Pre-Algebra check: ready for Algebra I?

For students who finished Pre-Algebra (usually grades 6–8) or are deciding whether to start Algebra I.

14 items drawn from the Pre-Algebra 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.

Print test with answer key

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1. By hand, evaluate 4 + 6 \times (9 - 5)^2 \div 3.

Answer: 4 + 6 \times 16 \div 3 = 4 + 96 \div 3 = 4 + 32 = 36
Lesson 1.4 Order of Operations

2. By hand, use prime factorization to find the GCF and the LCM of 45 and 75.

Answer: 45 = 3^2 \cdot 5 and 75 = 3 \cdot 5^2, so GCF 3 \cdot 5 = 15, LCM 3^2 \cdot 5^2 = 225
Lesson 2.6 Least Common Multiple

3. By hand: Hannah has 3\tfrac{3}{4} yards of fabric. She uses 1\tfrac{1}{2} yards for an apron and \dfrac{5}{8} yard for a pillow. How much fabric is left?

Answer: \dfrac{30}{8} - \dfrac{12}{8} - \dfrac{5}{8} = \dfrac{13}{8} = 1\tfrac{5}{8} yards
Lesson 3.7 Fraction Word Problems

4. By hand, write \dfrac{7}{40} as a decimal.

Answer: 0.175 (it terminates because 40 = 2^3 \cdot 5)
Lesson 4.5 Fractions and Decimals

5. Explain why 8 \div 0 is undefined. Use the fact that division undoes multiplication.

Answer: If 8 \div 0 equaled some number q, then q \times 0 would have to equal 8. But any number times 0 is 0, never 8. No number works, so 8 \div 0 is undefined.
Lesson 5.5 Dividing Integers

6. By hand, evaluate -3(4 - 9) + (-12) \div 4.

Answer: -3(-5) + (-3) = 15 - 3 = 12
Lesson 5.6 Operations with Rational Numbers

7. Write 0.00052 in scientific notation.

Answer: 5.2 \times 10^{-4}
Lesson 6.3 Scientific Notation

8. An 18-ounce box of oats costs $3.42, and a 28-ounce box costs $5.04. Which box is the better buy, and what is its unit price?

Answer: The 28-ounce box, at $0.18 per ounce (the 18-ounce box is $0.19 per ounce)
Lesson 7.2 Rates and Unit Rates

9. 18 is what percent of 72?

Answer: 18 \div 72 = 0.25 = 25\%
Lesson 8.3 Percent Equations and Proportions

10. Evaluate 3x^2 - 2x + 5 when x = -2.

Answer: 3(4) - 2(-2) + 5 = 12 + 4 + 5 = 21
Lesson 9.2 Evaluating Expressions

11. Solve 5x - 7 = 38 and check your solution.

Answer: x = 9 (check: 5(9) - 7 = 38)
Lesson 10.4 Two-Step Equations

12. Find the slope of the line through (-2, 5) and (4, -7).

Answer: \dfrac{-7 - 5}{4 - (-2)} = \dfrac{-12}{6} = -2
Lesson 11.4 Slope

13. Find the measure of each interior angle of a regular nonagon (9 sides).

Answer: (9 - 2) \times 180^\circ = 1260^\circ, and 1260^\circ \div 9 = 140^\circ
Lesson 12.2 Triangles and Polygons

14. Grace's first four test scores are 82, 91, 76 and 87. What score does she need on the fifth test to have a mean of 85?

Answer: The five scores must total 85 \times 5 = 425. The first four total 336, and 425 - 336 = 89, so a score of 89
Lesson 13.1 Mean, Median, Mode and Range

4-week summer review path

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

Pre-Algebra check: ready for Algebra I?

4-week summer review path

Week 1

Week 2

Week 3

Week 4