Math Worksheet for 13-Year-Olds — Middle School Math Practice (Grade 7–8)

Free worksheet covering Math for age 13 students. Created with Learning Corner's AI-powered tools.

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Instructions

Read each question carefully and answer to the best of your ability. Show your work where necessary. You may use a calculator for the geometry section if needed. Good luck!

Section 1: Algebraic Expressions & Equations

  1. Simplify the following expression:

    3(4x - 2) + 5 - 7x

    Answer: ____________________

  2. Solve for y:

    5y + 11 = 46

    Answer: y = ____________________

  3. Write an algebraic expression for the following phrase:

    "The product of a number n and 6, decreased by 10."

    Answer: ____________________

Section 2: Percentages and Proportions

  1. A map has a scale of 1 inch : 25 miles. If two cities are 4.5 inches apart on the map, what is the actual distance between them in miles?

    Answer: ____________________ miles

  2. A smartphone that normally costs $850 is on sale for 30% off. What is the sale price?

    Answer: $____________________

  3. You scored 40 out of 50 on a test. What is your score as a percentage?

    Answer: ____________________ %

Section 3: Geometry

  1. A circle has a radius of 8 cm. Using π ≈ 3.14, calculate:

    a) The circumference of the circle.

    Answer: ____________________ cm

    b) The area of the circle.

    Answer: ____________________ cm2

  2. A right-angled triangle has two legs measuring 9 cm and 12 cm. What is the length of the hypotenuse (the longest side)?

    (Hint: a2 + b2 = c2)

    Answer: ____________________ cm

Section 4: Integers and Order of Operations

  1. Evaluate the expression using the correct order of operations (PEMDAS/BODMAS):

    ( -8 + 2 ) × 3 + 42 ÷ 8

    Answer: ____________________



Answer Key

  1. 5x - 1
    Work: 12x - 6 + 5 - 7x = (12x - 7x) + (-6 + 5) = 5x - 1
  2. y = 7
    Work: 5y = 46 - 11 → 5y = 35 → y = 35 / 5 → y = 7
  3. 6n - 10
  4. 112.5 miles
    Work: 1 / 25 = 4.5 / x → x = 25 × 4.5 → x = 112.5
  5. $595
    Work: Discount = 0.30 × 850 = $255. Sale Price = $850 - $255 = $595
  6. 80%
    Work: (40 / 50) × 100 = 0.8 × 100 = 80

  7. a) 50.24 cm (Circumference = 2 × π × r = 2 × 3.14 × 8)

    b) 200.96 cm2 (Area = π × r2 = 3.14 × 82 = 3.14 × 64)

  8. 15 cm
    Work: 92 + 122 = c2 → 81 + 144 = c2 → 225 = c2 → c = 15
  9. -16
    Work: (-6) × 3 + 16 ÷ 8 → -18 + 2 = -16
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