Proportion · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Direct and Inverse Proportion

Mathematics · Ratio & Proportion · ages 12-14
Name ______________________   Date ____________

  1. A team is digging a hole. The more workers who join, the less time the job takes, since they're sharing the same total work. Is this direct or inverse proportion?

    • Direct proportion
    • Inverse proportion

  2. A recipe always uses the same ratio of flour to cookies: the more cookies you bake, the more flour you need, growing at a steady rate. Is this direct or inverse proportion?

    • Direct proportion
    • Inverse proportion

  3. A recipe uses 2 eggs for every 6 cupcakes. If you double the cupcakes, what happens to the eggs?

    • They also double
    • They stay the same
    • They halve

  4. A straight line through the origin represents inverse proportion.

    Circle one:   True   False

  5. Which graph shape matches inverse proportion?

    • A straight line through the origin
    • A curve that drops as one value rises
    • A horizontal straight line

  6. The graph of an inverse proportion relationship, like y = k/x, is a straight line.

    Circle one:   True   False

  7. 5 kg of apples cost $15. Find the cost of 8 kg of apples, in dollars.

    Answer: ______________

  8. 3 notebooks cost $9. How much would 7 notebooks cost, in dollars?

    Answer: ______________

  9. 6 identical tickets cost £18. Zara says 15 tickets will cost £45 because she found the price per ticket and multiplied by 15. Is her method correct?

    • No, she should have divided instead
    • No, proportional pricing only works below 10 tickets
    • Yes, £3 per ticket times 15 is £45

  10. 8 builders can build a wall in 6 days. Working at the same rate, how many days would 4 builders need?

    Answer: ______________

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Answer key

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

Direct and Inverse Proportion W1-mt_5mIcmKRCgA-s1

  1. Inverse proportion · As the number of workers goes up, the time needed goes down. One amount rising while the other falls is inverse proportion.
  2. Direct proportion · As the number of cookies goes up, the flour needed goes up too, at the same steady rate. That is direct proportion.
  3. They also double · Eggs and cupcakes grow at the same rate, so doubling one doubles the other. That's direct proportion.
  4. False · A straight line through the origin shows direct proportion. Inverse proportion makes a curve instead.
  5. A curve that drops as one value rises · Inverse proportion makes a curve: as one quantity rises, the other falls.
  6. False · Inverse proportion makes a curve, not a straight line, because y shrinks quickly at first and then more slowly as x grows.
  7. 24 · Find the cost of 1 kg first, then multiply by 8.
  8. 21 · Find the cost of one notebook first, then multiply by 7.
  9. Yes, £3 per ticket times 15 is £45 · 6 tickets at £18 means £3 each. Direct proportion holds for any number, so 15 tickets cost 15 × £3 = £45.
  10. 12 · 8 × 6 = 48 builder-days of work in total. With 4 builders: 48 ÷ 4 = 12 days.
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