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Math 8

Math 8 · Worksheets

Mixed review · Roots, integers and fractions

Ten questions of mixed difficulty, covering Fractions, Integers, Square roots and Pythagoras. Print it, or work through it on screen — the answer key starts on its own page.

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Mixed review · Roots, integers and fractions

Math 8 · maddyhelps.com

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

  1. The low temperatures in Edmonton on five days were −12 °C, −8 °C, 3 °C, −15 °C and 2 °C. What was the mean low temperature?

    1. a) −8 °C
    2. b) −30 °C
    3. c) −6 °C
    4. d) 6 °C

  2. 4 × 2/3 equals

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

  3. (−48) ÷ 6 equals

    1. a) −42
    2. b) −8
    3. c) −288
    4. d) 8

  4. Which list is in order from least to greatest?

    1. a) 6, √40, √50, 7
    2. b) 6, √40, 7, √50
    3. c) 6, 7, √40, √50
    4. d) √40, √50, 6, 7

  5. √50 lies between which two whole numbers?

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

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

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

  7. 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) 8/9
    2. b) ½
    3. c) 1/12
    4. d) 1 5/12

  8. A 13 m ladder leans against a wall with its foot 5 m from the bottom of the wall. How high up the wall does the ladder reach?

    1. a) 13.9 m
    2. b) 12 m
    3. c) 8 m
    4. d) 144 m

  9. Which product is positive?

    1. a) 2 × (−3) × (−1) × (−5)
    2. b) (−2) × (−3) × (−1) × (−5)
    3. c) (−2) × 3 × 1 × 5
    4. d) (−2) × (−3) × (−1) × 5

  10. A right triangle has legs of 5 cm and 12 cm. How long is its hypotenuse?

    1. a) 13 cm
    2. b) 17 cm
    3. c) 169 cm
    4. d) 7 cm

Answer key · Mixed review · Roots, integers and fractions

Math 8 · maddyhelps.com

  1. c) −6 °C — Add first, (−12) + (−8) + 3 + (−15) + 2 = −30, then share the total over the 5 days: (−30) ÷ 5 = −6 °C. −8 °C treats the 3 and the 2 as negative too, and 6 °C drops the sign — a negative total divided by a positive number of days is negative.
  2. d) 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.
  3. b) −8 — Division undoes multiplication: 6 × (−8) = −48, so (−48) ÷ 6 = −8. A negative divided by a positive is negative, just as a negative times a positive is. 8 drops the sign, and −42 adds 6 instead of dividing by it.
  4. b) 6, √40, 7, √50 — √40 is between 6 and 7, because 6² = 36 and 7² = 49, and √50 is just over 7, because 50 is just over 49. Putting √50 before 7 misses that 50 is more than 7² = 49, and putting both roots last compares 40 and 50 with 6 and 7 as if the root signs were not there.
  5. 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.
  6. b) 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. b) 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.
  8. b) 12 m — The ladder is the hypotenuse, so h² + 5² = 13²: h² = 169 − 25 = 144 and h = 12 m. 13.9 m adds the squares, √(169 + 25), which makes the height more than the ladder's length — impossible. 144 m forgets to take the square root.
  9. b) (−2) × (−3) × (−1) × (−5) — Negative factors cancel in pairs, so a product is positive when it has an even number of negative factors. (−2) × (−3) × (−1) × (−5) has four, which make two pairs, so it equals 30. The others have one or three, which leaves a negative without a partner — fewer negatives does not make a product positive.
  10. a) 13 cm — Use a² + b² = c²: 5² + 12² = 25 + 144 = 169, so c = √169 = 13 cm. 169 cm stops one step early — 169 is c², not c — and 17 cm adds the sides themselves, but only their squares add up.