Algebra I check: ready for Geometry?

For students who finished Algebra I (usually grades 8–9) or are deciding whether to start Geometry.

14 items drawn from the Algebra I final exam. About 30–40 minutes. Paper and pencil, no calculator unless an item says so. Work every item first, then check each answer and mark it.

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1. Simplify 2(3x - 4) - (5x - 9) + x.

Answer: 6x - 8 - 5x + 9 + x = 2x + 1
Lesson 1.4 Simplifying Expressions

2. Henry has $240 saved and adds $35 each week. After how many weeks will he have $660 saved?

Answer: 240 + 35w = 660, so 35w = 420 and w = 12: 12 weeks
Lesson 2.6 Problem Solving with Linear Equations

3. Solve |2x + 5| > 9.

Answer: 2x + 5 > 9 or 2x + 5 < -9, so x > 2 or x < -7
Lesson 3.5 Absolute Value Inequalities

4. If f(x) = 5 - 3x, solve f(x) = -16.

Answer: 5 - 3x = -16, so -3x = -21 and x = 7
Lesson 4.3 Function Notation

5. Write an equation in slope-intercept form for the line through (-2, 3) that is parallel to 2x + 5y = 10.

Answer: The slope of 2x + 5y = 10 is -\dfrac{2}{5}; y - 3 = -\dfrac{2}{5}(x + 2), so y = -\dfrac{2}{5}x + \dfrac{11}{5}
Lesson 5.6 Parallel and Perpendicular Lines

6. Solve by elimination: 4x + 3y = 6 and 2x - 3y = 12.

Answer: Add: 6x = 18, x = 3; then 12 + 3y = 6, y = -2. Solution (3, -2).
Lesson 6.3 Solving Systems by Elimination

7. The Miller farm mixes a feed that is 10% protein with a feed that is 25% protein to make 300 pounds of feed that is 15% protein. How many pounds of each feed do they use?

Answer: x + y = 300 and 0.10x + 0.25y = 45; substituting y = 300 - x gives -0.15x + 75 = 45, so x = 200 and y = 100: 200 pounds of the 10% feed and 100 pounds of the 25% feed
Lesson 6.5 Applications of Systems

8. By hand: simplify \dfrac{6a^{-2}b^5}{3a^4b^{-1}} so that all exponents are positive.

Answer: 2a^{-6}b^{6} = \dfrac{2b^6}{a^6}
Lesson 7.2 Zero and Negative Exponents

9. Subtract: (5x^2 - 3x + 8) - (2x^2 + 4x - 6).

Answer: 5x^2 - 3x + 8 - 2x^2 - 4x + 6 = 3x^2 - 7x + 14
Lesson 8.1 Polynomials and Their Terms

10. Factor 6x^2 + 7x - 20.

Answer: ac = -120; use 15 and -8: 6x^2 + 15x - 8x - 20 = 3x(2x + 5) - 4(2x + 5) = (3x - 4)(2x + 5)
Lesson 9.3 Factoring ax² + bx + c

11. By hand: simplify 3\sqrt{20} - \sqrt{45} + \sqrt{80}.

Answer: 6\sqrt{5} - 3\sqrt{5} + 4\sqrt{5} = 7\sqrt{5}
Lesson 10.3 Operations with Radical Expressions

12. For y = 2x^2 - 12x + 7, find the vertex and the axis of symmetry, and say whether the vertex is a maximum or a minimum.

Answer: x = -\dfrac{-12}{2(2)} = 3 and y = 18 - 36 + 7 = -11: vertex (3, -11), axis x = 3; since a = 2 > 0 the parabola opens up, so -11 is a minimum.
Lesson 11.2 Graphing y = ax² + bx + c

13. Simplify \dfrac{x^2 - 9}{x^2 + x - 6} and state the excluded values.

Answer: \dfrac{(x - 3)(x + 3)}{(x + 3)(x - 2)} = \dfrac{x - 3}{x - 2}, with x \ne -3 and x \ne 2
Lesson 12.2 Simplifying Rational Expressions

14. Henry measures a young sunflower and draws a line of fit on a scatter plot of day x and height y in centimeters. The line passes through (2, 15) and (10, 55). (a) Write the equation of the line of fit. (b) Use it to predict the height on day 14.

Answer: (a) m = \dfrac{55 - 15}{10 - 2} = 5 and b = 15 - 10 = 5, so y = 5x + 5 (b) y = 5(14) + 5 = 75 centimeters
Lesson 13.2 Lines of Best Fit

4-week summer review path

Four short days a week, 30–45 minutes: the 16 Algebra I lessons that appear most often on its exams and reviews, in course order. Do the lessons you missed on the test first.

Algebra I check: ready for Geometry?

4-week summer review path

Week 1

Week 2

Week 3

Week 4