Free 7th Grade Math Placement Test

Check proportional reasoning, rational numbers, equations, probability, geometry, and percent applications.

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Skills this preview checks

• proportions
• rational numbers
• equations
• probability
• geometry
• percent

All 6 questions with answers

1. A map uses 1 inch for 12 miles. Two towns are 3.5 inches apart. What is the actual distance?

   1. 15.5 miles
   2. 36 miles
   3. 48 miles
   4. 42 miles
   Answer and explanation

   Answer: D. Multiply 3.5 inches by 12 miles per inch to get 42 miles.

   Skill checked: Proportions

2. What is -6.4 + 2.9?

   1. -9.3
   2. -3.5
   3. 3.5
   4. 9.3
   Answer and explanation

   Answer: B. Starting at -6.4 and moving 2.9 toward zero gives -3.5.

   Skill checked: Rational numbers

3. Solve 4x - 7 = 21.

   1. x = 7
   2. x = 3.5
   3. x = 5
   4. x = 28
   Answer and explanation

   Answer: A. Add 7 to get 4x = 28, then divide by 4. x = 7.

   Skill checked: Equations

4. A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of choosing blue?

   1. 1/5
   2. 1/3
   3. 1/2
   4. 2/3
   Answer and explanation

   Answer: C. Five of the 10 marbles are blue, so the probability is 5/10, or 1/2.

   Skill checked: Probability

5. A circle has a radius of 4 cm. Using 3.14 for π, what is its area?

   1. 12.56 cm²
   2. 50.24 cm²
   3. 25.12 cm²
   4. 100.48 cm²
   Answer and explanation

   Answer: B. Area is πr²: 3.14 × 4² = 3.14 × 16 = 50.24 square centimeters.

   Skill checked: Geometry

6. A $60 jacket is discounted 25%. What is the sale price?

   1. $15
   2. $35
   3. $45
   4. $75
   Answer and explanation

   Answer: C. Twenty-five percent of $60 is $15. Subtract the discount: $60 - $15 = $45.

   Skill checked: Percent

Free printable worksheet

Download the 7th Grade math practice worksheet. It includes a separate set of practice items and an answer key.

Continue to the full diagnostic

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7th Grade math placement questions

What math should a 7th grader know?

Seventh grade math commonly emphasizes ratios and proportions, operations with rational numbers, expressions and equations, percent applications, probability, sampling, and geometry with scale, circles, area, and volume.

Is this an algebra readiness test?

The diagnostic includes equations and proportional reasoning, but it is not a dedicated Algebra 1 readiness test.

Can my child use scratch paper?

Yes. Scratch paper is encouraged because the method can reveal whether an error came from the concept or from arithmetic.