algebra II, Lesson 8.6 (grade 10–11) · Culinary Arts & Meal Planning, Lesson 5.2 (grade 9–12) · Food Science, Lesson 4.3 (grade 9–12) · +3 more
phase shiftEnglish
The horizontal shift c in y = a\sin(b(x - c)) + d. If c > 0 the graph moves c units right; if c < 0 it moves |c| units left.
Trigonometry, Lesson 4.4 (grade 11–12)
The horizontal shift c in y = a\sin(b(x - c)) + d. If c > 0 the graph moves c units right; if c < 0 it moves |c| units left.
Trigonometry, Lesson 4.4 (grade 11–12)
\pi (pi)English
The ratio of the circumference of any circle to its diameter, \pi = \dfrac{C}{d} \approx 3.14159. It is an irrational number, so its decimal never ends or repeats.
Geometry, Lesson 11.4 (grade 9–10)
The ratio of the circumference of any circle to its diameter, \pi = \dfrac{C}{d} \approx 3.14159. It is an irrational number, so its decimal never ends or repeats.
Geometry, Lesson 11.4 (grade 9–10)
pi (\pi)English
The number you get when you divide any circle's circumference by its diameter. It is about 3.14, but its decimal never ends and never repeats.
Pre-Algebra, Lesson 12.4 (grade 6–8)
The number you get when you divide any circle's circumference by its diameter. It is about 3.14, but its decimal never ends and never repeats.
Pre-Algebra, Lesson 12.4 (grade 6–8)
PictographEnglish
A graph that uses pictures (jars, baskets, people) instead of bars to show amounts.
Statistics, Lesson 1.2 (grade 11–12)
A graph that uses pictures (jars, baskets, people) instead of bars to show amounts.
Statistics, Lesson 1.2 (grade 11–12)
Pie chartEnglish
A circle divided into slices, one per category, whose sizes show each category's share of one whole.
Statistics, Lesson 1.2 (grade 11–12)
A circle divided into slices, one per category, whose sizes show each category's share of one whole.
Statistics, Lesson 1.2 (grade 11–12)
piecewise functionEnglish
A function defined by different formulas on different parts of its domain.
Algebra II, Lesson 1.3 (grade 10–11)
A function defined by different formulas on different parts of its domain.
Algebra II, Lesson 1.3 (grade 10–11)
PitchEnglish
The steepness of a roof given as rise over run, such as 6 in 12 (6 inches up for each 12 inches across); it is the tangent of the roof's angle.
Algebra II, Lesson 13.1 (grade 10–11) · Entrepreneurship & Sales, Lesson 10.5 (grade 9–12) · Grade 5 Business & Finance, Lesson 6.4 (grade 5) · +3 more
The steepness of a roof given as rise over run, such as 6 in 12 (6 inches up for each 12 inches across); it is the tangent of the roof's angle.
Algebra II, Lesson 13.1 (grade 10–11) · Entrepreneurship & Sales, Lesson 10.5 (grade 9–12) · Grade 5 Business & Finance, Lesson 6.4 (grade 5) · +3 more
placeboEnglish
A dummy treatment that looks like the real one but has no active ingredient. The improvement people often feel from any treatment at all is called the placebo effect.
Statistics, Lesson 5.5 (grade 11–12)
A dummy treatment that looks like the real one but has no active ingredient. The improvement people often feel from any treatment at all is called the placebo effect.
Statistics, Lesson 5.5 (grade 11–12)
placeholderEnglish
A term with coefficient 0, such as 0x^2, written in for a missing power so that the columns line up.
Algebra II, Lesson 4.3 (grade 10–11) · Grade 12 Composition & Creative Writing: Capstone: Rhetoric and the Senior Thesis, Lesson 2.2 (grade 12)
A term with coefficient 0, such as 0x^2, written in for a missing power so that the columns line up.
Algebra II, Lesson 4.3 (grade 10–11) · Grade 12 Composition & Creative Writing: Capstone: Rhetoric and the Senior Thesis, Lesson 2.2 (grade 12)
placeholder zeroEnglish
A zero written at the end of a decimal to fill an empty place, such as writing 3.5 as 3.50. It does not change the value.
Pre-Algebra, Lesson 4.2 (grade 6–8)
A zero written at the end of a decimal to fill an empty place, such as writing 3.5 as 3.50. It does not change the value.
Pre-Algebra, Lesson 4.2 (grade 6–8)
planeEnglish
A flat surface that extends forever in every direction, like an endless sheet of paper or the floor of a room continued without end.
Algebra II, Lesson 2.4 (grade 10–11) · Grade 6 Art, Lesson 2.3 (grade 6) · Grade 7 Art, Lesson 2.3 (grade 7) · +1 more
A flat surface that extends forever in every direction, like an endless sheet of paper or the floor of a room continued without end.
Algebra II, Lesson 2.4 (grade 10–11) · Grade 6 Art, Lesson 2.3 (grade 6) · Grade 7 Art, Lesson 2.3 (grade 7) · +1 more
planning value of \sigmaEnglish
A reasonable value for the population standard deviation, from past records or a small pilot study, used to choose a sample size for estimating a mean.
Statistics, Lesson 10.5 (grade 11–12)
A reasonable value for the population standard deviation, from past records or a small pilot study, used to choose a sample size for estimating a mean.
Statistics, Lesson 10.5 (grade 11–12)
planning value p^*English
A guess at the population proportion used only to choose a sample size; use p^* = 0.5 when you have no good guess.
Statistics, Lesson 10.5 (grade 11–12)
A guess at the population proportion used only to choose a sample size; use p^* = 0.5 when you have no good guess.
Statistics, Lesson 10.5 (grade 11–12)
Platonic solid (regular polyhedron)English
A convex polyhedron whose faces are all congruent regular polygons, with the same number of faces meeting at every vertex.
Geometry, Lesson 12.1 (grade 9–10)
A convex polyhedron whose faces are all congruent regular polygons, with the same number of faces meeting at every vertex.
Geometry, Lesson 12.1 (grade 9–10)
plausible valueEnglish
A value of the parameter that lies inside the confidence interval and so is consistent with the data at that confidence level.
Statistics, Lesson 10.4 (grade 11–12)
A value of the parameter that lies inside the confidence interval and so is consistent with the data at that confidence level.
Statistics, Lesson 10.4 (grade 11–12)
Playfair's AxiomEnglish
Through a point not on a given line there is exactly one line parallel to the given line.
Geometry, Lesson 3.2 (grade 9–10)
Through a point not on a given line there is exactly one line parallel to the given line.
Geometry, Lesson 3.2 (grade 9–10)
plus-or-minus (\pm)English
A short way to write two numbers at once: \pm 5 means 5 or -5.
Algebra I, Lesson 11.3 (grade 8–9)
A short way to write two numbers at once: \pm 5 means 5 or -5.
Algebra I, Lesson 11.3 (grade 8–9)
point estimateEnglish
A single statistic used as our best guess for a parameter, such as \bar{x} for \mu or \hat{p} for p.
Statistics, Lesson 10.1 (grade 11–12)
A single statistic used as our best guess for a parameter, such as \bar{x} for \mu or \hat{p} for p.
Statistics, Lesson 10.1 (grade 11–12)
point of intersectionEnglish
The point where two graphs cross or meet.
Algebra I, Lesson 6.1 (grade 8–9)
The point where two graphs cross or meet.
Algebra I, Lesson 6.1 (grade 8–9)
Point of tangencyEnglish
The single point where a tangent line meets a circle.
Geometry, Lesson 10.3 (grade 9–10)
The single point where a tangent line meets a circle.
Geometry, Lesson 10.3 (grade 9–10)
point-slope formEnglish
The form y - y_1 = m(x - x_1) of a linear equation, where m is the slope and (x_1, y_1) is a known point on the line.
Algebra I, Lesson 5.4 (grade 8–9) · Geometry, Lesson 3.5 (grade 9–10)
The form y - y_1 = m(x - x_1) of a linear equation, where m is the slope and (x_1, y_1) is a known point on the line.
Algebra I, Lesson 5.4 (grade 8–9) · Geometry, Lesson 3.5 (grade 9–10)
polar axisEnglish
A fixed ray starting at the pole, usually drawn pointing to the right (along the positive x-axis), from which angles are measured.
Trigonometry, Lesson 9.1 (grade 11–12)
A fixed ray starting at the pole, usually drawn pointing to the right (along the positive x-axis), from which angles are measured.
Trigonometry, Lesson 9.1 (grade 11–12)
polar coordinatesEnglish
A pair (r, \theta) locating a point by its directed distance r from the pole and the angle \theta measured from the polar axis, counterclockwise when positive.
Trigonometry, Lesson 9.1 (grade 11–12)
A pair (r, \theta) locating a point by its directed distance r from the pole and the angle \theta measured from the polar axis, counterclockwise when positive.
Trigonometry, Lesson 9.1 (grade 11–12)
polar equationEnglish
An equation in r and \theta whose graph is the set of all points having at least one polar name that satisfies it.
Trigonometry, Lesson 9.2 (grade 11–12)
An equation in r and \theta whose graph is the set of all points having at least one polar name that satisfies it.
Trigonometry, Lesson 9.2 (grade 11–12)
polygonEnglish
A closed plane figure made of three or more segments (its sides), each side meeting exactly two other sides, one at each endpoint (its vertices), so that sides meet only at their endpoints and no two sides with a common endpoint are collinear. A polygon with n sides is an n-gon; it is named by listing its vertices in order.
Geometry, Lesson 6.1 (grade 9–10) · Pre-Algebra, Lesson 12.2 (grade 6–8)
A closed plane figure made of three or more segments (its sides), each side meeting exactly two other sides, one at each endpoint (its vertices), so that sides meet only at their endpoints and no two sides with a common endpoint are collinear. A polygon with n sides is an n-gon; it is named by listing its vertices in order.
Geometry, Lesson 6.1 (grade 9–10) · Pre-Algebra, Lesson 12.2 (grade 6–8)
polyhedronEnglish
A closed solid whose surface is made entirely of polygons. The polygons are its faces; a segment where two faces meet is an edge; a point where three or more edges meet is a vertex (plural: vertices).
Geometry, Lesson 12.1 (grade 9–10)
A closed solid whose surface is made entirely of polygons. The polygons are its faces; a segment where two faces meet is an edge; a point where three or more edges meet is a vertex (plural: vertices).
Geometry, Lesson 12.1 (grade 9–10)
polynomialEnglish
A monomial or a sum of monomials, such as 5x^3 - 2x + 1. Each monomial is a term of the polynomial.
Algebra I, Lesson 8.1 (grade 8–9)
A monomial or a sum of monomials, such as 5x^3 - 2x + 1. Each monomial is a term of the polynomial.
Algebra I, Lesson 8.1 (grade 8–9)
polynomial functionEnglish
A function that is a sum of terms of the form a x^k, where each coefficient a is a real number and each exponent k is a whole number (0, 1, 2, ...).
Algebra II, Lesson 4.1 (grade 10–11)
A function that is a sum of terms of the form a x^k, where each coefficient a is a real number and each exponent k is a whole number (0, 1, 2, ...).
Algebra II, Lesson 4.1 (grade 10–11)
polynomial inequalityEnglish
An inequality such as f(x) > 0 or f(x) \le 0 where f is a polynomial; its solution is the set of x where the graph is above (or below) the x-axis.
Algebra II, Lesson 4.7 (grade 10–11)
An inequality such as f(x) > 0 or f(x) \le 0 where f is a polynomial; its solution is the set of x where the graph is above (or below) the x-axis.
Algebra II, Lesson 4.7 (grade 10–11)
Pooled (combined) proportionEnglish
\hat{p}_c = \dfrac{X_1 + X_2}{n_1 + n_2}: all the successes in both samples divided by all the individuals in both samples. It estimates the common proportion when H_0: p_1 = p_2 is true.
Statistics, Lesson 12.1 (grade 11–12)
\hat{p}_c = \dfrac{X_1 + X_2}{n_1 + n_2}: all the successes in both samples divided by all the individuals in both samples. It estimates the common proportion when H_0: p_1 = p_2 is true.
Statistics, Lesson 12.1 (grade 11–12)
Population and sampleEnglish
The population is the entire group we want to learn about. A sample is the part of the population we actually collect data from.
Statistics, Lesson 1.1 (grade 11–12)
The population is the entire group we want to learn about. A sample is the part of the population we actually collect data from.
Statistics, Lesson 1.1 (grade 11–12)
Population standard deviation \sigmaEnglish
The standard deviation of a whole population, written \sigma (sigma); its variance divides by n instead of n − 1, and the mean is written \mu (mu).
Statistics, Lesson 2.4 (grade 11–12)
The standard deviation of a whole population, written \sigma (sigma); its variance divides by n instead of n − 1, and the mean is written \mu (mu).
Statistics, Lesson 2.4 (grade 11–12)
Positive associationEnglish
Larger values of one variable tend to go with larger values of the other, so the points slope uphill from left to right.
Statistics, Lesson 4.1 (grade 11–12)
Larger values of one variable tend to go with larger values of the other, so the points slope uphill from left to right.
Statistics, Lesson 4.1 (grade 11–12)
positive numberEnglish
A number greater than zero, like 5. It sits to the right of 0 on the number line. Zero itself is neither positive nor negative.
Pre-Algebra, Lesson 5.1 (grade 6–8)
A number greater than zero, like 5. It sits to the right of 0 on the number line. Zero itself is neither positive nor negative.
Pre-Algebra, Lesson 5.1 (grade 6–8)
postulate (axiom)English
A statement accepted as true without proof and used as a starting point for reasoning.
Geometry, Lesson 1.1 (grade 9–10)
A statement accepted as true without proof and used as a starting point for reasoning.
Geometry, Lesson 1.1 (grade 9–10)
powerEnglish
An expression such as a^n that means the base a is used as a factor n times.
Algebra I, Lesson 7.1 (grade 8–9) · Food Science, Lesson 2.2 (grade 9–12) · Architecture & Civil Engineering, Lesson 7.2 (grade 9–12) · +3 more
An expression such as a^n that means the base a is used as a factor n times.
Algebra I, Lesson 7.1 (grade 8–9) · Food Science, Lesson 2.2 (grade 9–12) · Architecture & Civil Engineering, Lesson 7.2 (grade 9–12) · +3 more
power of 10English
A number such as 10, 100 or 1000; multiplying by it moves the decimal point to the right 1, 2 or 3 places.
Algebra I, Lesson 2.4 (grade 8–9) · Algebra I, Lesson 7.3 (grade 8–9) · Pre-Algebra, Lesson 4.3 (grade 6–8) · +1 more
A number such as 10, 100 or 1000; multiplying by it moves the decimal point to the right 1, 2 or 3 places.
Algebra I, Lesson 2.4 (grade 8–9) · Algebra I, Lesson 7.3 (grade 8–9) · Pre-Algebra, Lesson 4.3 (grade 6–8) · +1 more
power-of-a-power ruleEnglish
When you raise a power to another power, keep the base and multiply the exponents: (3^2)^4 = 3^8.
Pre-Algebra, Lesson 6.2 (grade 6–8)
When you raise a power to another power, keep the base and multiply the exponents: (3^2)^4 = 3^8.
Pre-Algebra, Lesson 6.2 (grade 6–8)
power-reducing formulasEnglish
The formulas \sin^2 x = \dfrac{1 - \cos 2x}{2} and \cos^2 x = \dfrac{1 + \cos 2x}{2}, which replace a square by a first power of cosine.
Trigonometry, Lesson 5.5 (grade 11–12)
The formulas \sin^2 x = \dfrac{1 - \cos 2x}{2} and \cos^2 x = \dfrac{1 + \cos 2x}{2}, which replace a square by a first power of cosine.
Trigonometry, Lesson 5.5 (grade 11–12)
practical importanceEnglish
Whether an effect is large enough to matter in the real situation. A statistically significant effect can be too small to matter.
Statistics, Lesson 11.5 (grade 11–12) · Statistics, Lesson 13.3 (grade 11–12)
Whether an effect is large enough to matter in the real situation. A statistically significant effect can be too small to matter.
Statistics, Lesson 11.5 (grade 11–12) · Statistics, Lesson 13.3 (grade 11–12)
Predicted value (\hat{y})English
The value of y that the line gives for a particular x. Read \hat{y} as "y-hat"; the hat means "predicted."
Statistics, Lesson 4.3 (grade 11–12)
The value of y that the line gives for a particular x. Read \hat{y} as "y-hat"; the hat means "predicted."
Statistics, Lesson 4.3 (grade 11–12)
predictionEnglish
An output value found by substituting an input into a model, often for an input not in the data.
Algebra I, Lesson 5.7 (grade 8–9) · Geopolitics: The Great Ideas, Lesson 1.5 (grade 9–12)
An output value found by substituting an input into a model, often for an input not in the data.
Algebra I, Lesson 5.7 (grade 8–9) · Geopolitics: The Great Ideas, Lesson 1.5 (grade 9–12)
preimage and imageEnglish
The preimage is the original point or figure; the image is the point or figure it is sent to. The image of A is written A' (read "A prime").
Geometry, Lesson 7.1 (grade 9–10)
The preimage is the original point or figure; the image is the point or figure it is sent to. The image of A is written A' (read "A prime").
Geometry, Lesson 7.1 (grade 9–10)
prime factorizationEnglish
A number written as a product of prime numbers only. The prime factorization of 12 is 2 \times 2 \times 3.
Pre-Algebra, Lesson 2.3 (grade 6–8)
A number written as a product of prime numbers only. The prime factorization of 12 is 2 \times 2 \times 3.
Pre-Algebra, Lesson 2.3 (grade 6–8)
prime numberEnglish
A whole number greater than 1 whose only factors are 1 and itself. Examples: 2, 3, 5, 7, 11.
Pre-Algebra, Lesson 2.2 (grade 6–8)
A whole number greater than 1 whose only factors are 1 and itself. Examples: 2, 3, 5, 7, 11.
Pre-Algebra, Lesson 2.2 (grade 6–8)
prime polynomialEnglish
A polynomial (other than a single number) that cannot be written as a product of polynomials of lower degree with integer coefficients, such as x^2 + 4x + 6.
Algebra I, Lesson 9.2 (grade 8–9)
A polynomial (other than a single number) that cannot be written as a product of polynomials of lower degree with integer coefficients, such as x^2 + 4x + 6.
Algebra I, Lesson 9.2 (grade 8–9)
principalEnglish
The amount of money first deposited or borrowed, P.
Algebra II, Lesson 7.2 (grade 10–11) · Algebra II, Lesson 9.5 (grade 10–11) · Accounting, Lesson 7.3 (grade 9–12) · +3 more
The amount of money first deposited or borrowed, P.
Algebra II, Lesson 7.2 (grade 10–11) · Algebra II, Lesson 9.5 (grade 10–11) · Accounting, Lesson 7.3 (grade 9–12) · +3 more
principal rangeEnglish
The restricted set of angles an inverse function returns: \left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right] for arcsine, [0, \pi] for arccosine and \left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right) for arctangent.
Trigonometry, Lesson 6.3 (grade 11–12)
The restricted set of angles an inverse function returns: \left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right] for arcsine, [0, \pi] for arccosine and \left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right) for arctangent.
Trigonometry, Lesson 6.3 (grade 11–12)
principal rootEnglish
The root that the radical sign stands for: for an even index, the nonnegative root (so \sqrt[4]{16} = 2, not -2); for an odd index, the one real root.
Algebra II, Lesson 6.1 (grade 10–11)
The root that the radical sign stands for: for an even index, the nonnegative root (so \sqrt[4]{16} = 2, not -2); for an odd index, the one real root.
Algebra II, Lesson 6.1 (grade 10–11)
principal square rootEnglish
The nonnegative square root of a number. Both 5 and -5 square to 25, but \sqrt{25} means only the principal root, 5.
Algebra I, Lesson 10.1 (grade 8–9) · Pre-Algebra, Lesson 6.4 (grade 6–8)
The nonnegative square root of a number. Both 5 and -5 square to 25, but \sqrt{25} means only the principal root, 5.
Algebra I, Lesson 10.1 (grade 8–9) · Pre-Algebra, Lesson 6.4 (grade 6–8)
principal valueEnglish
The single value an inverse trigonometric function returns, chosen from its restricted range.
Trigonometry, Lesson 6.1 (grade 11–12)
The single value an inverse trigonometric function returns, chosen from its restricted range.
Trigonometry, Lesson 6.1 (grade 11–12)
probability (equally likely outcomes)English
When all outcomes are equally likely, P(E) is the number of outcomes in the event E divided by the number of outcomes in the sample space; it is always between 0 and 1.
Algebra II, Lesson 10.4 (grade 10–11)
When all outcomes are equally likely, P(E) is the number of outcomes in the event E divided by the number of outcomes in the sample space; it is always between 0 and 1.
Algebra II, Lesson 10.4 (grade 10–11)
Probability histogramEnglish
A graph of a discrete probability distribution with a bar for each value whose height is the probability of that value.
Statistics, Lesson 7.1 (grade 11–12)
A graph of a discrete probability distribution with a bar for each value whose height is the probability of that value.
Statistics, Lesson 7.1 (grade 11–12)
probability modelEnglish
A description of a chance process that lists the sample space and gives a probability for each outcome.
Statistics, Lesson 6.2 (grade 11–12)
A description of a chance process that lists the sample space and gives a probability for each outcome.
Statistics, Lesson 6.2 (grade 11–12)
productEnglish
The result of multiplying. The product of two polynomials is found by multiplying every term of one by every term of the other and combining like terms.
Algebra I, Lesson 8.3 (grade 8–9) · Grade 1 Business & Finance, Lesson 6.1 (grade 1) · Grade 2 Business & Finance, Lesson 6.1 (grade 2) · +3 more
The result of multiplying. The product of two polynomials is found by multiplying every term of one by every term of the other and combining like terms.
Algebra I, Lesson 8.3 (grade 8–9) · Grade 1 Business & Finance, Lesson 6.1 (grade 1) · Grade 2 Business & Finance, Lesson 6.1 (grade 2) · +3 more
product of powers ruleEnglish
When you multiply powers with the same base, add the exponents: x^m \cdot x^n = x^{m + n} (from Lesson 7.1).
Algebra I, Lesson 8.2 (grade 8–9)
When you multiply powers with the same base, add the exponents: x^m \cdot x^n = x^{m + n} (from Lesson 7.1).
Algebra I, Lesson 8.2 (grade 8–9)
product property of radicalsEnglish
\sqrt[n]{ab} = \sqrt[n]{a} \cdot \sqrt[n]{b} when both roots are real: the root of a product is the product of the roots.
Algebra II, Lesson 6.2 (grade 10–11)
\sqrt[n]{ab} = \sqrt[n]{a} \cdot \sqrt[n]{b} when both roots are real: the root of a product is the product of the roots.
Algebra II, Lesson 6.2 (grade 10–11)
product ruleEnglish
When you multiply powers with the same base, keep the base and add the exponents: 2^3 \times 2^4 = 2^7.
Pre-Algebra, Lesson 6.2 (grade 6–8)
When you multiply powers with the same base, keep the base and add the exponents: 2^3 \times 2^4 = 2^7.
Pre-Algebra, Lesson 6.2 (grade 6–8)
projectileEnglish
An object that is thrown, kicked, hit or launched and then moves only under gravity (ignoring air resistance).
Algebra II, Lesson 3.6 (grade 10–11) · Physics, Lesson 2.5 (grade 11–12) · Body Mechanics of Sport, Lesson 2.4 (grade 8–12)
An object that is thrown, kicked, hit or launched and then moves only under gravity (ignoring air resistance).
Algebra II, Lesson 3.6 (grade 10–11) · Physics, Lesson 2.5 (grade 11–12) · Body Mechanics of Sport, Lesson 2.4 (grade 8–12)
proof of an identityEnglish
A chain of equalities, each justified by algebra or a known identity, that begins with one side of the equation and ends with the other.
Trigonometry, Lesson 5.3 (grade 11–12)
A chain of equalities, each justified by algebra or a known identity, that begins with one side of the equation and ends with the other.
Trigonometry, Lesson 5.3 (grade 11–12)
proper fractionEnglish
A fraction whose numerator is smaller than its denominator, like \dfrac{3}{5}. It is less than 1.
Pre-Algebra, Lesson 3.4 (grade 6–8)
A fraction whose numerator is smaller than its denominator, like \dfrac{3}{5}. It is less than 1.
Pre-Algebra, Lesson 3.4 (grade 6–8)
properties of equalityEnglish
The rules that say you may add, subtract, multiply or divide both sides of an equation by the same number (never dividing by 0) and the two sides stay equal.
Algebra I, Lesson 2.1 (grade 8–9) · Geometry, Lesson 1.5 (grade 9–10)
The rules that say you may add, subtract, multiply or divide both sides of an equation by the same number (never dividing by 0) and the two sides stay equal.
Algebra I, Lesson 2.1 (grade 8–9) · Geometry, Lesson 1.5 (grade 9–10)
proportionEnglish
An equation stating that two ratios are equal, such as \dfrac{x + 2}{5} = \dfrac{x - 1}{2}.
Algebra I, Lesson 12.5 (grade 8–9) · Algebra II, Lesson 5.5 (grade 10–11) · Grade 2 Art, Lesson 8.1 (grade 2) · +3 more
An equation stating that two ratios are equal, such as \dfrac{x + 2}{5} = \dfrac{x - 1}{2}.
Algebra I, Lesson 12.5 (grade 8–9) · Algebra II, Lesson 5.5 (grade 10–11) · Grade 2 Art, Lesson 8.1 (grade 2) · +3 more
proportionalEnglish
Two quantities are proportional when one is always the same multiple of the other; here, arc length and sector area are each proportional to the central angle.
Trigonometry, Lesson 3.4 (grade 11–12)
Two quantities are proportional when one is always the same multiple of the other; here, arc length and sector area are each proportional to the central angle.
Trigonometry, Lesson 3.4 (grade 11–12)
prove statementEnglish
The conclusion the proof must reach; usually the conclusion of the conditional. It is the last statement of the proof.
Geometry, Lesson 2.6 (grade 9–10)
The conclusion the proof must reach; usually the conclusion of the conditional. It is the last statement of the proof.
Geometry, Lesson 2.6 (grade 9–10)
Ptolemy's theoremEnglish
In a quadrilateral inscribed in a circle, the product of the diagonals equals the sum of the products of the two pairs of opposite sides.
Trigonometry, Lesson 5.4 (grade 11–12)
In a quadrilateral inscribed in a circle, the product of the diagonals equals the sum of the products of the two pairs of opposite sides.
Trigonometry, Lesson 5.4 (grade 11–12)
pure imaginary numberEnglish
A complex number bi with real part 0 and b \ne 0, such as 5i.
Algebra II, Lesson 3.3 (grade 10–11)
A complex number bi with real part 0 and b \ne 0, such as 5i.
Algebra II, Lesson 3.3 (grade 10–11)
P-valueEnglish
The probability, computed assuming H_0 is true, of getting a result at least as extreme as the one actually observed (extreme in the direction of H_a).
Statistics, Lesson 11.1 (grade 11–12)
The probability, computed assuming H_0 is true, of getting a result at least as extreme as the one actually observed (extreme in the direction of H_a).
Statistics, Lesson 11.1 (grade 11–12)
Pythagorean identitiesEnglish
The three identities \sin^2\theta + \cos^2\theta = 1, 1 + \tan^2\theta = \sec^2\theta and 1 + \cot^2\theta = \csc^2\theta.
Trigonometry, Lesson 5.2 (grade 11–12)
The three identities \sin^2\theta + \cos^2\theta = 1, 1 + \tan^2\theta = \sec^2\theta and 1 + \cot^2\theta = \csc^2\theta.
Trigonometry, Lesson 5.2 (grade 11–12)
Pythagorean identityEnglish
The equation \sin^2\theta + \cos^2\theta = 1, true for every acute angle \theta (Lesson 13.2 extends it to all angles); \sin^2\theta means (\sin\theta)^2.
Algebra II, Lesson 13.1 (grade 10–11)
The equation \sin^2\theta + \cos^2\theta = 1, true for every acute angle \theta (Lesson 13.2 extends it to all angles); \sin^2\theta means (\sin\theta)^2.
Algebra II, Lesson 13.1 (grade 10–11)
Pythagorean theoremEnglish
In a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 9.1 (grade 9–10) · Pre-Algebra, Lesson 12.6 (grade 6–8)
In a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 9.1 (grade 9–10) · Pre-Algebra, Lesson 12.6 (grade 6–8)
Pythagorean tripleEnglish
Three whole numbers that fit a^2 + b^2 = c^2, such as 3, 4, 5 or 5, 12, 13.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 9.2 (grade 9–10) · Pre-Algebra, Lesson 12.6 (grade 6–8)
Three whole numbers that fit a^2 + b^2 = c^2, such as 3, 4, 5 or 5, 12, 13.
Algebra I, Lesson 10.5 (grade 8–9) · Geometry, Lesson 9.2 (grade 9–10) · Pre-Algebra, Lesson 12.6 (grade 6–8)
Q
quadrantEnglish
One of the four regions the axes cut the plane into, numbered I, II, III, IV counterclockwise starting at the upper right.
Algebra I, Lesson 4.1 (grade 8–9) · Grade 4 Geography: The United States: Regions, Rivers and Routes, Lesson 1.2 (grade 4) · Grade 5 Geography: Explorers, Navigators and Missionaries, Lesson 2.1 (grade 5) · +1 more
One of the four regions the axes cut the plane into, numbered I, II, III, IV counterclockwise starting at the upper right.
Algebra I, Lesson 4.1 (grade 8–9) · Grade 4 Geography: The United States: Regions, Rivers and Routes, Lesson 1.2 (grade 4) · Grade 5 Geography: Explorers, Navigators and Missionaries, Lesson 2.1 (grade 5) · +1 more
quadrant signEnglish
Whether a trigonometric value is positive or negative, decided by the quadrant of the terminal side (Lesson 3.7). A square root gives only a size; the quadrant gives the sign.
Trigonometry, Lesson 5.2 (grade 11–12)
Whether a trigonometric value is positive or negative, decided by the quadrant of the terminal side (Lesson 3.7). A square root gives only a size; the quadrant gives the sign.
Trigonometry, Lesson 5.2 (grade 11–12)
quadrantal angleEnglish
An angle in standard position whose terminal side lies on an axis, such as 0^\circ, 90^\circ, 180^\circ or 270^\circ.
Trigonometry, Lesson 3.1 (grade 11–12) · Trigonometry, Lesson 3.8 (grade 11–12)
An angle in standard position whose terminal side lies on an axis, such as 0^\circ, 90^\circ, 180^\circ or 270^\circ.
Trigonometry, Lesson 3.1 (grade 11–12) · Trigonometry, Lesson 3.8 (grade 11–12)
quadratic equationEnglish
An equation that can be written as ax^2 + bx + c = 0 with a \ne 0.
Algebra I, Lesson 11.3 (grade 8–9) · Algebra I, Lesson 9.6 (grade 8–9) · Algebra II, Lesson 3.2 (grade 10–11)
An equation that can be written as ax^2 + bx + c = 0 with a \ne 0.
Algebra I, Lesson 11.3 (grade 8–9) · Algebra I, Lesson 9.6 (grade 8–9) · Algebra II, Lesson 3.2 (grade 10–11)
quadratic formEnglish
A polynomial that looks like au^2 + bu + c when some expression such as u = x^2 is used as the variable, for example x^4 - 13x^2 + 36.
Algebra II, Lesson 4.5 (grade 10–11) · Algebra II, Lesson 8.4 (grade 10–11)
A polynomial that looks like au^2 + bu + c when some expression such as u = x^2 is used as the variable, for example x^4 - 13x^2 + 36.
Algebra II, Lesson 4.5 (grade 10–11) · Algebra II, Lesson 8.4 (grade 10–11)
quadratic formulaEnglish
x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}, which gives the solutions of every quadratic equation ax^2 + bx + c = 0.
Algebra I, Lesson 11.5 (grade 8–9)
x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}, which gives the solutions of every quadratic equation ax^2 + bx + c = 0.
Algebra I, Lesson 11.5 (grade 8–9)
quadratic functionEnglish
A function that can be written as y = ax^2 + bx + c with a \ne 0; the highest power of x is 2.
Algebra I, Lesson 11.1 (grade 8–9) · Algebra II, Lesson 3.1 (grade 10–11)
A function that can be written as y = ax^2 + bx + c with a \ne 0; the highest power of x is 2.
Algebra I, Lesson 11.1 (grade 8–9) · Algebra II, Lesson 3.1 (grade 10–11)
quadratic inequalityEnglish
An inequality that can be written ax^2 + bx + c > 0 (or with <, \le, \ge), with a \ne 0.
Algebra II, Lesson 3.5 (grade 10–11)
An inequality that can be written ax^2 + bx + c > 0 (or with <, \le, \ge), with a \ne 0.
Algebra II, Lesson 3.5 (grade 10–11)
quadratic modelEnglish
A quadratic function used to describe a real situation, such as the height of a ball over time.
Algebra I, Lesson 11.7 (grade 8–9) · Algebra II, Lesson 3.6 (grade 10–11)
A quadratic function used to describe a real situation, such as the height of a ball over time.
Algebra I, Lesson 11.7 (grade 8–9) · Algebra II, Lesson 3.6 (grade 10–11)
quadratic trinomialEnglish
A trinomial of degree 2. In this lesson the leading coefficient is 1, so it looks like x^2 + bx + c.
Algebra I, Lesson 9.2 (grade 8–9)
A trinomial of degree 2. In this lesson the leading coefficient is 1, so it looks like x^2 + bx + c.
Algebra I, Lesson 9.2 (grade 8–9)
quadratic-type equationEnglish
An equation such as 2\sin^2 x - \sin x - 1 = 0 that is a quadratic in one trigonometric function.
Trigonometry, Lesson 6.5 (grade 11–12)
An equation such as 2\sin^2 x - \sin x - 1 = 0 that is a quadratic in one trigonometric function.
Trigonometry, Lesson 6.5 (grade 11–12)
Quantitative variableEnglish
A variable whose values are numbers that measure or count something, so that adding or averaging them makes sense. It is discrete if it counts (0, 1, 2, ...) and continuous if it measures and could take any value in a range (weight, time, rainfall).
Statistics, Lesson 1.1 (grade 11–12)
A variable whose values are numbers that measure or count something, so that adding or averaging them makes sense. It is discrete if it counts (0, 1, 2, ...) and continuous if it measures and could take any value in a range (weight, time, rainfall).
Statistics, Lesson 1.1 (grade 11–12)
quarter-periodEnglish
The horizontal distance from a maximum or minimum to the next midline crossing; one fourth of the period.
Trigonometry, Lesson 4.5 (grade 11–12)
The horizontal distance from a maximum or minimum to the next midline crossing; one fourth of the period.
Trigonometry, Lesson 4.5 (grade 11–12)
quotientEnglish
The result of the division, q(x), built one term at a time.
Algebra II, Lesson 4.3 (grade 10–11) · Pre-Algebra, Lesson 2.5 (grade 6–8) · Pre-Algebra, Lesson 3.6 (grade 6–8) · +3 more
The result of the division, q(x), built one term at a time.
Algebra II, Lesson 4.3 (grade 10–11) · Pre-Algebra, Lesson 2.5 (grade 6–8) · Pre-Algebra, Lesson 3.6 (grade 6–8) · +3 more
quotient identitiesEnglish
The identities \tan\theta = \dfrac{\sin\theta}{\cos\theta} and \cot\theta = \dfrac{\cos\theta}{\sin\theta}.
Trigonometry, Lesson 5.1 (grade 11–12)
The identities \tan\theta = \dfrac{\sin\theta}{\cos\theta} and \cot\theta = \dfrac{\cos\theta}{\sin\theta}.
Trigonometry, Lesson 5.1 (grade 11–12)
quotient of powers ruleEnglish
When you divide powers with the same base, subtract the exponents: \dfrac{x^m}{x^n} = x^{m - n} for x \ne 0 (from Lessons 7.1 and 7.2).
Algebra I, Lesson 8.5 (grade 8–9)
When you divide powers with the same base, subtract the exponents: \dfrac{x^m}{x^n} = x^{m - n} for x \ne 0 (from Lessons 7.1 and 7.2).
Algebra I, Lesson 8.5 (grade 8–9)
quotient property of radicalsEnglish
\sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}} when both roots are real and b \ne 0.
Algebra II, Lesson 6.2 (grade 10–11)
\sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}} when both roots are real and b \ne 0.
Algebra II, Lesson 6.2 (grade 10–11)
quotient property of square rootsEnglish
For a \ge 0 and b > 0, the square root of a fraction equals the square root of the top over the square root of the bottom: \sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b}}.
Algebra I, Lesson 10.2 (grade 8–9)
For a \ge 0 and b > 0, the square root of a fraction equals the square root of the top over the square root of the bottom: \sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b}}.
Algebra I, Lesson 10.2 (grade 8–9)
quotient ruleEnglish
When you divide powers with the same base, keep the base and subtract the exponents: 5^6 \div 5^2 = 5^4.
Pre-Algebra, Lesson 6.2 (grade 6–8)
When you divide powers with the same base, keep the base and subtract the exponents: 5^6 \div 5^2 = 5^4.
Pre-Algebra, Lesson 6.2 (grade 6–8)
R
RadianEnglish
The measure of a central angle whose arc is exactly as long as the circle's radius; \pi radians = 180^\circ, so 1 radian is about 57.3^\circ.
Algebra II, Lesson 13.2 (grade 10–11) · Body Mechanics of Sport, Lesson 1.4 (grade 8–12) · Geometry, Lesson 11.4 (grade 9–10) · +1 more
The measure of a central angle whose arc is exactly as long as the circle's radius; \pi radians = 180^\circ, so 1 radian is about 57.3^\circ.
Algebra II, Lesson 13.2 (grade 10–11) · Body Mechanics of Sport, Lesson 1.4 (grade 8–12) · Geometry, Lesson 11.4 (grade 9–10) · +1 more
radian measureEnglish
The ratio \theta = \dfrac{s}{r} of the arc length s to the radius r; it is a pure number with no units of length.
Trigonometry, Lesson 3.2 (grade 11–12)
The ratio \theta = \dfrac{s}{r} of the arc length s to the radius r; it is a pure number with no units of length.
Trigonometry, Lesson 3.2 (grade 11–12)
radicalEnglish
An expression with a root symbol, such as \sqrt{50} or \sqrt[3]{8}. The symbol \sqrt{\phantom{x}} itself is called the radical sign.
Algebra I, Lesson 10.1 (grade 8–9)
An expression with a root symbol, such as \sqrt{50} or \sqrt[3]{8}. The symbol \sqrt{\phantom{x}} itself is called the radical sign.
Algebra I, Lesson 10.1 (grade 8–9)
radical equationEnglish
An equation with the variable inside a radical, such as \sqrt{x + 4} = 6.
Algebra I, Lesson 10.4 (grade 8–9) · Algebra II, Lesson 6.5 (grade 10–11)
An equation with the variable inside a radical, such as \sqrt{x + 4} = 6.
Algebra I, Lesson 10.4 (grade 8–9) · Algebra II, Lesson 6.5 (grade 10–11)
radical functionEnglish
A function whose rule contains the variable under a radical, such as f(x) = 2\sqrt{x - 1} or g(x) = \sqrt[3]{x + 4}.
Algebra II, Lesson 6.4 (grade 10–11)
A function whose rule contains the variable under a radical, such as f(x) = 2\sqrt{x - 1} or g(x) = \sqrt[3]{x + 4}.
Algebra II, Lesson 6.4 (grade 10–11)
radical signEnglish
The symbol \sqrt{\phantom{0}}. It means the principal (nonnegative) square root, so \sqrt{49} = 7.
Pre-Algebra, Lesson 6.4 (grade 6–8)
The symbol \sqrt{\phantom{0}}. It means the principal (nonnegative) square root, so \sqrt{49} = 7.
Pre-Algebra, Lesson 6.4 (grade 6–8)
radicandEnglish
The number or expression under the radical sign. In \sqrt{50} the radicand is 50.
Algebra I, Lesson 10.1 (grade 8–9) · Algebra II, Lesson 6.1 (grade 10–11)
The number or expression under the radical sign. In \sqrt{50} the radicand is 50.
Algebra I, Lesson 10.1 (grade 8–9) · Algebra II, Lesson 6.1 (grade 10–11)
RadiusEnglish
A segment from the center to a point on the circle, or the length of such a segment. All radii of a circle are congruent; this comes straight from the definition of a circle.
Geometry, Lesson 10.1 (grade 9–10) · Grade 6 Life Science: Animal Design and Behavior, Lesson 5.2 (grade 6) · Pre-Algebra, Lesson 12.4 (grade 6–8)
A segment from the center to a point on the circle, or the length of such a segment. All radii of a circle are congruent; this comes straight from the definition of a circle.
Geometry, Lesson 10.1 (grade 9–10) · Grade 6 Life Science: Animal Design and Behavior, Lesson 5.2 (grade 6) · Pre-Algebra, Lesson 12.4 (grade 6–8)
radius of a regular polygonEnglish
A segment from the center to a vertex, or its length r.
Geometry, Lesson 11.3 (grade 9–10)
A segment from the center to a vertex, or its length r.
Geometry, Lesson 11.3 (grade 9–10)
rafterEnglish
A sloping roof beam running from the ridge to the wall. With the rise and the run it forms a right triangle.
Trigonometry, Lesson 1.3 (grade 11–12)
A sloping roof beam running from the ridge to the wall. With the rise and the run it forms a right triangle.
Trigonometry, Lesson 1.3 (grade 11–12)
random assignmentEnglish
Using a chance process (random digits, names drawn from a hat, a random number generator) to decide which experimental units receive which treatment.
Statistics, Lesson 5.5 (grade 11–12)
Using a chance process (random digits, names drawn from a hat, a random number generator) to decide which experimental units receive which treatment.
Statistics, Lesson 5.5 (grade 11–12)
random digitsEnglish
A list of the digits 0 to 9 in which each digit is equally likely in every position and has no connection to the digits around it.
Statistics, Lesson 6.1 (grade 11–12)
A list of the digits 0 to 9 in which each digit is equally likely in every position and has no connection to the digits around it.
Statistics, Lesson 6.1 (grade 11–12)
random phenomenonEnglish
A process whose single outcomes cannot be predicted, but which shows a regular pattern over many repetitions (a coin toss, whether a seed sprouts, whether a free throw goes in).
Statistics, Lesson 6.1 (grade 11–12)
A process whose single outcomes cannot be predicted, but which shows a regular pattern over many repetitions (a coin toss, whether a seed sprouts, whether a free throw goes in).
Statistics, Lesson 6.1 (grade 11–12)
random sampleEnglish
A sample chosen by a chance process (drawing names from a hat, random digits, a random number generator), so that no one's judgment or convenience decides who is included.
Statistics, Lesson 5.1 (grade 11–12)
A sample chosen by a chance process (drawing names from a hat, random digits, a random number generator), so that no one's judgment or convenience decides who is included.
Statistics, Lesson 5.1 (grade 11–12)
randomized block designEnglish
An experimental design in which the units are first divided into blocks, and then the treatments are randomly assigned separately within each block.
Statistics, Lesson 5.6 (grade 11–12)
An experimental design in which the units are first divided into blocks, and then the treatments are randomly assigned separately within each block.
Statistics, Lesson 5.6 (grade 11–12)
rangeEnglish
The set of all outputs (y-values) of a relation or function.
Algebra I, Lesson 4.4 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11) · Real Estate License Exam Prep: The National Exam, Lesson 1.4 (grade 9–12) · +3 more
The set of all outputs (y-values) of a relation or function.
Algebra I, Lesson 4.4 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11) · Real Estate License Exam Prep: The National Exam, Lesson 1.4 (grade 9–12) · +3 more
rate of changeEnglish
How much the output changes for each one-unit change in the input; the change in output divided by the change in input.
Algebra I, Lesson 5.1 (grade 8–9) · Pre-Algebra, Lesson 11.4 (grade 6–8)
How much the output changes for each one-unit change in the input; the change in output divided by the change in input.
Algebra I, Lesson 5.1 (grade 8–9) · Pre-Algebra, Lesson 11.4 (grade 6–8)
ratio of areasEnglish
For similar figures with scale factor a : b, the ratio of their areas, which is a^2 : b^2.
Geometry, Lesson 11.6 (grade 9–10)
For similar figures with scale factor a : b, the ratio of their areas, which is a^2 : b^2.
Geometry, Lesson 11.6 (grade 9–10)
ratio tableEnglish
A table with two rows (or columns) that lists equivalent ratios side by side.
Pre-Algebra, Lesson 7.1 (grade 6–8)
A table with two rows (or columns) that lists equivalent ratios side by side.
Pre-Algebra, Lesson 7.1 (grade 6–8)
rational equationEnglish
An equation that contains at least one rational expression with the variable in a denominator, such as \dfrac{5}{x} - \dfrac{1}{3} = \dfrac{1}{x}.
Algebra I, Lesson 12.5 (grade 8–9) · Algebra II, Lesson 5.5 (grade 10–11)
An equation that contains at least one rational expression with the variable in a denominator, such as \dfrac{5}{x} - \dfrac{1}{3} = \dfrac{1}{x}.
Algebra I, Lesson 12.5 (grade 8–9) · Algebra II, Lesson 5.5 (grade 10–11)
rational exponentEnglish
An exponent that is a fraction, such as \dfrac{2}{3} in 27^{2/3}. The denominator is the index of a root and the numerator is a power.
Algebra II, Lesson 6.1 (grade 10–11)
An exponent that is a fraction, such as \dfrac{2}{3} in 27^{2/3}. The denominator is the index of a root and the numerator is a power.
Algebra II, Lesson 6.1 (grade 10–11)
rational expressionEnglish
A fraction whose numerator and denominator are polynomials, such as \dfrac{x + 2}{x^2 - 9}. The denominator cannot be zero.
Algebra I, Lesson 12.2 (grade 8–9) · Algebra II, Lesson 5.1 (grade 10–11)
A fraction whose numerator and denominator are polynomials, such as \dfrac{x + 2}{x^2 - 9}. The denominator cannot be zero.
Algebra I, Lesson 12.2 (grade 8–9) · Algebra II, Lesson 5.1 (grade 10–11)
rational functionEnglish
A function whose rule is a rational expression, f(x) = \dfrac{P(x)}{Q(x)}, where P and Q are polynomials and Q is not the zero polynomial.
Algebra II, Lesson 5.3 (grade 10–11)
A function whose rule is a rational expression, f(x) = \dfrac{P(x)}{Q(x)}, where P and Q are polynomials and Q is not the zero polynomial.
Algebra II, Lesson 5.3 (grade 10–11)
Rational numberEnglish
A number that can be written as a fraction \dfrac{a}{b}, where a and b are integers and b \ne 0. Its decimal either ends (terminates) or repeats forever.
Algebra I, Lesson 1.1 (grade 8–9) · Pre-Algebra, Lesson 5.6 (grade 6–8) · Pre-Algebra, Lesson 6.5 (grade 6–8)
A number that can be written as a fraction \dfrac{a}{b}, where a and b are integers and b \ne 0. Its decimal either ends (terminates) or repeats forever.
Algebra I, Lesson 1.1 (grade 8–9) · Pre-Algebra, Lesson 5.6 (grade 6–8) · Pre-Algebra, Lesson 6.5 (grade 6–8)
Rational Root TheoremEnglish
If a polynomial with integer coefficients has a rational zero \dfrac{p}{q} in lowest terms, then p divides the constant term and q divides the leading coefficient.
Algebra II, Lesson 4.6 (grade 10–11)
If a polynomial with integer coefficients has a rational zero \dfrac{p}{q} in lowest terms, then p divides the constant term and q divides the leading coefficient.
Algebra II, Lesson 4.6 (grade 10–11)
rationalizing the denominatorEnglish
Rewriting a fraction so that no radical is left in the denominator, usually by multiplying the top and bottom by the same square root.
Algebra I, Lesson 10.2 (grade 8–9) · Algebra II, Lesson 6.2 (grade 10–11) · Trigonometry, Lesson 2.1 (grade 11–12)
Rewriting a fraction so that no radical is left in the denominator, usually by multiplying the top and bottom by the same square root.
Algebra I, Lesson 10.2 (grade 8–9) · Algebra II, Lesson 6.2 (grade 10–11) · Trigonometry, Lesson 2.1 (grade 11–12)
ratiosEnglish
The numbers found by dividing each y-value by the one before it, when the x-values go up by equal steps.
Algebra I, Lesson 13.3 (grade 8–9)
The numbers found by dividing each y-value by the one before it, when the x-values go up by equal steps.
Algebra I, Lesson 13.3 (grade 8–9)
rayEnglish
Ray \overrightarrow{AB} is made of the endpoint A, the point B, all points between them, and all points X of \overleftrightarrow{AB} such that B is between A and X. The endpoint is always named first.
Geometry, Lesson 2.1 (grade 9–10)
Ray \overrightarrow{AB} is made of the endpoint A, the point B, all points between them, and all points X of \overleftrightarrow{AB} such that B is between A and X. The endpoint is always named first.
Geometry, Lesson 2.1 (grade 9–10)
Real numbersEnglish
All the rational and irrational numbers together. Every point on the number line is a real number.
Algebra I, Lesson 1.1 (grade 8–9) · Pre-Algebra, Lesson 6.5 (grade 6–8)
All the rational and irrational numbers together. Every point on the number line is a real number.
Algebra I, Lesson 1.1 (grade 8–9) · Pre-Algebra, Lesson 6.5 (grade 6–8)
real solutionEnglish
A solution that is a real number, one you can place on the number line.
Algebra I, Lesson 11.6 (grade 8–9)
A solution that is a real number, one you can place on the number line.
Algebra I, Lesson 11.6 (grade 8–9)
reasonableEnglish
Making sense. A reasonable answer is close to what an estimate says it should be.
Pre-Algebra, Lesson 1.5 (grade 6–8)
Making sense. A reasonable answer is close to what an estimate says it should be.
Pre-Algebra, Lesson 1.5 (grade 6–8)
reasonable domainEnglish
The inputs that make sense in a real situation, such as times that are not negative or a number of people that is a whole number.
Algebra I, Lesson 4.4 (grade 8–9)
The inputs that make sense in a real situation, such as times that are not negative or a number of people that is a whole number.
Algebra I, Lesson 4.4 (grade 8–9)
reciprocalEnglish
The number or expression you multiply by to get 1. The reciprocal of \dfrac{c}{d} is \dfrac{d}{c}, because \dfrac{c}{d} \cdot \dfrac{d}{c} = 1.
Algebra I, Lesson 12.3 (grade 8–9) · Algebra I, Lesson 7.2 (grade 8–9) · Algebra I, Lesson 8.5 (grade 8–9) · +3 more
The number or expression you multiply by to get 1. The reciprocal of \dfrac{c}{d} is \dfrac{d}{c}, because \dfrac{c}{d} \cdot \dfrac{d}{c} = 1.
Algebra I, Lesson 12.3 (grade 8–9) · Algebra I, Lesson 7.2 (grade 8–9) · Algebra I, Lesson 8.5 (grade 8–9) · +3 more
reciprocal functionEnglish
The function \dfrac{1}{f(x)}, defined wherever f(x) \neq 0. Cosecant, secant and cotangent are the reciprocals of sine, cosine and tangent.
Trigonometry, Lesson 4.7 (grade 11–12)
The function \dfrac{1}{f(x)}, defined wherever f(x) \neq 0. Cosecant, secant and cotangent are the reciprocals of sine, cosine and tangent.
Trigonometry, Lesson 4.7 (grade 11–12)
reciprocal identitiesEnglish
The identities \csc\theta = \dfrac{1}{\sin\theta}, \sec\theta = \dfrac{1}{\cos\theta} and \cot\theta = \dfrac{1}{\tan\theta}.
Trigonometry, Lesson 5.1 (grade 11–12)
The identities \csc\theta = \dfrac{1}{\sin\theta}, \sec\theta = \dfrac{1}{\cos\theta} and \cot\theta = \dfrac{1}{\tan\theta}.
Trigonometry, Lesson 5.1 (grade 11–12)
Rectangle Area PostulateEnglish
The area of a rectangle is the product of its base and its height: A = bh. (A square of side s has area s^2.)
Geometry, Lesson 11.1 (grade 9–10)
The area of a rectangle is the product of its base and its height: A = bh. (A square of side s has area s^2.)
Geometry, Lesson 11.1 (grade 9–10)
rectangular coordinatesEnglish
The familiar (x, y) coordinates measured along two perpendicular axes; also called Cartesian coordinates.
Trigonometry, Lesson 9.2 (grade 11–12)
The familiar (x, y) coordinates measured along two perpendicular axes; also called Cartesian coordinates.
Trigonometry, Lesson 9.2 (grade 11–12)
recursive formulaEnglish
A rule that gives the first term and tells how to get each term from the one before it, such as a_1 = 3, a_n = 2a_{n-1}.
Algebra I, Lesson 7.6 (grade 8–9)
A rule that gives the first term and tells how to get each term from the one before it, such as a_1 = 3, a_n = 2a_{n-1}.
Algebra I, Lesson 7.6 (grade 8–9)
recursive ruleEnglish
A rule that gives the first term and tells how to get each term from the one before it, such as a_1 = 6, a_n = a_{n-1} + 4.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra II, Lesson 9.1 (grade 10–11)
A rule that gives the first term and tells how to get each term from the one before it, such as a_1 = 6, a_n = a_{n-1} + 4.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra II, Lesson 9.1 (grade 10–11)
reference angleEnglish
The acute angle \theta' between the terminal side of an angle in standard position and the x-axis.
Trigonometry, Lesson 3.7 (grade 11–12)
The acute angle \theta' between the terminal side of an angle in standard position and the x-axis.
Trigonometry, Lesson 3.7 (grade 11–12)
reference triangleEnglish
A right triangle drawn from the terminal side of an angle to the x-axis, with signed legs x and y and hypotenuse r > 0.
Trigonometry, Lesson 6.3 (grade 11–12)
A right triangle drawn from the terminal side of an angle to the x-axis, with signed legs x and y and hypotenuse r > 0.
Trigonometry, Lesson 6.3 (grade 11–12)
reflectionEnglish
A flip of the graph across a line. y = -f(x) flips across the x-axis and y = f(-x) flips across the y-axis.
Algebra II, Lesson 1.2 (grade 10–11) · Grade 2 Art, Lesson 8.2 (grade 2) · Grade 3 Art, Lesson 8.4 (grade 3) · +3 more
A flip of the graph across a line. y = -f(x) flips across the x-axis and y = f(-x) flips across the y-axis.
Algebra II, Lesson 1.2 (grade 10–11) · Grade 2 Art, Lesson 8.2 (grade 2) · Grade 3 Art, Lesson 8.4 (grade 3) · +3 more
reflection symmetryEnglish
The unit circle is unchanged by reflection in either axis, so points in different quadrants with the same reference angle have coordinates that differ only in sign.
Trigonometry, Lesson 3.7 (grade 11–12)
The unit circle is unchanged by reflection in either axis, so points in different quadrants with the same reference angle have coordinates that differ only in sign.
Trigonometry, Lesson 3.7 (grade 11–12)
Reflexive, Symmetric and Transitive PropertiesEnglish
Reflexive: a = a. Symmetric: if a = b, then b = a. Transitive: if a = b and b = c, then a = c.
Geometry, Lesson 1.5 (grade 9–10)
Reflexive: a = a. Symmetric: if a = b, then b = a. Transitive: if a = b and b = c, then a = c.
Geometry, Lesson 1.5 (grade 9–10)
Regression lineEnglish
A straight line \hat{y} = a + bx that describes how a response variable y changes as an explanatory variable x changes; used to predict y from x.
Statistics, Lesson 4.3 (grade 11–12)
A straight line \hat{y} = a + bx that describes how a response variable y changes as an explanatory variable x changes; used to predict y from x.
Statistics, Lesson 4.3 (grade 11–12)
Regression toward the meanEnglish
Because |r| is less than 1, the predicted y is fewer standard deviations from its mean than x is from its mean.
Statistics, Lesson 4.3 (grade 11–12)
Because |r| is less than 1, the predicted y is fewer standard deviations from its mean than x is from its mean.
Statistics, Lesson 4.3 (grade 11–12)
regroupingEnglish
Trading 1 whole for an equal number of fraction pieces (such as 1 = \dfrac{4}{4}), or trading a full set of pieces for 1 whole.
Pre-Algebra, Lesson 3.4 (grade 6–8)
Trading 1 whole for an equal number of fraction pieces (such as 1 = \dfrac{4}{4}), or trading a full set of pieces for 1 whole.
Pre-Algebra, Lesson 3.4 (grade 6–8)
regular polygonEnglish
A polygon that is both equilateral (all sides congruent) and equiangular (all angles congruent).
Geometry, Lesson 11.3 (grade 9–10) · Geometry, Lesson 6.1 (grade 9–10) · Pre-Algebra, Lesson 12.2 (grade 6–8)
A polygon that is both equilateral (all sides congruent) and equiangular (all angles congruent).
Geometry, Lesson 11.3 (grade 9–10) · Geometry, Lesson 6.1 (grade 9–10) · Pre-Algebra, Lesson 12.2 (grade 6–8)
regular pyramidEnglish
A pyramid whose base is a regular polygon and whose apex lies directly above the center of the base. Its lateral faces are congruent isosceles triangles.
Geometry, Lesson 12.3 (grade 9–10)
A pyramid whose base is a regular polygon and whose apex lies directly above the center of the base. Its lateral faces are congruent isosceles triangles.
Geometry, Lesson 12.3 (grade 9–10)
rejection ruleEnglish
The set of values of the statistic (for example, "\bar{x} \le 15.92") for which the test rejects H_0.
Statistics, Lesson 11.4 (grade 11–12)
The set of values of the statistic (for example, "\bar{x} \le 15.92") for which the test rejects H_0.
Statistics, Lesson 11.4 (grade 11–12)
relationEnglish
Any set of ordered pairs. It can be shown as a list, a table, a mapping diagram or a graph.
Algebra I, Lesson 4.1 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11)
Any set of ordered pairs. It can be shown as a list, a table, a mapping diagram or a graph.
Algebra I, Lesson 4.1 (grade 8–9) · Algebra II, Lesson 1.1 (grade 10–11)
relative maximum and minimumEnglish
A relative maximum is an output larger than every nearby output (a hilltop); a relative minimum is smaller than every nearby output (a valley).
Algebra II, Lesson 1.6 (grade 10–11)
A relative maximum is an output larger than every nearby output (a hilltop); a relative minimum is smaller than every nearby output (a valley).
Algebra II, Lesson 1.6 (grade 10–11)
relatively primeEnglish
Two numbers are relatively prime when their only common factor is 1, so their GCF is 1. Example: 8 and 15. Neither number has to be prime itself.
Pre-Algebra, Lesson 2.4 (grade 6–8)
Two numbers are relatively prime when their only common factor is 1, so their GCF is 1. Example: 8 and 15. Neither number has to be prime itself.
Pre-Algebra, Lesson 2.4 (grade 6–8)
remainderEnglish
What is left, r(x), when its degree is less than the degree of the divisor. If the remainder is 0, the divisor is a factor of the dividend.
Algebra II, Lesson 4.3 (grade 10–11) · Real Estate License Exam Prep: The National Exam, Lesson 2.1 (grade 9–12) · Pre-Algebra, Lesson 2.1 (grade 6–8) · +1 more
What is left, r(x), when its degree is less than the degree of the divisor. If the remainder is 0, the divisor is a factor of the dividend.
Algebra II, Lesson 4.3 (grade 10–11) · Real Estate License Exam Prep: The National Exam, Lesson 2.1 (grade 9–12) · Pre-Algebra, Lesson 2.1 (grade 6–8) · +1 more
Remainder TheoremEnglish
When a polynomial f(x) is divided by x - c, the remainder is f(c).
Algebra II, Lesson 4.4 (grade 10–11)
When a polynomial f(x) is divided by x - c, the remainder is f(c).
Algebra II, Lesson 4.4 (grade 10–11)
Remote interior anglesEnglish
The two interior angles of a triangle that are not adjacent to a given exterior angle (Euclid calls them the 'interior and opposite' angles).
Geometry, Lesson 4.1 (grade 9–10)
The two interior angles of a triangle that are not adjacent to a given exterior angle (Euclid calls them the 'interior and opposite' angles).
Geometry, Lesson 4.1 (grade 9–10)
repeated (double) rootEnglish
A solution that occurs twice, as x = 3 does in (x - 3)^2 = 0. It happens when the discriminant is 0.
Algebra II, Lesson 3.4 (grade 10–11)
A solution that occurs twice, as x = 3 does in (x - 3)^2 = 0. It happens when the discriminant is 0.
Algebra II, Lesson 3.4 (grade 10–11)
repeating decimalEnglish
A decimal in which a digit or group of digits repeats forever, such as 0.333\ldots
Pre-Algebra, Lesson 4.5 (grade 6–8)
A decimal in which a digit or group of digits repeats forever, such as 0.333\ldots
Pre-Algebra, Lesson 4.5 (grade 6–8)
repetendEnglish
The digit or group of digits that repeats in a repeating decimal.
Pre-Algebra, Lesson 4.5 (grade 6–8)
The digit or group of digits that repeats in a repeating decimal.
Pre-Algebra, Lesson 4.5 (grade 6–8)
RescaleEnglish
Multiplying every value by the same constant, as when changing units. The distribution is stretched or shrunk, but its shape stays the same.
Statistics, Lesson 2.6 (grade 11–12)
Multiplying every value by the same constant, as when changing units. The distribution is stretched or shrunk, but its shape stays the same.
Statistics, Lesson 2.6 (grade 11–12)
residualEnglish
The actual y-value minus the y-value predicted by the line. A positive residual means the point is above the line; a negative residual means it is below.
Algebra I, Lesson 13.2 (grade 8–9) · Statistics, Lesson 4.3 (grade 11–12) · Statistics, Lesson 4.4 (grade 11–12)
The actual y-value minus the y-value predicted by the line. A positive residual means the point is above the line; a negative residual means it is below.
Algebra I, Lesson 13.2 (grade 8–9) · Statistics, Lesson 4.3 (grade 11–12) · Statistics, Lesson 4.4 (grade 11–12)
Residual plotEnglish
A scatterplot of the residuals (vertical axis) against x (horizontal axis), with a horizontal line at 0.
Statistics, Lesson 4.4 (grade 11–12)
A scatterplot of the residuals (vertical axis) against x (horizontal axis), with a horizontal line at 0.
Statistics, Lesson 4.4 (grade 11–12)
ResistantEnglish
A statistic is resistant if a few extreme values (outliers) cannot change it very much. The median is resistant; the mean is not.
Statistics, Lesson 2.1 (grade 11–12) · Statistics, Lesson 4.2 (grade 11–12)
A statistic is resistant if a few extreme values (outliers) cannot change it very much. The median is resistant; the mean is not.
Statistics, Lesson 2.1 (grade 11–12) · Statistics, Lesson 4.2 (grade 11–12)
Resistant summaryEnglish
A summary not much affected by outliers or long tails: the median and the IQR (and the five-number summary).
Statistics, Lesson 2.5 (grade 11–12)
A summary not much affected by outliers or long tails: the median and the IQR (and the five-number summary).
Statistics, Lesson 2.5 (grade 11–12)
response biasEnglish
A systematic pattern of inaccurate answers, caused for example by people wanting to look good, misremembering, or leaning toward the answer they think the interviewer wants.
Statistics, Lesson 5.3 (grade 11–12)
A systematic pattern of inaccurate answers, caused for example by people wanting to look good, misremembering, or leaning toward the answer they think the interviewer wants.
Statistics, Lesson 5.3 (grade 11–12)
Response variableEnglish
The variable whose changes we want to understand or predict; it goes on the vertical (y) axis.
Statistics, Lesson 4.1 (grade 11–12)
The variable whose changes we want to understand or predict; it goes on the vertical (y) axis.
Statistics, Lesson 4.1 (grade 11–12)
restricted domainEnglish
A smaller domain chosen for a function so that it becomes one-to-one, such as y = x^2 for x \ge 0 only.
Algebra II, Lesson 1.5 (grade 10–11) · Algebra II, Lesson 6.4 (grade 10–11) · Trigonometry, Lesson 6.1 (grade 11–12)
A smaller domain chosen for a function so that it becomes one-to-one, such as y = x^2 for x \ge 0 only.
Algebra II, Lesson 1.5 (grade 10–11) · Algebra II, Lesson 6.4 (grade 10–11) · Trigonometry, Lesson 6.1 (grade 11–12)
revenueEnglish
The money a business takes in from sales: price per item times the number sold.
Algebra I, Lesson 6.5 (grade 8–9) · Algebra II, Lesson 3.6 (grade 10–11) · Grade 3 Business & Finance, Lesson 7.3 (grade 3) · +3 more
The money a business takes in from sales: price per item times the number sold.
Algebra I, Lesson 6.5 (grade 8–9) · Algebra II, Lesson 3.6 (grade 10–11) · Grade 3 Business & Finance, Lesson 7.3 (grade 3) · +3 more
reverse orderEnglish
Undoing steps in the opposite order from how they were done: the last thing done is the first thing undone.
Pre-Algebra, Lesson 10.4 (grade 6–8)
Undoing steps in the opposite order from how they were done: the last thing done is the first thing undone.
Pre-Algebra, Lesson 10.4 (grade 6–8)
revolutions per minute (rpm)English
The number of full turns made in one minute; each revolution is 2\pi radians.
Trigonometry, Lesson 3.5 (grade 11–12)
The number of full turns made in one minute; each revolution is 2\pi radians.
Trigonometry, Lesson 3.5 (grade 11–12)
rhombusEnglish
A parallelogram with four congruent sides. Its diagonals are perpendicular and bisect each other (Lesson 6.4).
Geometry, Lesson 11.2 (grade 9–10) · Geometry, Lesson 13.2 (grade 9–10) · Geometry, Lesson 6.4 (grade 9–10)
A parallelogram with four congruent sides. Its diagonals are perpendicular and bisect each other (Lesson 6.4).
Geometry, Lesson 11.2 (grade 9–10) · Geometry, Lesson 13.2 (grade 9–10) · Geometry, Lesson 6.4 (grade 9–10)
right angleEnglish
An angle of 90°, a quarter turn, like the corner of a square.
Algebra I, Lesson 5.6 (grade 8–9)
An angle of 90°, a quarter turn, like the corner of a square.
Algebra I, Lesson 5.6 (grade 8–9)
right coneEnglish
A cone whose apex lies directly above the center of its circular base.
Geometry, Lesson 12.3 (grade 9–10)
A cone whose apex lies directly above the center of its circular base.
Geometry, Lesson 12.3 (grade 9–10)
right cylinderEnglish
A cylinder whose axis (the segment joining the centers of the bases) is perpendicular to the bases.
Geometry, Lesson 12.2 (grade 9–10)
A cylinder whose axis (the segment joining the centers of the bases) is perpendicular to the bases.
Geometry, Lesson 12.2 (grade 9–10)
right prismEnglish
A prism whose lateral edges are perpendicular to its bases, so every lateral face is a rectangle. A prism that leans is an oblique prism.
Geometry, Lesson 12.2 (grade 9–10)
A prism whose lateral edges are perpendicular to its bases, so every lateral face is a rectangle. A prism that leans is an oblique prism.
Geometry, Lesson 12.2 (grade 9–10)
rigid motion (isometry)English
A transformation that preserves distance: for every two points A and B, A'B' = AB.
Geometry, Lesson 7.1 (grade 9–10)
A transformation that preserves distance: for every two points A and B, A'B' = AB.
Geometry, Lesson 7.1 (grade 9–10)
riseEnglish
The vertical change between two points, y_2 - y_1. Up is positive; down is negative.
Algebra I, Lesson 5.1 (grade 8–9) · Grade 1 Cooking & Food, Lesson 5.4 (grade 1) · Grade 2 Cooking & Food, Lesson 4.2 (grade 2) · +3 more
The vertical change between two points, y_2 - y_1. Up is positive; down is negative.
Algebra I, Lesson 5.1 (grade 8–9) · Grade 1 Cooking & Food, Lesson 5.4 (grade 1) · Grade 2 Cooking & Food, Lesson 4.2 (grade 2) · +3 more
Rise (height) of an arcEnglish
The distance from the midpoint of a chord to the arc, measured along the perpendicular bisector of the chord. Builders call it the rise of an arch.
Geometry, Lesson 10.2 (grade 9–10)
The distance from the midpoint of a chord to the arc, measured along the perpendicular bisector of the chord. Builders call it the rise of an arch.
Geometry, Lesson 10.2 (grade 9–10)
robustEnglish
A procedure is robust if its confidence level stays close to the stated level even when a condition, such as normality, is not exactly met.
Statistics, Lesson 10.4 (grade 11–12) · Statistics, Lesson 11.3 (grade 11–12)
A procedure is robust if its confidence level stays close to the stated level even when a condition, such as normality, is not exactly met.
Statistics, Lesson 10.4 (grade 11–12) · Statistics, Lesson 11.3 (grade 11–12)
root (solution)English
A value of the variable that makes the equation true. A quadratic equation can have two, one or no real roots.
Algebra I, Lesson 9.6 (grade 8–9)
A value of the variable that makes the equation true. A quadratic equation can have two, one or no real roots.
Algebra I, Lesson 9.6 (grade 8–9)
root (zero)English
A solution of ax^2 + bx + c = 0; it is also an x-value where the graph of y = ax^2 + bx + c has height 0.
Algebra I, Lesson 11.3 (grade 8–9)
A solution of ax^2 + bx + c = 0; it is also an x-value where the graph of y = ax^2 + bx + c has height 0.
Algebra I, Lesson 11.3 (grade 8–9)
rootsEnglish
Another word for the solutions of an equation such as ax^2 + bx + c = 0.
Algebra II, Lesson 3.4 (grade 10–11) · Grade 1 Gardening & Animals, Lesson 5.4 (grade 1) · Grade 2 Gardening & Animals, Lesson 5.3 (grade 2) · +1 more
Another word for the solutions of an equation such as ax^2 + bx + c = 0.
Algebra II, Lesson 3.4 (grade 10–11) · Grade 1 Gardening & Animals, Lesson 5.4 (grade 1) · Grade 2 Gardening & Animals, Lesson 5.3 (grade 2) · +1 more
rose curveEnglish
The graph of r = a\cos(n\theta) or r = a\sin(n\theta) for an integer n \ge 2; it has n petals when n is odd and 2n petals when n is even, each of length |a|.
Trigonometry, Lesson 9.3 (grade 11–12)
The graph of r = a\cos(n\theta) or r = a\sin(n\theta) for an integer n \ge 2; it has n petals when n is odd and 2n petals when n is even, each of length |a|.
Trigonometry, Lesson 9.3 (grade 11–12)
rotational symmetryEnglish
A figure has rotational symmetry if a rotation through an angle between 0^\circ and 360^\circ maps the figure onto itself.
Geometry, Lesson 7.3 (grade 9–10)
A figure has rotational symmetry if a rotation through an angle between 0^\circ and 360^\circ maps the figure onto itself.
Geometry, Lesson 7.3 (grade 9–10)
Roughly normalEnglish
Close enough to a normal shape that normal calculations give useful answers: single-peaked, roughly symmetric, with no outliers and tails about as long as a normal curve's.
Statistics, Lesson 3.6 (grade 11–12)
Close enough to a normal shape that normal calculations give useful answers: single-peaked, roughly symmetric, with no outliers and tails about as long as a normal curve's.
Statistics, Lesson 3.6 (grade 11–12)
roundingEnglish
Replacing a number with a nearby number that is easier to use, such as replacing 6,482 with 6,500.
Pre-Algebra, Lesson 1.5 (grade 6–8)
Replacing a number with a nearby number that is easier to use, such as replacing 6,482 with 6,500.
Pre-Algebra, Lesson 1.5 (grade 6–8)
row operationsEnglish
The three moves allowed on an augmented matrix: swap two rows; multiply a row by a nonzero number; add a multiple of one row to another row.
Algebra II, Lesson 12.4 (grade 10–11)
The three moves allowed on an augmented matrix: swap two rows; multiply a row by a nonzero number; add a multiple of one row to another row.
Algebra II, Lesson 12.4 (grade 10–11)
row-by-column ruleEnglish
The way each entry of a product is computed: first entry of the row times first entry of the column, plus second times second, and so on.
Algebra II, Lesson 12.2 (grade 10–11)
The way each entry of a product is computed: first entry of the row times first entry of the column, plus second times second, and so on.
Algebra II, Lesson 12.2 (grade 10–11)
row-echelon formEnglish
A staircase shape in which each row starts with more zeros than the row above it, so the last equation has the fewest variables.
Algebra II, Lesson 12.4 (grade 10–11)
A staircase shape in which each row starts with more zeros than the row above it, so the last equation has the fewest variables.
Algebra II, Lesson 12.4 (grade 10–11)
rule of 72English
A mental estimate: money growing at R percent per year doubles in about \dfrac{72}{R} years.
Algebra II, Lesson 8.6 (grade 10–11) · Grade 5 Business & Finance, Lesson 8.2 (grade 5) · Grade 6 Business & Finance, Lesson 8.1 (grade 6) · +3 more
A mental estimate: money growing at R percent per year doubles in about \dfrac{72}{R} years.
Algebra II, Lesson 8.6 (grade 10–11) · Grade 5 Business & Finance, Lesson 8.2 (grade 5) · Grade 6 Business & Finance, Lesson 8.1 (grade 6) · +3 more
Ruler PostulateEnglish
The points of a line can be matched one to one with the real numbers so that the distance between two points is the absolute value of the difference of their numbers (coordinates): AB = |a - b|.
Geometry, Lesson 2.2 (grade 9–10)
The points of a line can be matched one to one with the real numbers so that the distance between two points is the absolute value of the difference of their numbers (coordinates): AB = |a - b|.
Geometry, Lesson 2.2 (grade 9–10)
runEnglish
The horizontal change between two points, x_2 - x_1. Right is positive; left is negative.
Algebra I, Lesson 5.1 (grade 8–9) · Pre-Algebra, Lesson 11.4 (grade 6–8)
The horizontal change between two points, x_2 - x_1. Right is positive; left is negative.
Algebra I, Lesson 5.1 (grade 8–9) · Pre-Algebra, Lesson 11.4 (grade 6–8)
S
sale priceEnglish
The price after the discount is subtracted from the regular price.
Pre-Algebra, Lesson 8.5 (grade 6–8)
The price after the discount is subtracted from the regular price.
Pre-Algebra, Lesson 8.5 (grade 6–8)
same baseEnglish
Powers have the same base when the number being multiplied over and over is the same, like 7^2 and 7^5. The laws in this lesson work only for the same base.
Pre-Algebra, Lesson 6.2 (grade 6–8)
Powers have the same base when the number being multiplied over and over is the same, like 7^2 and 7^5. The laws in this lesson work only for the same base.
Pre-Algebra, Lesson 6.2 (grade 6–8)
same-side interior anglesEnglish
Two angles that lie between the two lines and on the same side of the transversal, at different intersection points. They are also called consecutive interior angles.
Geometry, Lesson 3.1 (grade 9–10)
Two angles that lie between the two lines and on the same side of the transversal, at different intersection points. They are also called consecutive interior angles.
Geometry, Lesson 3.1 (grade 9–10)
Sample mean \bar{x}English
The average of the n values in a sample. As a statistic, it changes from sample to sample.
Statistics, Lesson 9.3 (grade 11–12)
The average of the n values in a sample. As a statistic, it changes from sample to sample.
Statistics, Lesson 9.3 (grade 11–12)
sample proportion \hat{p}English
The fraction of the sample with the trait of interest: \hat{p} = \dfrac{X}{n}, where X is the number of successes.
Statistics, Lesson 10.2 (grade 11–12) · Statistics, Lesson 9.2 (grade 11–12)
The fraction of the sample with the trait of interest: \hat{p} = \dfrac{X}{n}, where X is the number of successes.
Statistics, Lesson 10.2 (grade 11–12) · Statistics, Lesson 9.2 (grade 11–12)
sample spaceEnglish
The list of all possible outcomes of an experiment, such as the 36 ordered results of rolling two number cubes.
Algebra II, Lesson 10.4 (grade 10–11) · Playing the Odds, Lesson 1.3 (grade 4–7) · Playing the Odds, Lesson 1.1 (grade 8–12) · +2 more
The list of all possible outcomes of an experiment, such as the 36 ordered results of rolling two number cubes.
Algebra II, Lesson 10.4 (grade 10–11) · Playing the Odds, Lesson 1.3 (grade 4–7) · Playing the Odds, Lesson 1.1 (grade 8–12) · +2 more
Sampling distributionEnglish
The distribution of the values a statistic takes in all possible samples of the same size from the same population.
Statistics, Lesson 9.1 (grade 11–12)
The distribution of the values a statistic takes in all possible samples of the same size from the same population.
Statistics, Lesson 9.1 (grade 11–12)
sampling errorEnglish
The random difference between a statistic and the parameter that comes from which individuals happened to be chosen; the margin of error measures this.
Statistics, Lesson 10.5 (grade 11–12) · Statistics, Lesson 5.3 (grade 11–12)
The random difference between a statistic and the parameter that comes from which individuals happened to be chosen; the margin of error measures this.
Statistics, Lesson 10.5 (grade 11–12) · Statistics, Lesson 5.3 (grade 11–12)
Sampling variabilityEnglish
The fact that different random samples from the same population give different values of a statistic.
Statistics, Lesson 9.1 (grade 11–12)
The fact that different random samples from the same population give different values of a statistic.
Statistics, Lesson 9.1 (grade 11–12)
SASEnglish
Given data of two sides and the angle between them (the included angle).
Trigonometry, Lesson 7.4 (grade 11–12)
Given data of two sides and the angle between them (the included angle).
Trigonometry, Lesson 7.4 (grade 11–12)
scalarEnglish
An ordinary real number, used to multiply every entry of a matrix. The name comes from the idea of scaling.
Algebra II, Lesson 12.1 (grade 10–11) · Physics, Lesson 1.5 (grade 11–12) · Trigonometry, Lesson 9.4 (grade 11–12)
An ordinary real number, used to multiply every entry of a matrix. The name comes from the idea of scaling.
Algebra II, Lesson 12.1 (grade 10–11) · Physics, Lesson 1.5 (grade 11–12) · Trigonometry, Lesson 9.4 (grade 11–12)
scale drawingEnglish
A drawing, map or blueprint whose lengths are all the same multiple of the real lengths; that multiple is the scale factor.
Geometry, Lesson 7.5 (grade 9–10) · Pre-Algebra, Lesson 7.4 (grade 6–8) · Fabrics & Sewing II, Lesson 7.1 (grade 6–8)
A drawing, map or blueprint whose lengths are all the same multiple of the real lengths; that multiple is the scale factor.
Geometry, Lesson 7.5 (grade 9–10) · Pre-Algebra, Lesson 7.4 (grade 6–8) · Fabrics & Sewing II, Lesson 7.1 (grade 6–8)
scale (of a drawing or model)English
The ratio of a length on a drawing or model to the corresponding real length, such as 1 in : 8 ft or 1 : 48.
Geometry, Lesson 8.2 (grade 9–10)
The ratio of a length on a drawing or model to the corresponding real length, such as 1 in : 8 ft or 1 : 48.
Geometry, Lesson 8.2 (grade 9–10)
Scalene, isosceles and equilateral trianglesEnglish
A triangle is scalene if no two sides are congruent, isosceles if at least two sides are congruent, and equilateral if all three sides are congruent.
Geometry, Lesson 4.1 (grade 9–10)
A triangle is scalene if no two sides are congruent, isosceles if at least two sides are congruent, and equilateral if all three sides are congruent.
Geometry, Lesson 4.1 (grade 9–10)
scatter plotEnglish
A graph of paired data in which each pair is plotted as a single point. The points are not connected.
Algebra I, Lesson 13.1 (grade 8–9)
A graph of paired data in which each pair is plotted as a single point. The points are not connected.
Algebra I, Lesson 13.1 (grade 8–9)
ScatterplotEnglish
A graph of two quantitative variables measured on the same individuals; each individual is one point (x, y).
Statistics, Lesson 4.1 (grade 11–12)
A graph of two quantitative variables measured on the same individuals; each individual is one point (x, y).
Statistics, Lesson 4.1 (grade 11–12)
scientific notationEnglish
A way of writing a number as a \times 10^n, where 1 \le a < 10 and n is an integer, such as 3.2 \times 10^5.
Algebra I, Lesson 7.3 (grade 8–9) · Pre-Algebra, Lesson 6.3 (grade 6–8)
A way of writing a number as a \times 10^n, where 1 \le a < 10 and n is an integer, such as 3.2 \times 10^5.
Algebra I, Lesson 7.3 (grade 8–9) · Pre-Algebra, Lesson 6.3 (grade 6–8)
scope of inferenceEnglish
How far the conclusions of a study can reach: random sampling allows generalizing to the population sampled, and random assignment allows concluding cause and effect.
Statistics, Lesson 5.6 (grade 11–12)
How far the conclusions of a study can reach: random sampling allows generalizing to the population sampled, and random assignment allows concluding cause and effect.
Statistics, Lesson 5.6 (grade 11–12)
secantEnglish
For an acute angle \theta, \sec\theta = \dfrac{\text{hyp}}{\text{adj}} = \dfrac{1}{\cos\theta}.
Trigonometry, Lesson 1.5 (grade 11–12)
For an acute angle \theta, \sec\theta = \dfrac{\text{hyp}}{\text{adj}} = \dfrac{1}{\cos\theta}.
Trigonometry, Lesson 1.5 (grade 11–12)
Secant and tangentEnglish
A secant is a line that meets a circle in two points. A tangent is a line in the plane of the circle that meets the circle in exactly one point, called the point of tangency.
Geometry, Lesson 10.1 (grade 9–10)
A secant is a line that meets a circle in two points. A tangent is a line in the plane of the circle that meets the circle in exactly one point, called the point of tangency.
Geometry, Lesson 10.1 (grade 9–10)
secant lineEnglish
A line through two points of a graph. Its slope is the average rate of change between those points.
Algebra II, Lesson 1.6 (grade 10–11)
A line through two points of a graph. Its slope is the average rate of change between those points.
Algebra II, Lesson 1.6 (grade 10–11)
Secant segmentEnglish
A segment of a secant line from a point outside the circle to the farther point where the line meets the circle, such as \overline{PB}. It is the 'whole' in the product rules.
Geometry, Lesson 10.6 (grade 9–10)
A segment of a secant line from a point outside the circle to the farther point where the line meets the circle, such as \overline{PB}. It is the 'whole' in the product rules.
Geometry, Lesson 10.6 (grade 9–10)
second differencesEnglish
The differences of the first differences: subtract each first difference from the next one.
Algebra I, Lesson 13.3 (grade 8–9) · Algebra II, Lesson 3.6 (grade 10–11)
The differences of the first differences: subtract each first difference from the next one.
Algebra I, Lesson 13.3 (grade 8–9) · Algebra II, Lesson 3.6 (grade 10–11)
sectorEnglish
The region bounded by two radii of a circle and the arc between them, shaped like a slice of pie.
Geometry, Lesson 11.5 (grade 9–10) · Trigonometry, Lesson 3.4 (grade 11–12)
The region bounded by two radii of a circle and the arc between them, shaped like a slice of pie.
Geometry, Lesson 11.5 (grade 9–10) · Trigonometry, Lesson 3.4 (grade 11–12)
Segment Addition PostulateEnglish
If B is between A and C, then AB + BC = AC.
Geometry, Lesson 2.2 (grade 9–10)
If B is between A and C, then AB + BC = AC.
Geometry, Lesson 2.2 (grade 9–10)
segment bisectorEnglish
A point, ray, line, segment or plane that intersects a segment at its midpoint.
Geometry, Lesson 2.2 (grade 9–10)
A point, ray, line, segment or plane that intersects a segment at its midpoint.
Geometry, Lesson 2.2 (grade 9–10)
segment of a circleEnglish
The region bounded by a chord and the arc it cuts off.
Geometry, Lesson 11.5 (grade 9–10) · Trigonometry, Lesson 3.4 (grade 11–12)
The region bounded by a chord and the arc it cuts off.
Geometry, Lesson 11.5 (grade 9–10) · Trigonometry, Lesson 3.4 (grade 11–12)
Segmented bar graphEnglish
A graph with one bar for each group, each bar standing for 100% of that group and divided into segments that show the conditional percents of the other variable.
Statistics, Lesson 1.3 (grade 11–12)
A graph with one bar for each group, each bar standing for 100% of that group and divided into segments that show the conditional percents of the other variable.
Statistics, Lesson 1.3 (grade 11–12)
Segments of a chordEnglish
When two chords cross at a point E, each chord is divided into two segments; for chord \overline{AC} they are \overline{AE} and \overline{EC}.
Geometry, Lesson 10.6 (grade 9–10)
When two chords cross at a point E, each chord is divided into two segments; for chord \overline{AC} they are \overline{AE} and \overline{EC}.
Geometry, Lesson 10.6 (grade 9–10)
Segments of the hypotenuseEnglish
The two parts \overline{AD} and \overline{DB} into which the foot D of the altitude divides the hypotenuse \overline{AB}.
Geometry, Lesson 9.3 (grade 9–10)
The two parts \overline{AD} and \overline{DB} into which the foot D of the altitude divides the hypotenuse \overline{AB}.
Geometry, Lesson 9.3 (grade 9–10)
semiperimeterEnglish
Half the perimeter of a triangle, usually written s = \dfrac{a + b + c}{2}.
Geometry, Lesson 5.2 (grade 9–10) · Trigonometry, Lesson 7.1 (grade 11–12)
Half the perimeter of a triangle, usually written s = \dfrac{a + b + c}{2}.
Geometry, Lesson 5.2 (grade 9–10) · Trigonometry, Lesson 7.1 (grade 11–12)
sequenceEnglish
An ordered list of numbers. Each number is a term; a_n (read "a sub n") is the term in position n.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra II, Lesson 9.1 (grade 10–11) · Grade 12 Composition & Creative Writing: Capstone: Rhetoric and the Senior Thesis, Lesson 5.1 (grade 12) · +3 more
An ordered list of numbers. Each number is a term; a_n (read "a sub n") is the term in position n.
Algebra I, Lesson 4.5 (grade 8–9) · Algebra II, Lesson 9.1 (grade 10–11) · Grade 12 Composition & Creative Writing: Capstone: Rhetoric and the Senior Thesis, Lesson 5.1 (grade 12) · +3 more
seriesEnglish
The sum of the terms of a sequence, such as 2 + 5 + 8 + 11.
Algebra II, Lesson 9.1 (grade 10–11) · Electronics & Microcontrollers, Lesson 2.1 (grade 9–12) · Grade 2 Engineering & Physics, Lesson 4.2 (grade 2) · +3 more
The sum of the terms of a sequence, such as 2 + 5 + 8 + 11.
Algebra II, Lesson 9.1 (grade 10–11) · Electronics & Microcontrollers, Lesson 2.1 (grade 9–12) · Grade 2 Engineering & Physics, Lesson 4.2 (grade 2) · +3 more
shearEnglish
A transformation that slides each point parallel to an axis by an amount proportional to its distance from that axis, turning squares into slanted parallelograms, as in \begin{bmatrix} 1 & k \\ 0 & 1 \end{bmatrix}.
Algebra II, Lesson 12.6 (grade 10–11) · Grade 5 Engineering & Physics, Lesson 2.1 (grade 5) · Shop & Trades, Lesson 2.5 (grade 9–12) · +2 more
A transformation that slides each point parallel to an axis by an amount proportional to its distance from that axis, turning squares into slanted parallelograms, as in \begin{bmatrix} 1 & k \\ 0 & 1 \end{bmatrix}.
Algebra II, Lesson 12.6 (grade 10–11) · Grade 5 Engineering & Physics, Lesson 2.1 (grade 5) · Shop & Trades, Lesson 2.5 (grade 9–12) · +2 more
Short legEnglish
In a 30^\circ-60^\circ-90^\circ triangle, the leg opposite the 30^\circ angle.
Geometry, Lesson 9.4 (grade 9–10) · Trigonometry, Lesson 2.2 (grade 11–12)
In a 30^\circ-60^\circ-90^\circ triangle, the leg opposite the 30^\circ angle.
Geometry, Lesson 9.4 (grade 9–10) · Trigonometry, Lesson 2.2 (grade 11–12)
Side-Angle-Side (SAS) PostulateEnglish
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Geometry, Lesson 4.3 (grade 9–10)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Geometry, Lesson 4.3 (grade 9–10)
Side-Angle-Side (SAS) Similarity TheoremEnglish
If an angle of one triangle is congruent to an angle of another triangle, and the sides including those angles are proportional, then the triangles are similar.
Geometry, Lesson 8.4 (grade 9–10)
If an angle of one triangle is congruent to an angle of another triangle, and the sides including those angles are proportional, then the triangles are similar.
Geometry, Lesson 8.4 (grade 9–10)
Side-Side-Side (SSS) PostulateEnglish
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Geometry, Lesson 4.3 (grade 9–10)
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Geometry, Lesson 4.3 (grade 9–10)
Side-Side-Side (SSS) Similarity TheoremEnglish
If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.
Geometry, Lesson 8.4 (grade 9–10)
If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.
Geometry, Lesson 8.4 (grade 9–10)
Sieve of EratosthenesEnglish
A method for finding primes by listing numbers and crossing out the multiples of each prime in turn. The numbers left are the primes.
Pre-Algebra, Lesson 2.2 (grade 6–8)
A method for finding primes by listing numbers and crossing out the multiples of each prime in turn. The numbers left are the primes.
Pre-Algebra, Lesson 2.2 (grade 6–8)
sigma (summation) notationEnglish
A short way to write a sum using the Greek capital letter sigma, \sum. In \sum_{k=1}^{5} a_k, k is the index, 1 is the lower limit and 5 is the upper limit.
Algebra II, Lesson 9.1 (grade 10–11)
A short way to write a sum using the Greek capital letter sigma, \sum. In \sum_{k=1}^{5} a_k, k is the index, 1 is the lower limit and 5 is the upper limit.
Algebra II, Lesson 9.1 (grade 10–11)
sign chartEnglish
A number line divided at the zeros of an expression, marked + or − on each interval to show where the expression is positive or negative.
Algebra II, Lesson 3.5 (grade 10–11) · Algebra II, Lesson 4.7 (grade 10–11) · Algebra II, Lesson 5.4 (grade 10–11)
A number line divided at the zeros of an expression, marked + or − on each interval to show where the expression is positive or negative.
Algebra II, Lesson 3.5 (grade 10–11) · Algebra II, Lesson 4.7 (grade 10–11) · Algebra II, Lesson 5.4 (grade 10–11)
sign rulesEnglish
The rules that tell whether a product is positive or negative: same signs give a positive product; different signs give a negative product.
Pre-Algebra, Lesson 5.4 (grade 6–8)
The rules that tell whether a product is positive or negative: same signs give a positive product; different signs give a negative product.
Pre-Algebra, Lesson 5.4 (grade 6–8)
significance level (\alpha)English
A cutoff chosen before the data are collected, often 0.05. If the P-value is less than \alpha, we reject H_0.
Statistics, Lesson 11.1 (grade 11–12)
A cutoff chosen before the data are collected, often 0.05. If the P-value is less than \alpha, we reject H_0.
Statistics, Lesson 11.1 (grade 11–12)
significance testEnglish
A method that uses data from a sample or experiment to weigh the evidence against a claim about a population parameter.
Statistics, Lesson 11.1 (grade 11–12)
A method that uses data from a sample or experiment to weigh the evidence against a claim about a population parameter.
Statistics, Lesson 11.1 (grade 11–12)
similar polygonsEnglish
Two polygons whose vertices can be matched so that every pair of corresponding angles is congruent and every pair of corresponding sides is in the same ratio. We write ABCD \sim EFGH.
Geometry, Lesson 8.2 (grade 9–10)
Two polygons whose vertices can be matched so that every pair of corresponding angles is congruent and every pair of corresponding sides is in the same ratio. We write ABCD \sim EFGH.
Geometry, Lesson 8.2 (grade 9–10)
similar solidsEnglish
Solids of the same shape whose corresponding lengths (edges, radii, heights) all have the same ratio, called the scale factor.
Geometry, Lesson 12.6 (grade 9–10)
Solids of the same shape whose corresponding lengths (edges, radii, heights) all have the same ratio, called the scale factor.
Geometry, Lesson 12.6 (grade 9–10)
similarity statementEnglish
A statement such as \triangle ABC \sim \triangle DEF that lists corresponding vertices in the same order, so A \leftrightarrow D, B \leftrightarrow E, C \leftrightarrow F.
Geometry, Lesson 8.2 (grade 9–10)
A statement such as \triangle ABC \sim \triangle DEF that lists corresponding vertices in the same order, so A \leftrightarrow D, B \leftrightarrow E, C \leftrightarrow F.
Geometry, Lesson 8.2 (grade 9–10)
similarity transformationEnglish
A dilation followed by zero or more rigid motions (translations, reflections, rotations).
Geometry, Lesson 8.2 (grade 9–10)
A dilation followed by zero or more rigid motions (translations, reflections, rotations).
Geometry, Lesson 8.2 (grade 9–10)
simple random sample (SRS)English
A sample of n individuals chosen so that every possible group of n individuals in the population has the same chance to be the sample.
Statistics, Lesson 5.2 (grade 11–12)
A sample of n individuals chosen so that every possible group of n individuals in the population has the same chance to be the sample.
Statistics, Lesson 5.2 (grade 11–12)
simplest formEnglish
A rational expression is in simplest form when its numerator and denominator have no common factor other than 1 (or -1).
Algebra I, Lesson 12.2 (grade 8–9) · Algebra II, Lesson 5.1 (grade 10–11)
A rational expression is in simplest form when its numerator and denominator have no common factor other than 1 (or -1).
Algebra I, Lesson 12.2 (grade 8–9) · Algebra II, Lesson 5.1 (grade 10–11)
simplest form (of an expression)English
An expression with all like terms combined, usually written with the highest exponent first and the constant last.
Pre-Algebra, Lesson 9.4 (grade 6–8)
An expression with all like terms combined, usually written with the highest exponent first and the constant last.
Pre-Algebra, Lesson 9.4 (grade 6–8)
simplest form (with exponents)English
An expression with one coefficient, each base written once, and no zero or negative exponents.
Algebra I, Lesson 7.2 (grade 8–9)
An expression with one coefficient, each base written once, and no zero or negative exponents.
Algebra I, Lesson 7.2 (grade 8–9)
simplest radical formEnglish
A square root is in simplest radical form when the radicand has no perfect-square factor other than 1 (more rules are added in Lesson 10.2).
Algebra I, Lesson 10.1 (grade 8–9) · Algebra I, Lesson 10.2 (grade 8–9) · Algebra II, Lesson 6.2 (grade 10–11) · +1 more
A square root is in simplest radical form when the radicand has no perfect-square factor other than 1 (more rules are added in Lesson 10.2).
Algebra I, Lesson 10.1 (grade 8–9) · Algebra I, Lesson 10.2 (grade 8–9) · Algebra II, Lesson 6.2 (grade 10–11) · +1 more
simplified monomialEnglish
A monomial written with one coefficient, each variable appearing only once, and no powers of powers or parentheses left to remove.
Algebra I, Lesson 7.1 (grade 8–9)
A monomial written with one coefficient, each variable appearing only once, and no powers of powers or parentheses left to remove.
Algebra I, Lesson 7.1 (grade 8–9)
SimplifyEnglish
To rewrite an expression in an equal but shorter form, with no parentheses left to remove and no like terms left to combine.
Algebra I, Lesson 1.4 (grade 8–9) · Grade 7 Art, Lesson 6.4 (grade 7) · Tactics & Strategy, Lesson 2.3 (grade 4–7) · +2 more
To rewrite an expression in an equal but shorter form, with no parentheses left to remove and no like terms left to combine.
Algebra I, Lesson 1.4 (grade 8–9) · Grade 7 Art, Lesson 6.4 (grade 7) · Tactics & Strategy, Lesson 2.3 (grade 4–7) · +2 more
Simpson's paradoxEnglish
A reversal in which a comparison that holds within every group turns the other way when the groups are combined, because a lurking variable (the variable that defines the groups) is combined with very unequal group sizes.
Statistics, Lesson 13.3 (grade 11–12)
A reversal in which a comparison that holds within every group turns the other way when the groups are combined, because a lurking variable (the variable that defines the groups) is combined with very unequal group sizes.
Statistics, Lesson 13.3 (grade 11–12)
\sin^2\thetaEnglish
Shorthand for (\sin\theta)^2, the square of the sine. It is not \sin(\theta^2).
Trigonometry, Lesson 5.2 (grade 11–12)
Shorthand for (\sin\theta)^2, the square of the sine. It is not \sin(\theta^2).
Trigonometry, Lesson 5.2 (grade 11–12)
SineEnglish
For an acute angle A of a right triangle, \sin A = \dfrac{\text{opposite leg}}{\text{hypotenuse}}.
Geometry, Lesson 9.6 (grade 9–10) · Trigonometry, Lesson 1.2 (grade 11–12)
For an acute angle A of a right triangle, \sin A = \dfrac{\text{opposite leg}}{\text{hypotenuse}}.
Geometry, Lesson 9.6 (grade 9–10) · Trigonometry, Lesson 1.2 (grade 11–12)
sinusoidEnglish
The wave-shaped curve of the sine function, or any stretch or shift of it.
Trigonometry, Lesson 4.1 (grade 11–12)
The wave-shaped curve of the sine function, or any stretch or shift of it.
Trigonometry, Lesson 4.1 (grade 11–12)
sinusoidal modelEnglish
An equation y = a\sin(b(x - c)) + d or y = a\cos(b(x - c)) + d chosen to describe a quantity that repeats regularly.
Trigonometry, Lesson 4.5 (grade 11–12)
An equation y = a\sin(b(x - c)) + d or y = a\cos(b(x - c)) + d chosen to describe a quantity that repeats regularly.
Trigonometry, Lesson 4.5 (grade 11–12)
skew linesEnglish
Lines that do not intersect and do not lie in the same plane.
Geometry, Lesson 3.1 (grade 9–10)
Lines that do not intersect and do not lie in the same plane.
Geometry, Lesson 3.1 (grade 9–10)
Skewed right and skewed leftEnglish
A distribution is skewed right if its right side (larger values) stretches out in a long tail, and skewed left if its left side (smaller values) has the long tail. The skew is named for the tail, not for the peak.
Statistics, Lesson 1.5 (grade 11–12)
A distribution is skewed right if its right side (larger values) stretches out in a long tail, and skewed left if its left side (smaller values) has the long tail. The skew is named for the tail, not for the peak.
Statistics, Lesson 1.5 (grade 11–12)
slant height of a regular pyramidEnglish
The height of one lateral face: the length of the segment from the apex perpendicular to a side of the base. It is written \ell.
Geometry, Lesson 12.3 (grade 9–10)
The height of one lateral face: the length of the segment from the apex perpendicular to a side of the base. It is written \ell.
Geometry, Lesson 12.3 (grade 9–10)
slant height of a right coneEnglish
The distance \ell from the apex to any point of the circle at the edge of the base.
Geometry, Lesson 12.3 (grade 9–10)
The distance \ell from the apex to any point of the circle at the edge of the base.
Geometry, Lesson 12.3 (grade 9–10)
slant (oblique) asymptoteEnglish
A slanted line y = mx + b that the graph approaches as |x| grows. It occurs when the numerator's degree is exactly one more than the denominator's.
Algebra II, Lesson 5.4 (grade 10–11)
A slanted line y = mx + b that the graph approaches as |x| grows. It occurs when the numerator's degree is exactly one more than the denominator's.
Algebra II, Lesson 5.4 (grade 10–11)
slopeEnglish
The steepness and direction of a line: the rise (vertical change) divided by the run (horizontal change) between any two points on it. Usually written m.
Algebra I, Lesson 5.1 (grade 8–9) · Grade 2 Earth Science: The Earth's Surface, Lesson 8.4 (grade 2) · Grade 2 Earth Science: The Earth's Surface, Lesson 9.1 (grade 2) · +3 more
The steepness and direction of a line: the rise (vertical change) divided by the run (horizontal change) between any two points on it. Usually written m.
Algebra I, Lesson 5.1 (grade 8–9) · Grade 2 Earth Science: The Earth's Surface, Lesson 8.4 (grade 2) · Grade 2 Earth Science: The Earth's Surface, Lesson 9.1 (grade 2) · +3 more
slope of the terminal sideEnglish
For an angle \theta in standard position, the slope of its terminal side is \dfrac{\sin\theta}{\cos\theta} = \tan\theta.
Trigonometry, Lesson 4.6 (grade 11–12)
For an angle \theta in standard position, the slope of its terminal side is \dfrac{\sin\theta}{\cos\theta} = \tan\theta.
Trigonometry, Lesson 4.6 (grade 11–12)
slope triangleEnglish
A right triangle drawn under (or over) a line, with a horizontal leg (the run), a vertical leg (the rise) and its long side lying on the line.
Algebra I, Lesson 5.1 (grade 8–9)
A right triangle drawn under (or over) a line, with a horizontal leg (the run), a vertical leg (the rise) and its long side lying on the line.
Algebra I, Lesson 5.1 (grade 8–9)
slope-intercept formEnglish
The form y = mx + b of a linear equation, where m is the slope and b is the y-intercept.
Algebra I, Lesson 5.3 (grade 8–9) · Pre-Algebra, Lesson 11.5 (grade 6–8)
The form y = mx + b of a linear equation, where m is the slope and b is the y-intercept.
Algebra I, Lesson 5.3 (grade 8–9) · Pre-Algebra, Lesson 11.5 (grade 6–8)
SOH-CAH-TOAEnglish
A memory aid: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Geometry, Lesson 9.6 (grade 9–10)
A memory aid: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Geometry, Lesson 9.6 (grade 9–10)
solutionEnglish
A value of the variable that makes the equation true.
Algebra I, Lesson 2.1 (grade 8–9) · Grade 3 Composition & Creative Writing: The Fable and the First Story, Lesson 3.3 (grade 3) · Pre-Algebra, Lesson 10.1 (grade 6–8)
A value of the variable that makes the equation true.
Algebra I, Lesson 2.1 (grade 8–9) · Grade 3 Composition & Creative Writing: The Fable and the First Story, Lesson 3.3 (grade 3) · Pre-Algebra, Lesson 10.1 (grade 6–8)
solution of a systemEnglish
An ordered pair that makes every equation in the system true at the same time. On a graph it is a point that lies on both lines.
Algebra I, Lesson 6.1 (grade 8–9) · Algebra II, Lesson 11.5 (grade 10–11) · Algebra II, Lesson 2.1 (grade 10–11)
An ordered pair that makes every equation in the system true at the same time. On a graph it is a point that lies on both lines.
Algebra I, Lesson 6.1 (grade 8–9) · Algebra II, Lesson 11.5 (grade 10–11) · Algebra II, Lesson 2.1 (grade 10–11)
solution of an equation in two variablesEnglish
An ordered pair (x, y) that makes the equation true when you substitute it. For y = x + 2, the pair (3, 5) is a solution because 5 = 3 + 2.
Pre-Algebra, Lesson 11.3 (grade 6–8)
An ordered pair (x, y) that makes the equation true when you substitute it. For y = x + 2, the pair (3, 5) is a solution because 5 = 3 + 2.
Pre-Algebra, Lesson 11.3 (grade 6–8)
solution of an inequalityEnglish
Any number that makes the inequality true when you substitute it for the variable. Most inequalities have infinitely many solutions.
Algebra I, Lesson 3.1 (grade 8–9) · Pre-Algebra, Lesson 10.7 (grade 6–8)
Any number that makes the inequality true when you substitute it for the variable. Most inequalities have infinitely many solutions.
Algebra I, Lesson 3.1 (grade 8–9) · Pre-Algebra, Lesson 10.7 (grade 6–8)
solution regionEnglish
The set of all points that satisfy every inequality in a system; on a graph it is the overlap of the half-planes.
Algebra II, Lesson 2.2 (grade 10–11)
The set of all points that satisfy every inequality in a system; on a graph it is the overlap of the half-planes.
Algebra II, Lesson 2.2 (grade 10–11)
solution setEnglish
The collection of all solutions of an inequality, such as every number greater than 4.
Algebra I, Lesson 3.1 (grade 8–9)
The collection of all solutions of an inequality, such as every number greater than 4.
Algebra I, Lesson 3.1 (grade 8–9)
solutions in one periodEnglish
The solutions that lie in a single period, usually [0, 2\pi) or [0^\circ, 360^\circ).
Trigonometry, Lesson 6.4 (grade 11–12)
The solutions that lie in a single period, usually [0, 2\pi) or [0^\circ, 360^\circ).
Trigonometry, Lesson 6.4 (grade 11–12)
Solve a right triangleEnglish
Find all three side lengths and all three angle measures from the given information.
Geometry, Lesson 9.6 (grade 9–10)
Find all three side lengths and all three angle measures from the given information.
Geometry, Lesson 9.6 (grade 9–10)
solve for a variableEnglish
Rewrite the equation so that one chosen variable is alone on one side and does not appear on the other side.
Algebra I, Lesson 2.5 (grade 8–9)
Rewrite the equation so that one chosen variable is alone on one side and does not appear on the other side.
Algebra I, Lesson 2.5 (grade 8–9)
solving a triangleEnglish
Finding all unknown sides and angles of a triangle from the parts that are given.
Trigonometry, Lesson 1.4 (grade 11–12) · Trigonometry, Lesson 7.2 (grade 11–12)
Finding all unknown sides and angles of a triangle from the parts that are given.
Trigonometry, Lesson 1.4 (grade 11–12) · Trigonometry, Lesson 7.2 (grade 11–12)
space diagonalEnglish
A segment joining two vertices of a box that do not lie on the same face, such as a bottom corner and the opposite top corner.
Trigonometry, Lesson 8.4 (grade 11–12)
A segment joining two vertices of a box that do not lie on the same face, such as a bottom corner and the opposite top corner.
Trigonometry, Lesson 8.4 (grade 11–12)
special anglesEnglish
Angles whose reference angle is \dfrac{\pi}{6}, \dfrac{\pi}{4} or \dfrac{\pi}{3} (30^\circ, 45^\circ, 60^\circ), together with the quadrantal angles; their trigonometric values can be written exactly.
Trigonometry, Lesson 3.8 (grade 11–12)
Angles whose reference angle is \dfrac{\pi}{6}, \dfrac{\pi}{4} or \dfrac{\pi}{3} (30^\circ, 45^\circ, 60^\circ), together with the quadrantal angles; their trigonometric values can be written exactly.
Trigonometry, Lesson 3.8 (grade 11–12)
special productsEnglish
The three patterns (a + b)^2 = a^2 + 2ab + b^2, (a - b)^2 = a^2 - 2ab + b^2 and (a + b)(a - b) = a^2 - b^2, which are worth knowing by heart.
Algebra I, Lesson 8.4 (grade 8–9)
The three patterns (a + b)^2 = a^2 + 2ab + b^2, (a - b)^2 = a^2 - 2ab + b^2 and (a + b)(a - b) = a^2 - b^2, which are worth knowing by heart.
Algebra I, Lesson 8.4 (grade 8–9)
Split stemsEnglish
A stemplot in which each stem appears twice, the first time with leaves 0 to 4 and the second with leaves 5 to 9, used when a plain stemplot has too few stems.
Statistics, Lesson 1.4 (grade 11–12)
A stemplot in which each stem appears twice, the first time with leaves 0 to 4 and the second with leaves 5 to 9, used when a plain stemplot has too few stems.
Statistics, Lesson 1.4 (grade 11–12)
splitting the middle termEnglish
Rewriting bx as a sum of two terms, such as 11x = 3x + 8x, so the trinomial becomes four terms that can be grouped.
Algebra I, Lesson 9.3 (grade 8–9)
Rewriting bx as a sum of two terms, such as 11x = 3x + 8x, so the trinomial becomes four terms that can be grouped.
Algebra I, Lesson 9.3 (grade 8–9)
square cornerEnglish
A builder's name for a right angle (90^\circ).
Pre-Algebra, Lesson 12.7 (grade 6–8)
A builder's name for a right angle (90^\circ).
Pre-Algebra, Lesson 12.7 (grade 6–8)
square matrixEnglish
A matrix with the same number of rows and columns, such as a 2 × 2 or 3 × 3 matrix.
Algebra II, Lesson 12.2 (grade 10–11)
A matrix with the same number of rows and columns, such as a 2 × 2 or 3 × 3 matrix.
Algebra II, Lesson 12.2 (grade 10–11)
square of a binomialEnglish
A product such as (a + b)^2 = (a + b)(a + b) or (a - b)^2 = (a - b)(a - b), a binomial multiplied by itself.
Algebra I, Lesson 8.4 (grade 8–9)
A product such as (a + b)^2 = (a + b)(a + b) or (a - b)^2 = (a - b)(a - b), a binomial multiplied by itself.
Algebra I, Lesson 8.4 (grade 8–9)
Square on a sideEnglish
Euclid's phrase for the square built with that side as one of its sides; its area is the square of the side's length.
Geometry, Lesson 9.1 (grade 9–10)
Euclid's phrase for the square built with that side as one of its sides; its area is the square of the side's length.
Geometry, Lesson 9.1 (grade 9–10)
square rootEnglish
A number that, when multiplied by itself, gives the original number. A square root of 49 is 7, because 7 \times 7 = 49.
Pre-Algebra, Lesson 6.4 (grade 6–8)
A number that, when multiplied by itself, gives the original number. A square root of 49 is 7, because 7 \times 7 = 49.
Pre-Algebra, Lesson 6.4 (grade 6–8)
square root functionEnglish
The parent function y = \sqrt{x}, with domain [0, \infty) and range [0, \infty).
Algebra II, Lesson 6.4 (grade 10–11)
The parent function y = \sqrt{x}, with domain [0, \infty) and range [0, \infty).
Algebra II, Lesson 6.4 (grade 10–11)
squared and cubedEnglish
Special names for exponents 2 and 3: 6^2 is read "6 squared" and 6^3 is read "6 cubed."
Pre-Algebra, Lesson 6.1 (grade 6–8)
Special names for exponents 2 and 3: 6^2 is read "6 squared" and 6^3 is read "6 cubed."
Pre-Algebra, Lesson 6.1 (grade 6–8)
squaring both sidesEnglish
Raising both sides of an equation to the second power to remove a square root, since (\sqrt{a})^2 = a.
Algebra I, Lesson 10.4 (grade 8–9)
Raising both sides of an equation to the second power to remove a square root, since (\sqrt{a})^2 = a.
Algebra I, Lesson 10.4 (grade 8–9)
SSAEnglish
Given data of two sides and an angle that is not between them (the angle is opposite one of the given sides).
Trigonometry, Lesson 7.3 (grade 11–12)
Given data of two sides and an angle that is not between them (the angle is opposite one of the given sides).
Trigonometry, Lesson 7.3 (grade 11–12)
standard basis vectorsEnglish
The two unit vectors \mathbf{e}_1 = \langle 1, 0 \rangle and \mathbf{e}_2 = \langle 0, 1 \rangle along the axes.
Algebra II, Lesson 12.6 (grade 10–11)
The two unit vectors \mathbf{e}_1 = \langle 1, 0 \rangle and \mathbf{e}_2 = \langle 0, 1 \rangle along the axes.
Algebra II, Lesson 12.6 (grade 10–11)
Standard deviation of a random variableEnglish
The square root of the variance, written \sigma_X. It measures how far the values of X typically fall from the mean, in the units of X.
Statistics, Lesson 7.2 (grade 11–12)
The square root of the variance, written \sigma_X. It measures how far the values of X typically fall from the mean, in the units of X.
Statistics, Lesson 7.2 (grade 11–12)
Standard deviation of \bar{x}English
\sigma_{\bar{x}} = \dfrac{\sigma}{\sqrt{n}}: the typical distance between a sample mean and the population mean \mu over many random samples of size n.
Statistics, Lesson 9.3 (grade 11–12)
\sigma_{\bar{x}} = \dfrac{\sigma}{\sqrt{n}}: the typical distance between a sample mean and the population mean \mu over many random samples of size n.
Statistics, Lesson 9.3 (grade 11–12)
Standard deviation of \hat{p}English
\sigma_{\hat{p}} = \sqrt{\dfrac{p(1 - p)}{n}}: the typical distance between the sample proportion and the true proportion p over many random samples.
Statistics, Lesson 9.2 (grade 11–12)
\sigma_{\hat{p}} = \sqrt{\dfrac{p(1 - p)}{n}}: the typical distance between the sample proportion and the true proportion p over many random samples.
Statistics, Lesson 9.2 (grade 11–12)
Standard deviation of the residuals (s)English
The typical size of a prediction error: about how far actual y-values fall from the regression line.
Statistics, Lesson 4.4 (grade 11–12)
The typical size of a prediction error: about how far actual y-values fall from the regression line.
Statistics, Lesson 4.4 (grade 11–12)
Standard deviation sEnglish
The square root of the variance. It measures a typical distance of the values from their mean, in the original units.
Statistics, Lesson 2.4 (grade 11–12)
The square root of the variance. It measures a typical distance of the values from their mean, in the original units.
Statistics, Lesson 2.4 (grade 11–12)
Standard error of \bar{x}_1 - \bar{x}_2English
SE = \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}, our estimate from the data of how far \bar{x}_1 - \bar{x}_2 typically falls from \mu_1 - \mu_2.
Statistics, Lesson 12.2 (grade 11–12)
SE = \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}, our estimate from the data of how far \bar{x}_1 - \bar{x}_2 typically falls from \mu_1 - \mu_2.
Statistics, Lesson 12.2 (grade 11–12)
standard error of the meanEnglish
The estimate \dfrac{s}{\sqrt{n}} of the standard deviation of \bar{x}, used when \sigma is unknown.
Statistics, Lesson 10.3 (grade 11–12) · Statistics, Lesson 11.3 (grade 11–12)
The estimate \dfrac{s}{\sqrt{n}} of the standard deviation of \bar{x}, used when \sigma is unknown.
Statistics, Lesson 10.3 (grade 11–12) · Statistics, Lesson 11.3 (grade 11–12)
standard formEnglish
The form Ax + By = C of a linear equation, where A, B and C are integers, A and B are not both 0, and usually A \ge 0.
Algebra I, Lesson 5.5 (grade 8–9) · Algebra I, Lesson 7.3 (grade 8–9) · Algebra I, Lesson 8.1 (grade 8–9) · +3 more
The form Ax + By = C of a linear equation, where A, B and C are integers, A and B are not both 0, and usually A \ge 0.
Algebra I, Lesson 5.5 (grade 8–9) · Algebra I, Lesson 7.3 (grade 8–9) · Algebra I, Lesson 8.1 (grade 8–9) · +3 more
standard form of a quadratic equationEnglish
ax^2 + bx + c = 0 with a \ne 0: everything on one side, 0 on the other, terms in order of decreasing power.
Algebra I, Lesson 11.5 (grade 8–9) · Algebra I, Lesson 9.6 (grade 8–9)
ax^2 + bx + c = 0 with a \ne 0: everything on one side, 0 on the other, terms in order of decreasing power.
Algebra I, Lesson 11.5 (grade 8–9) · Algebra I, Lesson 9.6 (grade 8–9)
standard form of a quadratic functionEnglish
y = ax^2 + bx + c with a \ne 0.
Algebra I, Lesson 11.2 (grade 8–9)
y = ax^2 + bx + c with a \ne 0.
Algebra I, Lesson 11.2 (grade 8–9)
Standard form of the equation of a circleEnglish
(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
Geometry, Lesson 10.7 (grade 9–10)
(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
Geometry, Lesson 10.7 (grade 9–10)
standard logistic functionEnglish
The function \sigma(x) = \dfrac{1}{1 + e^{-x}}, called the sigmoid. It turns any real number into a number between 0 and 1.
Algebra II, Lesson 7.4 (grade 10–11)
The function \sigma(x) = \dfrac{1}{1 + e^{-x}}, called the sigmoid. It turns any real number into a number between 0 and 1.
Algebra II, Lesson 7.4 (grade 10–11)
Standard normal distributionEnglish
The normal distribution with mean 0 and standard deviation 1, written N(0, 1). Its values are z-scores, and the letter Z is used for it.
Statistics, Lesson 3.4 (grade 11–12)
The normal distribution with mean 0 and standard deviation 1, written N(0, 1). Its values are z-scores, and the letter Z is used for it.
Statistics, Lesson 3.4 (grade 11–12)
Standard normal tableEnglish
A table that gives the area under the standard normal curve to the LEFT of each z-value, from about z = -3.49 to z = 3.49.
Statistics, Lesson 3.4 (grade 11–12)
A table that gives the area under the standard normal curve to the LEFT of each z-value, from about z = -3.49 to z = 3.49.
Statistics, Lesson 3.4 (grade 11–12)
Standard positionEnglish
An angle drawn with its vertex at the origin and its initial side along the positive x-axis.
Algebra II, Lesson 13.2 (grade 10–11) · Trigonometry, Lesson 3.1 (grade 11–12)
An angle drawn with its vertex at the origin and its initial side along the positive x-axis.
Algebra II, Lesson 13.2 (grade 10–11) · Trigonometry, Lesson 3.1 (grade 11–12)
Standardized value (z-score)English
How many standard deviations a value lies above (positive) or below (negative) its mean: z = \dfrac{x - \bar{x}}{s_x}.
Statistics, Lesson 4.2 (grade 11–12)
How many standard deviations a value lies above (positive) or below (negative) its mean: z = \dfrac{x - \bar{x}}{s_x}.
Statistics, Lesson 4.2 (grade 11–12)
StandardizingEnglish
Turning a value into its z-score, so that it is measured in standard deviations from the mean instead of in its original units.
Statistics, Lesson 3.1 (grade 11–12)
Turning a value into its z-score, so that it is measured in standard deviations from the mean instead of in its original units.
Statistics, Lesson 3.1 (grade 11–12)
statistically significantEnglish
Describes a result whose P-value is less than \alpha: a result too unlikely to be explained by chance alone if H_0 were true.
Statistics, Lesson 11.1 (grade 11–12) · Statistics, Lesson 5.5 (grade 11–12)
Describes a result whose P-value is less than \alpha: a result too unlikely to be explained by chance alone if H_0 were true.
Statistics, Lesson 11.1 (grade 11–12) · Statistics, Lesson 5.5 (grade 11–12)
StemplotEnglish
A display that splits each value into a stem (all but the last digit) and a leaf (the last digit), listing the leaves beside their stems so that the actual values can still be read.
Statistics, Lesson 1.4 (grade 11–12)
A display that splits each value into a stem (all but the last digit) and a leaf (the last digit), listing the leaves beside their stems so that the actual values can still be read.
Statistics, Lesson 1.4 (grade 11–12)
step functionEnglish
A piecewise function that is constant on each piece, so its graph looks like a staircase.
Algebra II, Lesson 1.3 (grade 10–11)
A piecewise function that is constant on each piece, so its graph looks like a staircase.
Algebra II, Lesson 1.3 (grade 10–11)
stratified random sampleEnglish
A sample chosen by first dividing the population into groups of similar individuals, called strata, and then choosing a separate SRS from each stratum.
Statistics, Lesson 5.2 (grade 11–12)
A sample chosen by first dividing the population into groups of similar individuals, called strata, and then choosing a separate SRS from each stratum.
Statistics, Lesson 5.2 (grade 11–12)
strong and weak correlationEnglish
A correlation is strong when the points lie close to a line and weak when they are widely scattered around it.
Algebra I, Lesson 13.1 (grade 8–9)
A correlation is strong when the points lie close to a line and weak when they are widely scattered around it.
Algebra I, Lesson 13.1 (grade 8–9)
SubstitutionEnglish
Replacing a variable with a number (or another expression).
Algebra I, Lesson 1.3 (grade 8–9) · Real Estate License Exam Prep: The National Exam, Lesson 4.1 (grade 9–12)
Replacing a variable with a number (or another expression).
Algebra I, Lesson 1.3 (grade 8–9) · Real Estate License Exam Prep: The National Exam, Lesson 4.1 (grade 9–12)
substitution methodEnglish
A way to solve a system: solve one equation for one variable, replace that variable in the other equation with the expression, and solve the resulting one-variable equation.
Algebra I, Lesson 6.2 (grade 8–9)
A way to solve a system: solve one equation for one variable, replace that variable in the other equation with the expression, and solve the resulting one-variable equation.
Algebra I, Lesson 6.2 (grade 8–9)
substitution property of equalityEnglish
If two quantities are equal, either one may replace the other in any equation or expression.
Algebra I, Lesson 6.2 (grade 8–9) · Geometry, Lesson 1.5 (grade 9–10)
If two quantities are equal, either one may replace the other in any equation or expression.
Algebra I, Lesson 6.2 (grade 8–9) · Geometry, Lesson 1.5 (grade 9–10)
subtendEnglish
To cut off: a central angle subtends the arc that lies between its two sides.
Trigonometry, Lesson 3.2 (grade 11–12)
To cut off: a central angle subtends the arc that lies between its two sides.
Trigonometry, Lesson 3.2 (grade 11–12)
Success and failureEnglish
The two possible outcomes of a trial. A success is simply the outcome we are counting; it does not have to be a good thing (a blemished apple can be a success).
Statistics, Lesson 8.1 (grade 11–12)
The two possible outcomes of a trial. A success is simply the outcome we are counting; it does not have to be a good thing (a blemished apple can be a success).
Statistics, Lesson 8.1 (grade 11–12)
successive discountsEnglish
Two or more discounts taken one after another, each on the price left by the one before.
Pre-Algebra, Lesson 8.5 (grade 6–8)
Two or more discounts taken one after another, each on the price left by the one before.
Pre-Algebra, Lesson 8.5 (grade 6–8)
sufficient conditionEnglish
A condition that, when it is true, guarantees the conclusion. Each theorem in this lesson names a sufficient condition for a quadrilateral to be a parallelogram.
Geometry, Lesson 6.3 (grade 9–10)
A condition that, when it is true, guarantees the conclusion. Each theorem in this lesson names a sufficient condition for a quadrilateral to be a parallelogram.
Geometry, Lesson 6.3 (grade 9–10)
sum and difference of cubesEnglish
Expressions of the form a^3 + b^3 and a^3 - b^3, which have the special factorizations (a + b)(a^2 - ab + b^2) and (a - b)(a^2 + ab + b^2).
Algebra II, Lesson 4.2 (grade 10–11)
Expressions of the form a^3 + b^3 and a^3 - b^3, which have the special factorizations (a + b)(a^2 - ab + b^2) and (a - b)(a^2 + ab + b^2).
Algebra II, Lesson 4.2 (grade 10–11)
sum, difference, product and quotient of functionsEnglish
New functions made by combining outputs: (f + g)(x) = f(x) + g(x), (f - g)(x) = f(x) - g(x), (fg)(x) = f(x) \cdot g(x), \left(\dfrac{f}{g}\right)(x) = \dfrac{f(x)}{g(x)}.
Algebra II, Lesson 1.4 (grade 10–11)
New functions made by combining outputs: (f + g)(x) = f(x) + g(x), (f - g)(x) = f(x) - g(x), (fg)(x) = f(x) \cdot g(x), \left(\dfrac{f}{g}\right)(x) = \dfrac{f(x)}{g(x)}.
Algebra II, Lesson 1.4 (grade 10–11)
sum formulaEnglish
A formula that expresses a function of A + B, such as \sin(A + B), in terms of functions of A and of B.
Trigonometry, Lesson 5.4 (grade 11–12)
A formula that expresses a function of A + B, such as \sin(A + B), in terms of functions of A and of B.
Trigonometry, Lesson 5.4 (grade 11–12)
Sum of independent normal random variablesEnglish
If X and Y are independent and both normal, then X + Y and X - Y are also normal, with mean and standard deviation found by the rules of Lesson 7.3.
Statistics, Lesson 7.4 (grade 11–12)
If X and Y are independent and both normal, then X + Y and X - Y are also normal, with mean and standard deviation found by the rules of Lesson 7.3.
Statistics, Lesson 7.4 (grade 11–12)
Sum of random variablesEnglish
A new random variable X + Y formed by adding the values of X and Y, such as the total weight of two items.
Statistics, Lesson 7.3 (grade 11–12)
A new random variable X + Y formed by adding the values of X and Y, such as the total weight of two items.
Statistics, Lesson 7.3 (grade 11–12)
sum of two squaresEnglish
A binomial of the form a^2 + b^2, such as x^2 + 9. It does not factor over the integers.
Algebra I, Lesson 9.4 (grade 8–9)
A binomial of the form a^2 + b^2, such as x^2 + 9. It does not factor over the integers.
Algebra I, Lesson 9.4 (grade 8–9)
\sum (sigma)English
The Greek capital letter S, used to mean "add them up". \sum x is the sum of all the values of x.
Statistics, Lesson 2.1 (grade 11–12)
The Greek capital letter S, used to mean "add them up". \sum x is the sum of all the values of x.
Statistics, Lesson 2.1 (grade 11–12)
supplementary anglesEnglish
Two angles whose measures add to 180^\circ. Each is the supplement of the other.
Geometry, Lesson 2.4 (grade 9–10) · Trigonometry, Lesson 7.3 (grade 11–12)
Two angles whose measures add to 180^\circ. Each is the supplement of the other.
Geometry, Lesson 2.4 (grade 9–10) · Trigonometry, Lesson 7.3 (grade 11–12)
SymmetricEnglish
A distribution is roughly symmetric if the left and right sides of its graph are close to mirror images of each other.
Statistics, Lesson 1.5 (grade 11–12)
A distribution is roughly symmetric if the left and right sides of its graph are close to mirror images of each other.
Statistics, Lesson 1.5 (grade 11–12)
symmetry testEnglish
A substitution that, if it produces an equivalent equation, guarantees that the graph has a certain symmetry.
Trigonometry, Lesson 9.3 (grade 11–12)
A substitution that, if it produces an equivalent equation, guarantees that the graph has a certain symmetry.
Trigonometry, Lesson 9.3 (grade 11–12)
synthetic divisionEnglish
A shortcut for dividing a polynomial by x - c that works only with the coefficients: bring down, multiply by c, add, and repeat.
Algebra II, Lesson 4.4 (grade 10–11)
A shortcut for dividing a polynomial by x - c that works only with the coefficients: bring down, multiply by c, add, and repeat.
Algebra II, Lesson 4.4 (grade 10–11)
synthetic proofEnglish
A proof that reasons directly from definitions, postulates and earlier theorems about figures, without coordinates, as Euclid did.
Geometry, Lesson 13.3 (grade 9–10)
A proof that reasons directly from definitions, postulates and earlier theorems about figures, without coordinates, as Euclid did.
Geometry, Lesson 13.3 (grade 9–10)
synthetic substitutionEnglish
Using synthetic division to find the value f(c); the last number in the bottom row is f(c).
Algebra II, Lesson 4.4 (grade 10–11)
Using synthetic division to find the value f(c); the last number in the bottom row is f(c).
Algebra II, Lesson 4.4 (grade 10–11)
system of linear equationsEnglish
Two or more linear equations that use the same variables and are considered together, such as y = x + 1 and y = -2x + 7.
Algebra I, Lesson 6.1 (grade 8–9) · Algebra II, Lesson 2.1 (grade 10–11)
Two or more linear equations that use the same variables and are considered together, such as y = x + 1 and y = -2x + 7.
Algebra I, Lesson 6.1 (grade 8–9) · Algebra II, Lesson 2.1 (grade 10–11)
system of linear inequalitiesEnglish
Two or more linear inequalities considered together. Its solutions are the points in the region where all the shaded half-planes overlap.
Algebra I, Lesson 6.6 (grade 8–9)
Two or more linear inequalities considered together. Its solutions are the points in the region where all the shaded half-planes overlap.
Algebra I, Lesson 6.6 (grade 8–9)
systematic random sampleEnglish
A sample chosen from a list by picking a random starting point among the first k individuals and then taking every kth individual after it.
Statistics, Lesson 5.2 (grade 11–12)
A sample chosen from a list by picking a random starting point among the first k individuals and then taking every kth individual after it.
Statistics, Lesson 5.2 (grade 11–12)
T
t distributionEnglish
A symmetric, bell-shaped distribution centered at 0 with heavier tails than the standard normal; it describes t = \dfrac{\bar{x} - \mu}{s/\sqrt{n}} for samples from a normal population.
Statistics, Lesson 10.3 (grade 11–12)
A symmetric, bell-shaped distribution centered at 0 with heavier tails than the standard normal; it describes t = \dfrac{\bar{x} - \mu}{s/\sqrt{n}} for samples from a normal population.
Statistics, Lesson 10.3 (grade 11–12)
t statisticEnglish
The number of standard errors the sample mean lies from the null value: t = (\bar{x} - \mu_0)/(s/\sqrt{n}).
Statistics, Lesson 11.3 (grade 11–12)
The number of standard errors the sample mean lies from the null value: t = (\bar{x} - \mu_0)/(s/\sqrt{n}).
Statistics, Lesson 11.3 (grade 11–12)
table of random digitsEnglish
A long list of the digits 0 to 9 produced by a chance process: every position is equally likely to hold any digit, and knowing some digits tells you nothing about the others.
Statistics, Lesson 5.2 (grade 11–12)
A long list of the digits 0 to 9 produced by a chance process: every position is equally likely to hold any digit, and knowing some digits tells you nothing about the others.
Statistics, Lesson 5.2 (grade 11–12)
TangentEnglish
For an acute angle A of a right triangle, \tan A = \dfrac{\text{length of leg opposite } \angle A}{\text{length of leg adjacent to } \angle A}.
Geometry, Lesson 9.5 (grade 9–10) · Trigonometry, Lesson 1.2 (grade 11–12)
For an acute angle A of a right triangle, \tan A = \dfrac{\text{length of leg opposite } \angle A}{\text{length of leg adjacent to } \angle A}.
Geometry, Lesson 9.5 (grade 9–10) · Trigonometry, Lesson 1.2 (grade 11–12)
tangent lineEnglish
A line that touches a curve at exactly one point without crossing it there; algebraically, substitution gives a quadratic with a repeated root (discriminant 0).
Algebra II, Lesson 11.5 (grade 10–11) · Physics, Lesson 2.4 (grade 11–12)
A line that touches a curve at exactly one point without crossing it there; algebraically, substitution gives a quadratic with a repeated root (discriminant 0).
Algebra II, Lesson 11.5 (grade 10–11) · Physics, Lesson 2.4 (grade 11–12)
tangent line of the unit circleEnglish
The vertical line x = 1, which touches the unit circle only at (1, 0); the value \tan\theta is the height at which the terminal side (extended) meets this line.
Trigonometry, Lesson 4.6 (grade 11–12)
The vertical line x = 1, which touches the unit circle only at (1, 0); the value \tan\theta is the height at which the terminal side (extended) meets this line.
Trigonometry, Lesson 4.6 (grade 11–12)
Tangent segmentEnglish
A segment of a tangent line that has one endpoint at the point of tangency, such as \overline{PT} from an outside point P to the point of tangency T.
Geometry, Lesson 10.3 (grade 9–10)
A segment of a tangent line that has one endpoint at the point of tangency, such as \overline{PT} from an outside point P to the point of tangency T.
Geometry, Lesson 10.3 (grade 9–10)
Tangent-chord angleEnglish
An angle formed by a tangent and a chord that meet at the point of tangency. Its intercepted arc is the arc that lies inside the angle.
Geometry, Lesson 10.5 (grade 9–10)
An angle formed by a tangent and a chord that meet at the point of tangency. Its intercepted arc is the arc that lies inside the angle.
Geometry, Lesson 10.5 (grade 9–10)
target valueEnglish
The ideal or intended measurement, the center of the allowed interval.
Algebra I, Lesson 3.5 (grade 8–9)
The ideal or intended measurement, the center of the allowed interval.
Algebra I, Lesson 3.5 (grade 8–9)
tenthsEnglish
The first place to the right of the decimal point. One tenth is one of 10 equal parts of a whole: 0.1 = \dfrac{1}{10}.
Pre-Algebra, Lesson 4.1 (grade 6–8)
The first place to the right of the decimal point. One tenth is one of 10 equal parts of a whole: 0.1 = \dfrac{1}{10}.
Pre-Algebra, Lesson 4.1 (grade 6–8)
TermEnglish
A number, a variable, or a product of numbers and variables. Terms are the parts of an expression separated by + and − signs; in 4x^2 - x + 9 the terms are 4x^2, -x and 9.
Algebra I, Lesson 1.4 (grade 8–9) · Entrepreneurship & Sales, Lesson 5.2 (grade 9–12) · Pre-Algebra, Lesson 9.1 (grade 6–8)
A number, a variable, or a product of numbers and variables. Terms are the parts of an expression separated by + and − signs; in 4x^2 - x + 9 the terms are 4x^2, -x and 9.
Algebra I, Lesson 1.4 (grade 8–9) · Entrepreneurship & Sales, Lesson 5.2 (grade 9–12) · Pre-Algebra, Lesson 9.1 (grade 6–8)
terminal pointEnglish
The point where the terminal side of an angle in standard position meets the unit circle.
Trigonometry, Lesson 3.6 (grade 11–12) · Trigonometry, Lesson 3.8 (grade 11–12)
The point where the terminal side of an angle in standard position meets the unit circle.
Trigonometry, Lesson 3.6 (grade 11–12) · Trigonometry, Lesson 3.8 (grade 11–12)
terminal sideEnglish
The ray where the rotation that forms an angle ends.
Trigonometry, Lesson 3.1 (grade 11–12)
The ray where the rotation that forms an angle ends.
Trigonometry, Lesson 3.1 (grade 11–12)
terminating decimalEnglish
A decimal that ends, such as 0.375. The division eventually has a remainder of 0.
Pre-Algebra, Lesson 4.5 (grade 6–8)
A decimal that ends, such as 0.375. The division eventually has a remainder of 0.
Pre-Algebra, Lesson 4.5 (grade 6–8)
terms of a ratioEnglish
The two numbers being compared. In 3:5, the terms are 3 and 5.
Pre-Algebra, Lesson 7.1 (grade 6–8)
The two numbers being compared. In 3:5, the terms are 3 and 5.
Pre-Algebra, Lesson 7.1 (grade 6–8)
test pointEnglish
A point not on the boundary line that you substitute into the inequality to decide which side to shade. (0, 0) is easiest when the line does not pass through it.
Algebra I, Lesson 6.6 (grade 8–9) · Algebra II, Lesson 2.2 (grade 10–11) · Algebra II, Lesson 3.5 (grade 10–11)
A point not on the boundary line that you substitute into the inequality to decide which side to shade. (0, 0) is easiest when the line does not pass through it.
Algebra I, Lesson 6.6 (grade 8–9) · Algebra II, Lesson 2.2 (grade 10–11) · Algebra II, Lesson 3.5 (grade 10–11)
test statisticEnglish
A number that measures how far the sample statistic is from the null value, in standard deviations: (statistic − null value) ÷ (standard deviation of the statistic).
Statistics, Lesson 11.2 (grade 11–12)
A number that measures how far the sample statistic is from the null value, in standard deviations: (statistic − null value) ÷ (standard deviation of the statistic).
Statistics, Lesson 11.2 (grade 11–12)
the number eEnglish
The number, about 2.71828, that \left(1 + \frac{1}{n}\right)^n gets closer and closer to as n grows. Like \pi, it is irrational.
Algebra II, Lesson 7.2 (grade 10–11)
The number, about 2.71828, that \left(1 + \frac{1}{n}\right)^n gets closer and closer to as n grows. Like \pi, it is irrational.
Algebra II, Lesson 7.2 (grade 10–11)
the rest (the remainder)English
What is left after part has been used or given away. A fraction "of the rest" is a fraction of that leftover amount, not of the original.
Pre-Algebra, Lesson 3.7 (grade 6–8)
What is left after part has been used or given away. A fraction "of the rest" is a fraction of that leftover amount, not of the original.
Pre-Algebra, Lesson 3.7 (grade 6–8)
theoremEnglish
A statement that has been proved from undefined terms, definitions, postulates and earlier theorems. Euclid called his theorems and constructions propositions.
Geometry, Lesson 1.1 (grade 9–10)
A statement that has been proved from undefined terms, definitions, postulates and earlier theorems. Euclid called his theorems and constructions propositions.
Geometry, Lesson 1.1 (grade 9–10)
theoretical probabilityEnglish
The probability found by reasoning about equally likely outcomes, without doing the experiment.
Pre-Algebra, Lesson 13.3 (grade 6–8)
The probability found by reasoning about equally likely outcomes, without doing the experiment.
Pre-Algebra, Lesson 13.3 (grade 6–8)
Third Angles TheoremEnglish
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Geometry, Lesson 4.2 (grade 9–10)
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Geometry, Lesson 4.2 (grade 9–10)
Third quartile (Q3)English
The median of the upper half of the ordered data. About three quarters of the values lie below it.
Statistics, Lesson 2.2 (grade 11–12)
The median of the upper half of the ordered data. About three quarters of the values lie below it.
Statistics, Lesson 2.2 (grade 11–12)
thousandthsEnglish
The third place to the right of the decimal point. One thousandth is one of 1,000 equal parts: 0.001 = \dfrac{1}{1000}.
Pre-Algebra, Lesson 4.1 (grade 6–8)
The third place to the right of the decimal point. One thousandth is one of 1,000 equal parts: 0.001 = \dfrac{1}{1000}.
Pre-Algebra, Lesson 4.1 (grade 6–8)
tipEnglish
Extra money, usually a percent of the bill, given to a server or worker for good service. Also called a gratuity.
Pre-Algebra, Lesson 8.5 (grade 6–8)
Extra money, usually a percent of the bill, given to a server or worker for good service. Also called a gratuity.
Pre-Algebra, Lesson 8.5 (grade 6–8)
toleranceEnglish
The amount a measurement is allowed to differ from its target value. A board cut to 36 inches with a tolerance of \dfrac{1}{8} inch must satisfy |L - 36| \le \dfrac{1}{8}.
Algebra I, Lesson 3.5 (grade 8–9) · Real Estate License Exam Prep: The National Exam, Lesson 6.2 (grade 9–12) · Electronics & Microcontrollers, Lesson 3.1 (grade 9–12) · +3 more
The amount a measurement is allowed to differ from its target value. A board cut to 36 inches with a tolerance of \dfrac{1}{8} inch must satisfy |L - 36| \le \dfrac{1}{8}.
Algebra I, Lesson 3.5 (grade 8–9) · Real Estate License Exam Prep: The National Exam, Lesson 6.2 (grade 9–12) · Electronics & Microcontrollers, Lesson 3.1 (grade 9–12) · +3 more
touches and turnsEnglish
The graph meets the x-axis at a zero but stays on the same side, like a parabola at its vertex. This happens at zeros of even multiplicity.
Algebra II, Lesson 4.7 (grade 10–11)
The graph meets the x-axis at a zero but stays on the same side, like a parabola at its vertex. This happens at zeros of even multiplicity.
Algebra II, Lesson 4.7 (grade 10–11)
transformationEnglish
A change that moves or reshapes a graph: a translation (slide), a reflection (flip), or a stretch or compression.
Algebra II, Lesson 1.2 (grade 10–11) · Geometry, Lesson 7.1 (grade 9–10)
A change that moves or reshapes a graph: a translation (slide), a reflection (flip), or a stretch or compression.
Algebra II, Lesson 1.2 (grade 10–11) · Geometry, Lesson 7.1 (grade 9–10)
Transitive Property of InequalityEnglish
If a > b and b > c, then a > c.
Geometry, Lesson 5.5 (grade 9–10)
If a > b and b > c, then a > c.
Geometry, Lesson 5.5 (grade 9–10)
translationEnglish
A slide of the whole graph up, down, left or right without changing its shape.
Algebra II, Lesson 1.2 (grade 10–11) · Grade 5 Geography: Explorers, Navigators and Missionaries, Lesson 6.1 (grade 5) · Grade 7 Geography: Regions of the World, Lesson 5.4 (grade 7) · +2 more
A slide of the whole graph up, down, left or right without changing its shape.
Algebra II, Lesson 1.2 (grade 10–11) · Grade 5 Geography: Explorers, Navigators and Missionaries, Lesson 6.1 (grade 5) · Grade 7 Geography: Regions of the World, Lesson 5.4 (grade 7) · +2 more
transversalEnglish
A line that intersects two or more coplanar lines at different points.
Geometry, Lesson 3.1 (grade 9–10) · Geometry, Lesson 8.5 (grade 9–10) · Pre-Algebra, Lesson 12.1 (grade 6–8)
A line that intersects two or more coplanar lines at different points.
Geometry, Lesson 3.1 (grade 9–10) · Geometry, Lesson 8.5 (grade 9–10) · Pre-Algebra, Lesson 12.1 (grade 6–8)
transverse axisEnglish
The segment joining the two vertices; it has length 2a and lies on the line through the foci.
Algebra II, Lesson 11.3 (grade 10–11)
The segment joining the two vertices; it has length 2a and lies on the line through the foci.
Algebra II, Lesson 11.3 (grade 10–11)
trapezoidEnglish
A quadrilateral with exactly one pair of parallel sides, called the bases; the other two sides are the legs. An isosceles trapezoid has congruent legs.
Geometry, Lesson 13.2 (grade 9–10) · Geometry, Lesson 6.5 (grade 9–10) · Pre-Algebra, Lesson 12.3 (grade 6–8)
A quadrilateral with exactly one pair of parallel sides, called the bases; the other two sides are the legs. An isosceles trapezoid has congruent legs.
Geometry, Lesson 13.2 (grade 9–10) · Geometry, Lesson 6.5 (grade 9–10) · Pre-Algebra, Lesson 12.3 (grade 6–8)
treatmentEnglish
A specific condition applied to the individuals in an experiment. With two or more factors, a treatment is a combination of one level of each factor.
Statistics, Lesson 5.4 (grade 11–12)
A specific condition applied to the individuals in an experiment. With two or more factors, a treatment is a combination of one level of each factor.
Statistics, Lesson 5.4 (grade 11–12)
tree diagramEnglish
A picture that shows every outcome of a several-stage choice as a path of branches; each first-stage branch splits into the options for the next stage.
Algebra II, Lesson 10.1 (grade 10–11) · Playing the Odds, Lesson 1.4 (grade 8–12) · Pre-Algebra, Lesson 13.4 (grade 6–8) · +1 more
A picture that shows every outcome of a several-stage choice as a path of branches; each first-stage branch splits into the options for the next stage.
Algebra II, Lesson 10.1 (grade 10–11) · Playing the Odds, Lesson 1.4 (grade 8–12) · Pre-Algebra, Lesson 13.4 (grade 6–8) · +1 more
Triangle Angle Bisector TheoremEnglish
An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides.
Geometry, Lesson 8.5 (grade 9–10)
An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides.
Geometry, Lesson 8.5 (grade 9–10)
Triangle Inequality TheoremEnglish
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Geometry, Lesson 5.6 (grade 9–10)
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Geometry, Lesson 5.6 (grade 9–10)
Triangle Proportionality Theorem (side-splitter)English
If a line parallel to one side of a triangle meets the other two sides at different points, it divides those sides proportionally.
Geometry, Lesson 8.5 (grade 9–10)
If a line parallel to one side of a triangle meets the other two sides at different points, it divides those sides proportionally.
Geometry, Lesson 8.5 (grade 9–10)
Trichotomy PropertyEnglish
For any two numbers a and b, exactly one of these is true: a < b, a = b, or a > b.
Geometry, Lesson 5.5 (grade 9–10)
For any two numbers a and b, exactly one of these is true: a < b, a = b, or a > b.
Geometry, Lesson 5.5 (grade 9–10)
trigonometric equationEnglish
An equation involving trigonometric functions that is true only for certain values of the variable, unlike an identity, which is true for every value.
Trigonometry, Lesson 6.4 (grade 11–12)
An equation involving trigonometric functions that is true only for certain values of the variable, unlike an identity, which is true for every value.
Trigonometry, Lesson 6.4 (grade 11–12)
trigonometric functionEnglish
A function that assigns to each angle \theta a number such as \sin\theta or \cos\theta, defined from a point on the terminal side of \theta.
Trigonometry, Lesson 3.6 (grade 11–12)
A function that assigns to each angle \theta a number such as \sin\theta or \cos\theta, defined from a point on the terminal side of \theta.
Trigonometry, Lesson 3.6 (grade 11–12)
Trigonometric ratioEnglish
One of the ratios \sin\theta, \cos\theta or \tan\theta of two sides of a right triangle; its value depends only on the acute angle \theta.
Algebra II, Lesson 13.1 (grade 10–11) · Geometry, Lesson 9.5 (grade 9–10)
One of the ratios \sin\theta, \cos\theta or \tan\theta of two sides of a right triangle; its value depends only on the acute angle \theta.
Algebra II, Lesson 13.1 (grade 10–11) · Geometry, Lesson 9.5 (grade 9–10)
trinomialEnglish
A polynomial with three terms, such as x^2 + 7x + 12.
Algebra I, Lesson 9.2 (grade 8–9)
A polynomial with three terms, such as x^2 + 7x + 12.
Algebra I, Lesson 9.2 (grade 8–9)
true bearingEnglish
A direction given as an angle measured clockwise from north, from 000^\circ up to (but not including) 360^\circ, written with three figures: east is 090^\circ, south is 180^\circ, west is 270^\circ. Also called a three-figure bearing.
Trigonometry, Lesson 8.2 (grade 11–12)
A direction given as an angle measured clockwise from north, from 000^\circ up to (but not including) 360^\circ, written with three figures: east is 090^\circ, south is 180^\circ, west is 270^\circ. Also called a three-figure bearing.
Trigonometry, Lesson 8.2 (grade 11–12)
turning pointEnglish
A point where a graph changes from rising to falling or from falling to rising; it is a relative maximum or relative minimum.
Algebra II, Lesson 4.1 (grade 10–11) · Grade 6 Composition & Creative Writing: Maxim, Refutation and Confirmation, Lesson 4.3 (grade 6) · Grade 8 Composition & Creative Writing: Comparison, Characterization and Description, Lesson 2.2 (grade 8) · +3 more
A point where a graph changes from rising to falling or from falling to rising; it is a relative maximum or relative minimum.
Algebra II, Lesson 4.1 (grade 10–11) · Grade 6 Composition & Creative Writing: Maxim, Refutation and Confirmation, Lesson 4.3 (grade 6) · Grade 8 Composition & Creative Writing: Comparison, Characterization and Description, Lesson 2.2 (grade 8) · +3 more
two-column proofEnglish
A proof written as numbered statements in the left column with a reason for each in the right column, starting from the given information and ending with the statement to be proved.
Geometry, Lesson 1.5 (grade 9–10) · Geometry, Lesson 2.6 (grade 9–10)
A proof written as numbered statements in the left column with a reason for each in the right column, starting from the given information and ending with the statement to be proved.
Geometry, Lesson 1.5 (grade 9–10) · Geometry, Lesson 2.6 (grade 9–10)
Two-observation methodEnglish
Finding a height whose base cannot be reached by measuring angles of elevation from two points a known distance apart in line with the object.
Geometry, Lesson 9.7 (grade 9–10)
Finding a height whose base cannot be reached by measuring angles of elevation from two points a known distance apart in line with the object.
Geometry, Lesson 9.7 (grade 9–10)
Two-proportion z intervalEnglish
A confidence interval for p_1 - p_2: the observed difference plus or minus z^* times the unpooled standard error.
Statistics, Lesson 12.1 (grade 11–12)
A confidence interval for p_1 - p_2: the observed difference plus or minus z^* times the unpooled standard error.
Statistics, Lesson 12.1 (grade 11–12)
Two-proportion z testEnglish
A significance test of H_0: p_1 = p_2 that measures how many standard errors the observed difference \hat{p}_1 - \hat{p}_2 is from 0, using the pooled standard error.
Statistics, Lesson 12.1 (grade 11–12)
A significance test of H_0: p_1 = p_2 that measures how many standard errors the observed difference \hat{p}_1 - \hat{p}_2 is from 0, using the pooled standard error.
Statistics, Lesson 12.1 (grade 11–12)
Two-sample problemEnglish
A study that compares two populations or two treatments using two separate, independent groups (two random samples, or two groups formed by random assignment).
Statistics, Lesson 12.1 (grade 11–12)
A study that compares two populations or two treatments using two separate, independent groups (two random samples, or two groups formed by random assignment).
Statistics, Lesson 12.1 (grade 11–12)
Two-sample t intervalEnglish
A confidence interval for \mu_1 - \mu_2: (\bar{x}_1 - \bar{x}_2) \pm t^* \cdot SE.
Statistics, Lesson 12.2 (grade 11–12)
A confidence interval for \mu_1 - \mu_2: (\bar{x}_1 - \bar{x}_2) \pm t^* \cdot SE.
Statistics, Lesson 12.2 (grade 11–12)
Two-sample t testEnglish
A significance test of H_0: \mu_1 = \mu_2 using t = \dfrac{\bar{x}_1 - \bar{x}_2}{SE}.
Statistics, Lesson 12.2 (grade 11–12)
A significance test of H_0: \mu_1 = \mu_2 using t = \dfrac{\bar{x}_1 - \bar{x}_2}{SE}.
Statistics, Lesson 12.2 (grade 11–12)
two-sided P-valueEnglish
For H_a: p \ne p_0, the probability of a result at least as far from p_0 as the observed one in EITHER direction; it is twice the area in one tail.
Statistics, Lesson 11.2 (grade 11–12)
For H_a: p \ne p_0, the probability of a result at least as far from p_0 as the observed one in EITHER direction; it is twice the area in one tail.
Statistics, Lesson 11.2 (grade 11–12)
two-step equationEnglish
An equation that takes two inverse operations to solve, such as 3x + 5 = 26 (subtract 5, then divide by 3).
Pre-Algebra, Lesson 10.4 (grade 6–8)
An equation that takes two inverse operations to solve, such as 3x + 5 = 26 (subtract 5, then divide by 3).
Pre-Algebra, Lesson 10.4 (grade 6–8)
Two-way tableEnglish
A table of counts that classifies individuals by two categorical variables at once: one variable for the rows and one for the columns, with totals in the margins.
Statistics, Lesson 1.3 (grade 11–12)
A table of counts that classifies individuals by two categorical variables at once: one variable for the rows and one for the columns, with totals in the margins.
Statistics, Lesson 1.3 (grade 11–12)
Type I errorEnglish
Rejecting H_0 when H_0 is actually true: a false alarm. Its probability is \alpha.
Statistics, Lesson 11.4 (grade 11–12)
Rejecting H_0 when H_0 is actually true: a false alarm. Its probability is \alpha.
Statistics, Lesson 11.4 (grade 11–12)
Type II errorEnglish
Failing to reject H_0 when H_0 is actually false: a missed effect. Its probability is called \beta.
Statistics, Lesson 11.4 (grade 11–12)
Failing to reject H_0 when H_0 is actually false: a missed effect. Its probability is called \beta.
Statistics, Lesson 11.4 (grade 11–12)
U
Unbiased estimatorEnglish
A statistic whose sampling distribution has its mean (center) exactly equal to the parameter it estimates. It does not systematically overestimate or underestimate.
Statistics, Lesson 9.1 (grade 11–12)
A statistic whose sampling distribution has its mean (center) exactly equal to the parameter it estimates. It does not systematically overestimate or underestimate.
Statistics, Lesson 9.1 (grade 11–12)
undefinedEnglish
Having no value. A slope is undefined when the run is 0, because we cannot divide by 0.
Pre-Algebra, Lesson 11.4 (grade 6–8) · Pre-Algebra, Lesson 5.5 (grade 6–8) · Trigonometry, Lesson 3.6 (grade 11–12)
Having no value. A slope is undefined when the run is 0, because we cannot divide by 0.
Pre-Algebra, Lesson 11.4 (grade 6–8) · Pre-Algebra, Lesson 5.5 (grade 6–8) · Trigonometry, Lesson 3.6 (grade 11–12)
undefined slopeEnglish
The slope of a vertical line. The run is 0, and we cannot divide by 0, so the slope is not a number.
Algebra I, Lesson 5.1 (grade 8–9)
The slope of a vertical line. The run is 0, and we cannot divide by 0, so the slope is not a number.
Algebra I, Lesson 5.1 (grade 8–9)
undefined termEnglish
A basic word, such as point, line or plane, that is described and pictured but not defined, because every definition must use other words, and we have to start somewhere.
Geometry, Lesson 1.1 (grade 9–10)
A basic word, such as point, line or plane, that is described and pictured but not defined, because every definition must use other words, and we have to start somewhere.
Geometry, Lesson 1.1 (grade 9–10)
undefined termsEnglish
The words point, line and plane. They are not defined; they are described, and their behavior is fixed by the postulates. Every other geometric word is defined from them.
Geometry, Lesson 2.1 (grade 9–10)
The words point, line and plane. They are not defined; they are described, and their behavior is fixed by the postulates. Every other geometric word is defined from them.
Geometry, Lesson 2.1 (grade 9–10)
undercoverageEnglish
When some groups in the population have no chance to be in the sample, often because the list used to choose the sample leaves them out.
Statistics, Lesson 5.3 (grade 11–12)
When some groups in the population have no chance to be in the sample, often because the list used to choose the sample leaves them out.
Statistics, Lesson 5.3 (grade 11–12)
Uniform distributionEnglish
A distribution whose density curve is flat (a rectangle): every interval of the same width has the same proportion of values.
Statistics, Lesson 3.2 (grade 11–12)
A distribution whose density curve is flat (a rectangle): every interval of the same width has the same proportion of values.
Statistics, Lesson 3.2 (grade 11–12)
union ("or")English
The numbers that make AT LEAST ONE of the inequalities true. Its graph includes everything shaded in either graph.
Algebra I, Lesson 3.3 (grade 8–9)
The numbers that make AT LEAST ONE of the inequalities true. Its graph includes everything shaded in either graph.
Algebra I, Lesson 3.3 (grade 8–9)
unit cancelingEnglish
Crossing out a unit that appears on both the top and the bottom of a product of fractions, just as you cancel a common factor.
Pre-Algebra, Lesson 7.5 (grade 6–8)
Crossing out a unit that appears on both the top and the bottom of a product of fractions, just as you cancel a common factor.
Pre-Algebra, Lesson 7.5 (grade 6–8)
Unit circleEnglish
The circle of radius 1 centered at the origin, x^2 + y^2 = 1. The terminal side of an angle \theta meets it at the point (\cos\theta, \sin\theta).
Algebra II, Lesson 13.2 (grade 10–11) · Trigonometry, Lesson 3.6 (grade 11–12)
The circle of radius 1 centered at the origin, x^2 + y^2 = 1. The terminal side of an angle \theta meets it at the point (\cos\theta, \sin\theta).
Algebra II, Lesson 13.2 (grade 10–11) · Trigonometry, Lesson 3.6 (grade 11–12)
unit fractionEnglish
A fraction with numerator 1, like \dfrac{1}{5}. It names just one of the equal parts.
Pre-Algebra, Lesson 3.1 (grade 6–8)
A fraction with numerator 1, like \dfrac{1}{5}. It names just one of the equal parts.
Pre-Algebra, Lesson 3.1 (grade 6–8)
unit rateEnglish
A rate for one unit of the input, such as dollars per pound or miles per hour. In a direct variation the unit rate is k.
Algebra I, Lesson 5.2 (grade 8–9) · Pre-Algebra, Lesson 7.2 (grade 6–8)
A rate for one unit of the input, such as dollars per pound or miles per hour. In a direct variation the unit rate is k.
Algebra I, Lesson 5.2 (grade 8–9) · Pre-Algebra, Lesson 7.2 (grade 6–8)
unit vectorEnglish
A vector of length 1. Dividing any nonzero vector by its magnitude gives the unit vector in the same direction.
Algebra II, Lesson 12.5 (grade 10–11) · Trigonometry, Lesson 9.4 (grade 11–12)
A vector of length 1. Dividing any nonzero vector by its magnitude gives the unit vector in the same direction.
Algebra II, Lesson 12.5 (grade 10–11) · Trigonometry, Lesson 9.4 (grade 11–12)
unknown sideEnglish
The side whose length the problem asks you to find.
Trigonometry, Lesson 1.3 (grade 11–12)
The side whose length the problem asks you to find.
Trigonometry, Lesson 1.3 (grade 11–12)
unlike fractionsEnglish
Fractions with different denominators, like \dfrac{1}{4} and \dfrac{2}{3}.
Pre-Algebra, Lesson 3.3 (grade 6–8)
Fractions with different denominators, like \dfrac{1}{4} and \dfrac{2}{3}.
Pre-Algebra, Lesson 3.3 (grade 6–8)
unlike radicalsEnglish
Radicals with different radicands (after simplifying), such as \sqrt{2} and \sqrt{3}. Their sum cannot be written as a single term.
Algebra I, Lesson 10.3 (grade 8–9)
Radicals with different radicands (after simplifying), such as \sqrt{2} and \sqrt{3}. Their sum cannot be written as a single term.
Algebra I, Lesson 10.3 (grade 8–9)
unlike termsEnglish
Terms whose variable parts are different, such as 3x and 3y, or x and x^2.
Pre-Algebra, Lesson 9.4 (grade 6–8)
Terms whose variable parts are different, such as 3x and 3y, or x and x^2.
Pre-Algebra, Lesson 9.4 (grade 6–8)
UnstandardizingEnglish
Turning a z-score back into the original units with x = \mu + z\sigma: start at the mean and step z standard deviations.
Statistics, Lesson 3.5 (grade 11–12)
Turning a z-score back into the original units with x = \mu + z\sigma: start at the mean and step z standard deviations.
Statistics, Lesson 3.5 (grade 11–12)
U-shaped branchEnglish
One piece of a cosecant or secant graph: it touches the guide graph at a peak or trough and rises (or falls) toward two asymptotes.
Trigonometry, Lesson 4.7 (grade 11–12)
One piece of a cosecant or secant graph: it touches the guide graph at a peak or trough and rises (or falls) toward two asymptotes.
Trigonometry, Lesson 4.7 (grade 11–12)
V
valid argumentEnglish
An argument in which the conclusion must be true whenever all the premises are true. Validity depends on the form of the argument, not on whether the premises are actually true.
Geometry, Lesson 1.4 (grade 9–10)
An argument in which the conclusion must be true whenever all the premises are true. Validity depends on the form of the argument, not on whether the premises are actually true.
Geometry, Lesson 1.4 (grade 9–10)
value of an expressionEnglish
The single number you get after you evaluate it.
Pre-Algebra, Lesson 9.2 (grade 6–8)
The single number you get after you evaluate it.
Pre-Algebra, Lesson 9.2 (grade 6–8)
Variability of a statisticEnglish
The spread of its sampling distribution: how far the statistic typically lands from sample to sample. Larger random samples give smaller variability.
Statistics, Lesson 9.1 (grade 11–12)
The spread of its sampling distribution: how far the statistic typically lands from sample to sample. Larger random samples give smaller variability.
Statistics, Lesson 9.1 (grade 11–12)
VariableEnglish
A letter that stands for a number, either one we do not know yet or one that can change.
Algebra I, Lesson 1.5 (grade 8–9) · Grade 6 Cooking & Food, Lesson 2.3 (grade 6) · Electronics & Microcontrollers, Lesson 7.2 (grade 9–12) · +3 more
A letter that stands for a number, either one we do not know yet or one that can change.
Algebra I, Lesson 1.5 (grade 8–9) · Grade 6 Cooking & Food, Lesson 2.3 (grade 6) · Electronics & Microcontrollers, Lesson 7.2 (grade 9–12) · +3 more
variables on both sidesEnglish
An equation such as 5x + 2 = 2x + 14, where the variable appears on the left side and on the right side.
Pre-Algebra, Lesson 10.5 (grade 6–8)
An equation such as 5x + 2 = 2x + 14, where the variable appears on the left side and on the right side.
Pre-Algebra, Lesson 10.5 (grade 6–8)
Variance of a random variableEnglish
The probability-weighted average of the squared deviations from the mean, written \sigma_X^2.
Statistics, Lesson 7.2 (grade 11–12)
The probability-weighted average of the squared deviations from the mean, written \sigma_X^2.
Statistics, Lesson 7.2 (grade 11–12)
Variance s^2English
The sum of the squared deviations divided by n − 1: roughly the average squared distance from the mean. Its units are squared units.
Statistics, Lesson 2.4 (grade 11–12)
The sum of the squared deviations divided by n − 1: roughly the average squared distance from the mean. Its units are squared units.
Statistics, Lesson 2.4 (grade 11–12)
vectorEnglish
A quantity with both size and direction, drawn as an arrow and written by its components, such as \mathbf{u} = \langle 3, 1 \rangle (3 right, 1 up). More generally, any ordered list of numbers \langle u_1, u_2, \ldots, u_n \rangle.
Algebra II, Lesson 12.5 (grade 10–11) · Physics, Lesson 1.5 (grade 11–12) · Grade 4 Gardening & Animals, Lesson 8.1 (grade 4) · +3 more
A quantity with both size and direction, drawn as an arrow and written by its components, such as \mathbf{u} = \langle 3, 1 \rangle (3 right, 1 up). More generally, any ordered list of numbers \langle u_1, u_2, \ldots, u_n \rangle.
Algebra II, Lesson 12.5 (grade 10–11) · Physics, Lesson 1.5 (grade 11–12) · Grade 4 Gardening & Animals, Lesson 8.1 (grade 4) · +3 more
Venn diagramEnglish
A drawing that shows sets as circles; “all A are B” is shown by drawing the circle for A inside the circle for B.
Geometry, Lesson 1.4 (grade 9–10) · Statistics, Lesson 6.2 (grade 11–12)
A drawing that shows sets as circles; “all A are B” is shown by drawing the circle for A inside the circle for B.
Geometry, Lesson 1.4 (grade 9–10) · Statistics, Lesson 6.2 (grade 11–12)
vertexEnglish
The turning point of a parabola: its lowest point if it opens up, its highest point if it opens down.
Algebra I, Lesson 11.1 (grade 8–9) · Algebra II, Lesson 11.1 (grade 10–11) · Algebra II, Lesson 3.1 (grade 10–11)
The turning point of a parabola: its lowest point if it opens up, its highest point if it opens down.
Algebra I, Lesson 11.1 (grade 8–9) · Algebra II, Lesson 11.1 (grade 10–11) · Algebra II, Lesson 3.1 (grade 10–11)
Vertex angleEnglish
The angle formed by the two legs of an isosceles triangle; it lies opposite the base.
Geometry, Lesson 4.6 (grade 9–10)
The angle formed by the two legs of an isosceles triangle; it lies opposite the base.
Geometry, Lesson 4.6 (grade 9–10)
vertex (corner point)English
A point where two boundary lines meet on the edge of the solution region.
Algebra II, Lesson 2.2 (grade 10–11)
A point where two boundary lines meet on the edge of the solution region.
Algebra II, Lesson 2.2 (grade 10–11)
vertex formEnglish
y = a(x - h)^2 + k with a \ne 0; the vertex is (h, k).
Algebra I, Lesson 11.7 (grade 8–9) · Algebra II, Lesson 3.1 (grade 10–11)
y = a(x - h)^2 + k with a \ne 0; the vertex is (h, k).
Algebra I, Lesson 11.7 (grade 8–9) · Algebra II, Lesson 3.1 (grade 10–11)
vertical anglesEnglish
Two angles whose sides form two pairs of opposite rays. When two lines cross, they form two pairs of vertical angles.
Geometry, Lesson 2.4 (grade 9–10) · Pre-Algebra, Lesson 12.1 (grade 6–8)
Two angles whose sides form two pairs of opposite rays. When two lines cross, they form two pairs of vertical angles.
Geometry, Lesson 2.4 (grade 9–10) · Pre-Algebra, Lesson 12.1 (grade 6–8)
vertical asymptoteEnglish
A vertical line x = h that the graph approaches as its values grow without bound (toward \infty or -\infty) when x gets close to h.
Algebra II, Lesson 5.3 (grade 10–11) · Algebra II, Lesson 8.2 (grade 10–11) · Trigonometry, Lesson 4.6 (grade 11–12)
A vertical line x = h that the graph approaches as its values grow without bound (toward \infty or -\infty) when x gets close to h.
Algebra II, Lesson 5.3 (grade 10–11) · Algebra II, Lesson 8.2 (grade 10–11) · Trigonometry, Lesson 4.6 (grade 11–12)
vertical lineEnglish
An up-and-down line x = h; every point on it has the same x-coordinate h, and its slope is undefined.
Algebra I, Lesson 5.5 (grade 8–9) · Grade 1 Art, Lesson 1.2 (grade 1)
An up-and-down line x = h; every point on it has the same x-coordinate h, and its slope is undefined.
Algebra I, Lesson 5.5 (grade 8–9) · Grade 1 Art, Lesson 1.2 (grade 1)
vertical line testEnglish
A graph is a function exactly when no vertical line crosses the graph at more than one point.
Algebra I, Lesson 4.2 (grade 8–9)
A graph is a function exactly when no vertical line crosses the graph at more than one point.
Algebra I, Lesson 4.2 (grade 8–9)
vertical shiftEnglish
The number d in y = a\sin(b(x - c)) + d, which moves the whole graph up (d > 0) or down (d < 0).
Trigonometry, Lesson 4.4 (grade 11–12)
The number d in y = a\sin(b(x - c)) + d, which moves the whole graph up (d > 0) or down (d < 0).
Trigonometry, Lesson 4.4 (grade 11–12)
vertical stretchEnglish
Multiplying the output of a function by a constant, which stretches the graph away from (or shrinks it toward) the x-axis.
Trigonometry, Lesson 4.3 (grade 11–12)
Multiplying the output of a function by a constant, which stretches the graph away from (or shrinks it toward) the x-axis.
Trigonometry, Lesson 4.3 (grade 11–12)
vertical stretch or compressionEnglish
Multiplying every output by a positive number a: a stretch away from the x-axis if a > 1, a compression toward it if 0 < a < 1.
Algebra II, Lesson 1.2 (grade 10–11)
Multiplying every output by a positive number a: a stretch away from the x-axis if a > 1, a compression toward it if 0 < a < 1.
Algebra II, Lesson 1.2 (grade 10–11)
Volume PostulatesEnglish
Every solid has a unique positive volume; congruent solids have equal volumes; the volume of a solid is the sum of the volumes of nonoverlapping parts; a rectangular box with length \ell, width w and height h has volume \ell wh.
Geometry, Lesson 12.4 (grade 9–10)
Every solid has a unique positive volume; congruent solids have equal volumes; the volume of a solid is the sum of the volumes of nonoverlapping parts; a rectangular box with length \ell, width w and height h has volume \ell wh.
Geometry, Lesson 12.4 (grade 9–10)
voluntary response sampleEnglish
A sample made of people who choose themselves by answering a general invitation, such as a call-in radio question, a comment box or a website poll. People with strong opinions are overrepresented.
Statistics, Lesson 5.1 (grade 11–12)
A sample made of people who choose themselves by answering a general invitation, such as a call-in radio question, a comment box or a website poll. People with strong opinions are overrepresented.
Statistics, Lesson 5.1 (grade 11–12)
W
Weighted meanEnglish
A mean in which each value counts according to its weight (how many items or how much importance it carries): multiply each value by its weight, add, and divide by the total weight.
Statistics, Lesson 2.1 (grade 11–12)
A mean in which each value counts according to its weight (how many items or how much importance it carries): multiply each value by its weight, add, and divide by the total weight.
Statistics, Lesson 2.1 (grade 11–12)
wholeEnglish
The full amount you are comparing to. The whole is always 100%.
Pre-Algebra, Lesson 8.1 (grade 6–8) · Pre-Algebra, Lesson 8.3 (grade 6–8)
The full amount you are comparing to. The whole is always 100%.
Pre-Algebra, Lesson 8.1 (grade 6–8) · Pre-Algebra, Lesson 8.3 (grade 6–8)
Whole numbersEnglish
The natural numbers together with zero: 0, 1, 2, 3, and so on.
Algebra I, Lesson 1.1 (grade 8–9)
The natural numbers together with zero: 0, 1, 2, 3, and so on.
Algebra I, Lesson 1.1 (grade 8–9)
within c of aEnglish
At a distance of at most c (or less than c) from the number a; written |x - a| \le c (or |x - a| < c).
Algebra I, Lesson 3.5 (grade 8–9)
At a distance of at most c (or less than c) from the number a; written |x - a| \le c (or |x - a| < c).
Algebra I, Lesson 3.5 (grade 8–9)
without replacementEnglish
Choosing items one after another without putting them back, so each choice changes what is left for the next one.
Statistics, Lesson 6.3 (grade 11–12)
Choosing items one after another without putting them back, so each choice changes what is left for the next one.
Statistics, Lesson 6.3 (grade 11–12)
wording biasEnglish
Bias caused by the way a question is asked: leading or loaded words, confusing phrasing, or asking about two things at once.
Statistics, Lesson 5.3 (grade 11–12)
Bias caused by the way a question is asked: leading or loaded words, confusing phrasing, or asking about two things at once.
Statistics, Lesson 5.3 (grade 11–12)
work rateEnglish
The fraction of a job done in one unit of time. Someone who finishes a job in 6 hours alone has a work rate of \dfrac{1}{6} of the job per hour.
Algebra I, Lesson 12.5 (grade 8–9) · Algebra II, Lesson 5.5 (grade 10–11)
The fraction of a job done in one unit of time. Someone who finishes a job in 6 hours alone has a work rate of \dfrac{1}{6} of the job per hour.
Algebra I, Lesson 12.5 (grade 8–9) · Algebra II, Lesson 5.5 (grade 10–11)
X
x-axis and y-axisEnglish
The x-axis is the horizontal (left-right) number line. The y-axis is the vertical (up-down) number line.
Pre-Algebra, Lesson 11.1 (grade 6–8)
The x-axis is the horizontal (left-right) number line. The y-axis is the vertical (up-down) number line.
Pre-Algebra, Lesson 11.1 (grade 6–8)
x-interceptEnglish
A point where a graph crosses or touches the x-axis; its y-coordinate is 0.
Algebra I, Lesson 11.3 (grade 8–9) · Algebra I, Lesson 5.5 (grade 8–9) · Pre-Algebra, Lesson 11.3 (grade 6–8)
A point where a graph crosses or touches the x-axis; its y-coordinate is 0.
Algebra I, Lesson 11.3 (grade 8–9) · Algebra I, Lesson 5.5 (grade 8–9) · Pre-Algebra, Lesson 11.3 (grade 6–8)
Y
y-interceptEnglish
The point where the graph crosses the y-axis; for y = ax^2 + bx + c it is (0, c).
Algebra I, Lesson 11.2 (grade 8–9) · Algebra I, Lesson 5.3 (grade 8–9) · Algebra I, Lesson 5.5 (grade 8–9) · +1 more
The point where the graph crosses the y-axis; for y = ax^2 + bx + c it is (0, c).
Algebra I, Lesson 11.2 (grade 8–9) · Algebra I, Lesson 5.3 (grade 8–9) · Algebra I, Lesson 5.5 (grade 8–9) · +1 more
Z
zeroEnglish
An input that makes the function equal 0. The real zeros are the x-coordinates of the x-intercepts.
Algebra II, Lesson 3.1 (grade 10–11) · Trigonometry, Lesson 4.1 (grade 11–12)
An input that makes the function equal 0. The real zeros are the x-coordinates of the x-intercepts.
Algebra II, Lesson 3.1 (grade 10–11) · Trigonometry, Lesson 4.1 (grade 11–12)
zero exponentEnglish
For any nonzero number a, a^0 = 1.
Algebra I, Lesson 7.2 (grade 8–9) · Pre-Algebra, Lesson 6.2 (grade 6–8)
For any nonzero number a, a^0 = 1.
Algebra I, Lesson 7.2 (grade 8–9) · Pre-Algebra, Lesson 6.2 (grade 6–8)
zero matrixEnglish
A matrix whose entries are all 0, written O. Adding it to a matrix of the same size changes nothing.
Algebra II, Lesson 12.1 (grade 10–11)
A matrix whose entries are all 0, written O. Adding it to a matrix of the same size changes nothing.
Algebra II, Lesson 12.1 (grade 10–11)
zero of a polynomialEnglish
A number c with f(c) = 0. Real zeros are the x-intercepts of the graph and the solutions of f(x) = 0.
Algebra II, Lesson 4.5 (grade 10–11)
A number c with f(c) = 0. Real zeros are the x-intercepts of the graph and the solutions of f(x) = 0.
Algebra II, Lesson 4.5 (grade 10–11)
zero of a rational functionEnglish
An x-value where the function equals 0; after simplifying, these are the zeros of the numerator. Each gives an x-intercept.
Algebra II, Lesson 5.4 (grade 10–11)
An x-value where the function equals 0; after simplifying, these are the zeros of the numerator. Each gives an x-intercept.
Algebra II, Lesson 5.4 (grade 10–11)
Zero Product PropertyEnglish
If a product of numbers is 0, then at least one of the factors is 0.
Algebra II, Lesson 3.2 (grade 10–11)
If a product of numbers is 0, then at least one of the factors is 0.
Algebra II, Lesson 3.2 (grade 10–11)
zero property of multiplicationEnglish
Any number times 0 equals 0.
Pre-Algebra, Lesson 1.2 (grade 6–8)
Any number times 0 equals 0.
Pre-Algebra, Lesson 1.2 (grade 6–8)
zero-product propertyEnglish
If the product of two numbers is 0, then at least one of the numbers is 0: if ab = 0, then a = 0 or b = 0.
Algebra I, Lesson 9.6 (grade 8–9) · Trigonometry, Lesson 6.5 (grade 11–12)
If the product of two numbers is 0, then at least one of the numbers is 0: if ab = 0, then a = 0 or b = 0.
Algebra I, Lesson 9.6 (grade 8–9) · Trigonometry, Lesson 6.5 (grade 11–12)
zeros of a functionEnglish
The input values that make the output 0; for a quadratic they are the x-intercepts of its graph.
Algebra I, Lesson 11.7 (grade 8–9)
The input values that make the output 0; for a quadratic they are the x-intercepts of its graph.
Algebra I, Lesson 11.7 (grade 8–9)
z-scoreEnglish
The number of standard deviations a value lies above (positive) or below (negative) the mean: z = \dfrac{x - \text{mean}}{\text{standard deviation}}.
Statistics, Lesson 3.1 (grade 11–12)
The number of standard deviations a value lies above (positive) or below (negative) the mean: z = \dfrac{x - \text{mean}}{\text{standard deviation}}.
Statistics, Lesson 3.1 (grade 11–12)