Calculating with Bounds in Compound Measures · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Best and worst your measurements allow

Mathematics · Number Representation & Place Value · ages 15-16
Name ______________________   Date ____________

  1. Distance 100 m to nearest 10, time 8 s to nearest integer. What is the greatest speed in m/s?

    Answer: ______________

  2. Distance and time are both rounded. Which pair gives the greatest possible speed?

    • Upper distance with lower time
    • Lower distance with upper time
    • Upper with upper
    • Lower with lower

  3. Distance and time are both rounded. Which pair gives the greatest speed?

    • Upper distance, lower time
    • Lower distance, upper time
    • Upper with upper

  4. A speed built from 2-figure inputs can be quoted to 5 significant figures.

    Circle one:   True   False

  5. Mass 400 g to nearest 10, volume 50 cm cubed to nearest 10. What is the greatest density in g per cm cubed?

    Answer: ______________

  6. Length 6 cm (5.5 to 6.5) and width 4 cm (3.5 to 4.5). What is the greatest area?

    • 24
    • 26
    • 29.25

  7. Same bounds: 95 to 105 m, 7.5 to 8.5 s. Which calculation gives the SMALLEST speed?

    • 105 ÷ 7.5
    • 95 ÷ 7.5
    • 95 ÷ 8.5
    • 105 ÷ 8.5

  8. Maya says the smallest division uses the smallest numerator with the largest denominator. Is Maya right?

    Circle one:   True   False

  9. Force 195 to 205 N, area 9.5 to 10.5. Which calculation gives maximum pressure?

    • 195 divided by 10.5
    • 205 divided by 9.5
    • 205 divided by 10.5

  10. Distance 100 m to nearest 10, time 4 s to nearest integer. What is the greatest speed in m/s?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Best and worst your measurements allow W1-mt_zfMz7x8dlf-s1

  1. 14 · 105 over 7.5 = 14.
  2. Upper distance with lower time · Big top with small bottom maximises a division. Lower with upper gives the minimum instead.
  3. Upper distance, lower time · Big top with small bottom maximises a division.
  4. False · Bounds support about 2 figures. Longer decimals fake extra knowledge.
  5. 9 · 405 over 45 = 9.
  6. 29.25 · Upper times upper: 6.5 times 4.5 = 29.25.
  7. 95 ÷ 8.5 · Small top with big bottom minimises. The 105 over 7.5 option is the maximum.
  8. True · Small top with big bottom is the minimising pair.
  9. 205 divided by 9.5 · Pressure divides, so maximum is upper force over lower area.
  10. 30 · 105 over 3.5 = 30.
Worksheet · LightMySky