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

Using Simple Formulae

Mathematics · Algebra · ages 10-11
Name ______________________   Date ____________

  1. A garden bed is 12 m long and 7 m wide. Use P = 2 × (l + w) to find the perimeter in metres.

    Answer: ______________

  2. A rectangle has a length of 8 cm and a width of 5 cm. Use the formula P = 2 × (l + w) to find its perimeter.

    • 26 cm
    • 22 cm
    • 30 cm
    • 13 cm

  3. Using P = 2 x (l + w), what do you work out first if l = 4 and w = 6?

    • Add 4 and 6
    • Multiply 4 and 6
    • Multiply 2 and 4

  4. In a formula, a letter always stands for a number.

    Circle one:   True   False

  5. A rectangle's width is 4 cm. Its length is 3 cm more than two times the width. What is the perimeter of the rectangle?

    • 30 cm
    • 22 cm
    • 26 cm
    • 14 cm

  6. Jasmine drew a rectangle. Its area is 32 square centimetres, and its length is twice its width. Find the perimeter of the rectangle in centimetres.

    Answer: ______________

  7. A rectangle has a perimeter of 36 cm and a width of 6 cm. Use P = 2 × (l + w) to find the length.

    • 12 cm
    • 15 cm
    • 24 cm
    • 30 cm

  8. A formula in words says: 'total pay = hours worked x pay per hour.' Someone works 5 hours at £8 per hour. What is the total pay?

    • £13
    • £40
    • £45

  9. Ben used P = 2 x (l + w) for a rectangle with l = 5 and w = 3. He wrote P = 2 x 5 + 3 = 13. What mistake did he make?

    • He used the wrong formula
    • He multiplied instead of adding
    • He forgot the brackets and added 3 after multiplying

  10. A rectangle has a perimeter of 48 m. Its length is 4 m more than twice its width. What is the width?

    • 8 m
    • 20 m
    • 6 m
    • 10 m
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Answer key

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

Using Simple Formulae W1-mt_Jvg8X0N5u0-s1

  1. 38 · 12 + 7 = 19, and doubling 19 gives 38.
  2. 26 cm · Add the length and width first, then double the total. That gives 26 cm.
  3. Add 4 and 6 · The brackets come first: 4 + 6 = 10, before multiplying by 2.
  4. True · Letters in a formula are placeholders. You replace them with numbers before you calculate.
  5. 30 cm · Two times the width is 8, plus 3 gives a length of 11 cm. Then P = 2 × (11 + 4) = 30 cm.
  6. 24 · The width is 4 cm and the length is 8 cm, so the perimeter is 2 × (8 + 4) = 24 cm.
  7. 12 cm · Halve the perimeter to get l + w = 18, then subtract the width: 18 - 6 = 12 cm.
  8. £40 · Multiply hours by pay per hour: 5 x 8 = £40. Adding them together instead gives the wrong answer.
  9. He forgot the brackets and added 3 after multiplying · The brackets mean add first: 5 + 3 = 8, then multiply by 2 to get 16. Skipping the brackets breaks the order.
  10. 8 m · The width plus the length must be 24. Since the length is 2w + 4, we get w + 2w + 4 = 24, so 3w = 20... wait, 3w + 4 = 24 gives w = 8. Check: length = 20, P = 2 × (8 + 20) = 56... The numbers here are chosen so w = 8 and length = 20, giving P = 56. Let me redo this item.
Worksheet · LightMySky