Free printable summer review

7th Grade Summer Math Review

A free 7th grade summer math review with 40 problems, proportional tables, visual geometry, rational numbers, percent, equations, probability, and an answer key.

40 problems8 skill areasAbout 90 minutesAnswer key included
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What this review measures

Eighth-grade algebra depends on more than equation steps. Students need signed-number fluency, proportional reasoning, and the ability to translate between tables, diagrams, equations, and verbal situations. This expanded packet gives each prerequisite meaningful space and uses visual models where the diagram is part of the mathematics.

For parents and educators

Have the student mark each answer C (confident), U (unsure), or G (guessed). Those labels often reveal more than the raw score and help choose what to review next.

Preview the complete review

Every question below appears in the printable packet. Students should show their work and simplify answers unless directed otherwise.

Rational numbers

Compute accurately with positive and negative fractions and decimals.

  1. 1Find -14 + 5.6.
  2. 2Find (-3/5)(25/9).
  3. 3Find -4.2 / 0.7 + 9.
  4. 4Find -3 1/2 + 1 3/4.
  5. 5Order from least to greatest: -1.8, -7/4, 0.2, -2.

Proportions and scale

Solve proportions and interpret scale drawings.

  1. 6Solve 7/12 = x/60.
  2. 7On a map, 1.5 cm represents 12 km. How far does 6 cm represent?
  3. 8Determine whether the relationship in the table is proportional. State the constant of proportionality.
    xy
    27
    517.5
    828
  4. 9A scale drawing uses 2.5 inches to represent 15 feet. How many feet does 7 inches represent?
  5. 10The ratio of red to blue tiles is 4:7. There are 33 tiles total. How many are blue?

Percent applications

Solve tax, discount, markup, and percent-change problems.

  1. 11A $72 meal has 8% tax. Find the total.
  2. 12A price increases from $45 to $54. Find the percent increase.
  3. 13A $120 item is marked down 25%, then discounted another 10% of the sale price. Find the final price.
  4. 14A store marks up a $48 item by 35%. Find the selling price.
  5. 15A student estimated a length as 26 cm. The actual length is 25 cm. Find the percent error.

Expressions and equations

Use properties, solve multi-step equations, and interpret solutions.

  1. 16Simplify 4(2x - 3) - 5x.
  2. 17Solve 5x - 7 = 2x + 20.
  3. 18Solve -3(x + 4) = 18.
  4. 19Factor 18x + 30 using the greatest common factor.
  5. 20Solve 3(x - 2) + 4 = 19.
  6. 21Solve x/3 + 5/2 = 9/2.

Geometry

Use diagrams to reason about angles, circles, area, coordinates, surface area, and volume.

  1. 22The angle shown measures 118 degrees. Find the measure of its supplement.118 degrees
  2. 23Find the circumference of the circle. Use π = 3.14.6 cm
  3. 24Find the area of the circle. Give the exact answer in terms of π.10 m
  4. 25Find the volume of the rectangular prism.6 in.7 in.3 in.
  5. 26Find the area of the triangle.base 14; height 9
  6. 27Find the area of the trapezoid. Use A = 1/2(b1 + b2)h.bases 11 and 17; height 6
  7. 28Points P and Q are shown. Find the vertical distance between them.PQ
  8. 29Find the surface area of the rectangular prism.423

Probability and data

Use probability models and compare distributions.

  1. 30A bag has 4 red, 5 blue, and 3 green marbles. Find P(not blue).
  2. 31A coin is flipped and a six-sided die is rolled. How many possible outcomes are there?
  3. 32The mean of 6, 9, 11, x, and 14 is 10. Find x.
  4. 33A number cube is rolled 120 times and lands on 5 a total of 18 times. Find the experimental probability of rolling a 5.
  5. 34The data are 4, 7, 7, 8, 9, and 13. Find the median and range.

Word problems

Build and solve equations from rates and constraints.

  1. 35A gym charges $18 plus $7 per visit. The bill is $74. How many visits?
  2. 36A runner travels 4.5 miles in 36 minutes. At the same pace, how far in 80 minutes?
  3. 37The length of a rectangle is 3 more than twice its width. Its perimeter is 42. Find its dimensions.
  4. 38A tank is 3/8 full. After 30 gallons are added, it is 3/4 full. What is the tank's capacity?

Challenge

Compare methods and test reasonableness.

  1. 39Which is farther from zero: -7/3 or 2.4?
  2. 40An item is discounted 20% and then increased 20%. Is the final price the original price? Explain.
View the complete answer key

Open-ended explanations may use different wording while showing the same reasoning.

Rational numbers

1. -8.4

2. -5/3, or -1 2/3

3. 3

4. -1 3/4

5. -2, -1.8, -7/4, 0.2

Proportions and scale

6. x = 35

7. 48 km

8. Yes; y/x = 3.5

9. 42 feet

10. 21 blue tiles

Percent applications

11. $77.76

12. 20%

13. $81

14. $64.80

15. 4%

Expressions and equations

16. 3x - 12

17. x = 9

18. x = -10

19. 6(3x + 5)

20. x = 7

21. x = 6

Geometry

22. 62 degrees

23. 37.68 cm

24. 25π square m

25. 126 cubic inches

26. 63 square units

27. 84 square units

28. 6 units

29. 52 square units

Probability and data

30. 7/12

31. 12

32. 10

33. 3/20, or 15%

34. Median 7.5; range 9

Word problems

35. 8 visits

36. 10 miles

37. Width 6, length 15

38. 80 gallons

Challenge

39. 2.4, because 2.4 > 7/3

40. No; it is 96% of the original price

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