Modelling Situations with Formulae and Graphs · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Turning situations into formulas and graphs

Mathematics · Algebra · ages 11-13
Name ______________________   Date ____________

  1. One angle in a drawing measures x degrees. Another angle is 20 degrees bigger. Which expression shows the bigger angle?

    • x + 20
    • x - 20
    • 20x
    • x / 20

  2. A number n is increased by 7. Which expression shows the new number?

    • n + 7
    • n - 7
    • 7n
    • n / 7

  3. Mia has n stickers. Tom has 3 times as many stickers as Mia. How many stickers does Tom have?

    • 3n
    • n + 3
    • n - 3
    • n / 3

  4. Using c = 2 + 1.5m, what is c when m = 0?

    • £0
    • £1.50
    • £2

  5. A plumber charges £30 call-out plus £25 per hour, h hours: c = 30 + 25h. What is the cost for a 3-hour job?

    Answer: ______________

  6. A ribbon 24 cm long is cut into n equal pieces. How long is each piece?

    • 24 / n
    • 24n
    • n / 24
    • 24 + n

  7. Two numbers add up to 15. One of the numbers is n. Which expression shows the other number?

    • 15 - n
    • n - 15
    • 15n
    • 15 + n

  8. A baby plant is 5 cm tall. It grows 2 cm every week. Its height after w weeks is 2w + 5. How tall is the plant after 8 weeks?

    Answer: ______________

  9. A rule says: each output is 6 more than the input. Which table matches the rule?

    • input 1, 2, 3 gives output 7, 8, 9
    • input 1, 2, 3 gives output 6, 12, 18
    • input 1, 2, 3 gives output 7, 12, 15
    • input 1, 2, 3 gives output 6, 7, 8

  10. Ravi built a table for c = 5 + 2m and wrote the pair (m = 3, c = 10). What did he do wrong?

    • He multiplied 5 by m instead of 2
    • He added the numbers instead of multiplying 2 by m first
    • He used the wrong value of m
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Answer key

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

Turning situations into formulas and graphs W1-mt_z5iwdZyeDr-s1

  1. x + 20 · 'Bigger' means you add 20 to the first angle, giving x + 20.
  2. n + 7 · 'Increased by' tells you to add, so the expression is n + 7.
  3. 3n · '3 times as many' means multiply by 3, so Tom has 3n stickers.
  4. £2 · When m = 0 there are no miles yet, so only the £2 starting fee counts.
  5. 105 · c = 30 + 25 × 3 = 30 + 75 = 105, so the job costs £105.
  6. 24 / n · Cutting into equal pieces means sharing evenly, which is division: 24 divided by n.
  7. 15 - n · If the total is 15 and one part is n, the missing part is 15 minus n.
  8. 21 · Put w = 8 into 2w + 5: 2 times 8 is 16, plus 5 is 21 cm.
  9. input 1, 2, 3 gives output 7, 8, 9 · Adding 6 to each input gives 7, 8, and 9, so the first table matches the rule.
  10. He added the numbers instead of multiplying 2 by m first · 5 + 2 + 3 = 10, but the rule needs 2 multiplied by m first: 5 + 2 × 3 = 11.
Worksheet · LightMySky