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Math 8

Math 8 · Worksheets

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Ten questions of mixed difficulty, covering Equations and graphs, Integers, Percents, ratios and rates, Square roots and Pythagoras, Surface area and volume. Print it, or work through it on screen — the answer key starts on its own page.

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Math 8 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A $60 jacket is on sale for 25% off. Then 5% GST is added to the sale price. What is the total cost?

    1. a) $45.00
    2. b) $47.25
    3. c) $48.00
    4. d) $42.75

  2. A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. Which equation gives the other leg, b?

    1. a) b = 10 − 6
    2. b) b² = 10² − 6²
    3. c) b² = 6² − 10²
    4. d) b² = 10² + 6²

  3. A candle is 30 cm tall and burns down 2 cm every hour. Its table of values starts (0, 30), (1, 28), (2, 26), (3, 24). After how many hours will it be 10 cm tall?

    1. a) 5 hours
    2. b) 20 hours
    3. c) 10 hours
    4. d) 15 hours

  4. What is the surface area of a cube with edges of 4 cm?

    1. a) 48 cm²
    2. b) 16 cm²
    3. c) 96 cm²
    4. d) 64 cm²

  5. 18 ÷ (−3) − (−4) × 2 equals

    1. a) 2
    2. b) 14
    3. c) −4
    4. d) −14

  6. √50 lies between which two whole numbers?

    1. a) 25 and 26
    2. b) 49 and 64
    3. c) 7 and 8
    4. d) 6 and 7

  7. Solve x/3 = −5.

    1. a) x = −8
    2. b) x = −2
    3. c) x = −15
    4. d) x = 15

  8. (−5 + 11) ÷ (−2) × 3 equals

    1. a) 9
    2. b) −9
    3. c) −1
    4. d) 1

  9. Solve −2(x − 5) = 18.

    1. a) x = 14
    2. b) x = −14
    3. c) x = −4
    4. d) x = 4

  10. A triangular prism is 10 cm long. Its ends are right triangles with sides of 3 cm, 4 cm and 5 cm. What is its surface area?

    1. a) 144 cm²
    2. b) 132 cm²
    3. c) 60 cm²
    4. d) 126 cm²

Answer key · Cumulative review

Math 8 · maddyhelps.com

  1. b) $47.25 — 25% off $60 is $15, so the sale price is $45. GST is 5% of what you actually pay, 0.05 × $45 = $2.25, for a total of $47.25. $48.00 takes off 25% − 5% = 20% in one step, but the two percents are of different amounts, so they cannot be combined like that.
  2. b) b² = 10² − 6² — The hypotenuse is the longest side, so 6² + b² = 10², and taking 6² from both sides gives b² = 10² − 6² = 64, so b = 8 cm. Adding the squares would make b longer than the hypotenuse, and 6² − 10² is negative, which no square can be.
  3. c) 10 hours — The candle has to lose 30 − 10 = 20 cm at 2 cm an hour, which takes 20 ÷ 2 = 10 hours — extend the table and you reach (10, 10). 15 hours is when it burns down completely, and 20 hours counts the centimetres it loses as if they were hours.
  4. c) 96 cm² — A cube has 6 square faces, each 4 × 4 = 16 cm², so its surface area is 6 × 16 = 96 cm². 64 is 4 × 4 × 4, the volume in cm³ — a different measurement — and 48 cm² counts only the three faces you can see at once.
  5. a) 2 — Divide and multiply first: 18 ÷ (−3) = −6 and (−4) × 2 = −8. Then −6 − (−8) = −6 + 8 = 2. −14 subtracts 8 instead of subtracting −8, and −4 works from left to right, subtracting before it multiplies.
  6. c) 7 and 8 — 7² = 49 and 8² = 64, and 50 is between them, so √50 is between 7 and 8 — just above 7, since 50 is so close to 49. 49 and 64 are the perfect squares on either side, not their roots, and 25 and 26 come from halving 50, but a square root is not half.
  7. c) x = −15 — x divided by 3 gives −5, so multiply both sides by 3: x = −15. Check: −15 ÷ 3 = −5 ✓. x = 15 loses the sign, and −8 subtracts 3 instead of multiplying — a division is undone by multiplying.
  8. b) −9 — Brackets first: −5 + 11 = 6. Multiplying and dividing share a step, so go left to right: 6 ÷ (−2) = −3, then −3 × 3 = −9. −1 multiplies first, 6 ÷ (−6), but multiplying does not come before dividing — whichever comes first, reading left to right, goes first.
  9. c) x = −4 — Divide both sides by −2, x − 5 = −9, then add 5: x = −4. Check: −2 × (−4 − 5) = −2 × (−9) = 18 ✓. x = 14 divides 18 by 2 instead of −2, and x = −14 multiplies out as −2x − 10, forgetting that −2 × (−5) = +10.
  10. b) 132 cm² — Each triangular end is ½ × 3 × 4 = 6 cm² — the two shorter sides are the base and the height, because they meet at the right angle. The three rectangles are 3 × 10, 4 × 10 and 5 × 10, which add to 120 cm², so the total is 6 + 6 + 120 = 132 cm². 144 cm² forgets to halve for the triangles, and 126 cm² counts only one end.