Free beginning-of-year diagnostic

7th Grade Back-to-School Math Diagnostic

A printable 24-question 7th grade math diagnostic covering rational-number operations, ratios, unit rates, percent, equations, geometry, and statistics.

24 questions6 skill areasAbout 60 minutesAnswer key and scoring guide
Download the free diagnostic PDF

What this diagnostic measures

Seventh-grade mathematics depends on proportional reasoning and fluent work with signed rational numbers. This check-in separates those foundations into short skill groups, making follow-up practice easier to target.

Administration note

A student who sets up ratio and percent questions correctly but makes arithmetic errors needs a different plan from one who cannot identify the relationship. Preserve all work for that distinction.

Preview all 24 questions

Give one point per correct answer. Also record each section score out of three so the follow-up plan stays specific.

Rational-number fluency

Section score: ____ / 4

Compute with fractions, decimals, and signed numbers.

  1. 1Find [[\frac{7}{8}]] - [[\frac{5}{12}]].
  2. 2Find 3.6 / 0.12.
  3. 3Find -8 + 13 - 6.
  4. 4Evaluate [[-2\frac{1}{3}+\frac{5}{6}]].

Ratios and unit rates

Section score: ____ / 4

Represent equivalent ratios and compare rates.

  1. 5Solve [[\frac{4}{7}]] = x/35.
  2. 6A cyclist travels 42 miles in 3.5 hours. Find the unit rate.
  3. 7Which is less expensive per ounce: 10 oz for $3.20 or 14 oz for $4.20?
  4. 8A map uses [[1.5]] inches for [[24]] miles. How many miles does [[4.25]] inches represent?

Percent

Section score: ____ / 4

Connect percent, decimals, and real-world changes.

  1. 9Find [[28\%]] of 150.
  2. 1036 is what percent of 48?
  3. 11A $64 item is discounted [[15\%]]. Find the sale price.
  4. 12A quantity increases from [[80]] to [[94]]. Find the percent increase.

Expressions and equations

Section score: ____ / 4

Evaluate expressions, combine terms, and solve equations.

  1. 13Evaluate 2a - 3b when a = 5 and b = -2.
  2. 14Simplify 7x + 4 - 3x + 9.
  3. 15Solve x/6 + 5 = 12.
  4. 16Solve [[3(2x-5)+4=25]].

Geometry

Section score: ____ / 4

Use area, surface area, and volume relationships.

  1. 17Find the area of a triangle with base 15 and height 8.
  2. 18A prism has base area 24 square cm and height 6 cm. Find its volume.
  3. 19A rectangle has length 11 and width 7. Find its perimeter.
  4. 20A circle has diameter [[14]]. Find its circumference in terms of [[\pi]].

Statistics and modeling

Section score: ____ / 4

Summarize data and write an equation for a situation.

  1. 21The mean of five values is 12. Four values are 8, 10, 13, and 14. Find the fifth.
  2. 22A club charges $12 to join plus $5 per meeting. Write the cost for m meetings.
  3. 23Nine movie tickets cost $103.50. At the same rate, what do 4 tickets cost?
  4. 24A random sample of [[40]] students includes [[26]] who prefer later start times. Predict how many of [[300]] students would agree.
Open the answer key

Equivalent forms and clearly justified open-ended responses should receive credit.

Rational-number fluency

1. [[\frac{11}{24}]]

2. 30

3. -1

4. [[-\frac{3}{2}]]

Ratios and unit rates

5. x = 20

6. 12 miles per hour

7. 14 oz for $4.20; $0.30 per ounce

8. [[68]] miles

Percent

9. 42

10. [[75\%]]

11. $54.40

12. [[17.5\%]]

Expressions and equations

13. 16

14. 4x + 13

15. x = 42

16. [[x=6]]

Geometry

17. 60 square units

18. 144 cubic cm

19. 36 units

20. [[14\pi]] units

Statistics and modeling

21. 15

22. C = 5m + 12

23. $46

24. [[195]] students

Readiness score

Turn the answer key into a next step.

Count one point for each correct answer. Partial understanding is best noted beside the problem rather than counted as half a point.

All back-to-school diagnostics6th Grade Back-to-School Math Diagnostic8th Grade Back-to-School Math DiagnosticFull-length summer review packetsTarget one prerequisite skill