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Math 8

Math 8 · Worksheets

Year-end challenge

Ten questions of mixed difficulty, covering Data and probability, Equations and graphs, Fractions, 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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Year-end challenge

Math 8 · maddyhelps.com

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

  1. A basketball player makes 80% of her free throws, and each shot is independent of the others. What is the probability that she makes two shots in a row?

    1. a) 64%
    2. b) 40%
    3. c) 80%
    4. d) 160%

  2. Solve x/3 = −5.

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

  3. Without calculating, which of these is less than 6?

    1. a) 6 × 5/4
    2. b) 6 ÷ 4/5
    3. c) 6 × 4/5
    4. d) 6 ÷ 1/3

  4. Solve x/4 − 3 = 2.

    1. a) x = 20
    2. b) x = 1.25
    3. c) x = 11
    4. d) x = −4

  5. 4 × 2/3 equals

    1. a) 2 2/3
    2. b) 4 2/3
    3. c) 1/6
    4. d) 8/12

  6. A recipe for 12 muffins uses 2¼ cups of flour. How much flour is needed for 8 muffins?

    1. a) 18 cups
    2. b) 1 7/12 cups
    3. c) 3 3/8 cups
    4. d) 1½ cups

  7. A fair coin has landed heads 5 times in a row. What is the probability that the next flip is heads?

    1. a) 1/2
    2. b) 1/32
    3. c) 1/64
    4. d) 1/6

  8. How many whole numbers have a square root that is between 8 and 9, but not equal to either?

    1. a) 16
    2. b) 15
    3. c) 17
    4. d) 18

  9. A cylinder has a diameter of 10 cm and a height of 10 cm. Using π ≈ 3.14, what is its volume?

    1. a) 314 cm³
    2. b) 157 cm³
    3. c) 785 cm³
    4. d) 3140 cm³

  10. In a class, ⅔ of the students play a sport, and ¾ of those play hockey. What fraction of the class plays hockey?

    1. a) 1 5/12
    2. b) 8/9
    3. c) ½
    4. d) 1/12

Answer key · Year-end challenge

Math 8 · maddyhelps.com

  1. a) 64% — Independent events multiply: 0.8 × 0.8 = 0.64, or 64%. It is less than 80% because a miss on either shot spoils the pair — answering 80% treats two shots as if they were one. 160% adds the chances and gives a probability over 100%, which is impossible.
  2. a) 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.
  3. c) 6 × 4/5 — Multiplying by a fraction less than 1 takes only part of the number, so 6 × 4/5 = 4 4/5 is less than 6. Dividing by 4/5 asks how many 4/5s fit into 6, which is more than 6 (7½). Multiplying does not always make a number bigger, and dividing does not always make it smaller — it depends on whether the other number is more or less than 1.
  4. a) x = 20 — Add 3 to both sides, x/4 = 5, then multiply both sides by 4: x = 20. Check: 20 ÷ 4 − 3 = 5 − 3 = 2 ✓. x = 11 multiplies the 2 by 4 but not the 3 — whatever you do to a side, you do to all of it — and x = −4 subtracts 3 instead of adding it.
  5. a) 2 2/3 — 4 × 2/3 is four lots of 2/3: 2/3 + 2/3 + 2/3 + 2/3 = 8/3 = 2 2/3. 8/12 multiplies the denominator by 4 as well, which only renames 2/3, and 4 2/3 puts the 4 beside the fraction instead of multiplying.
  6. d) 1½ cups — 8 muffins is 8/12 = ⅔ of the recipe, and ⅔ × 2¼ = ⅔ × 9/4 = 18/12 = 1½ cups. 3 3/8 cups scales by 12/8 instead, which gives more flour for fewer muffins, and 1 7/12 cups takes ⅔ of the 2 but forgets to take ⅔ of the ¼.
  7. a) 1/2 — The coin has no memory: each flip is independent, so the next one is heads with probability 1/2, whatever came before. 1/64 = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2 is the chance of six heads in a row worked out before any flips — but five of those have already happened, so only one flip is still uncertain.
  8. a) 16 — √n is between 8 and 9 when n is between 8² = 64 and 9² = 81. Leaving out 64 and 81, whose roots are exactly 8 and 9, that is 65 to 80: 16 numbers. 81 − 64 = 17 counts one of the ends, and 18 counts both.
  9. c) 785 cm³ — The base is a circle of radius 5 cm, half the diameter, with area 3.14 × 5 × 5 = 78.5 cm², and the volume is 78.5 × 10 = 785 cm³. 3140 cm³ uses the diameter as the radius, which makes the base four times too big, and 314 cm³ multiplies the circumference by the height, which is the area of the curved side, not a volume.
  10. c) ½ — ¾ of the ⅔ who play a sport is ¾ × ⅔ = 6/12 = ½ of the class. Adding the fractions gives 1 5/12 — more than the whole class — and 1/12 subtracts them; 'of' means multiply.