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Substitution and Formulas Worksheet

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Substitution and Formulas Worksheet

Replace each letter with its given value, then calculate using the order of operations. Include units where needed. Show your working for calculation questions.

Substitution and formulas

Substitution means putting a number in place of a letter. For example, if r = 4m − 1 and m = 3, then r = 4 × 3 − 1 = 11. In a formula such as A = bh, substitute the values for b and h before calculating.

Choose and calculate

Select the correct value in each question.

1.If y = 5x + 2 and x = 4, what is y?
  • 18
  • 20
  • 22
  • 26
2.The area of a rectangle is A = lw. Find A when l = 7 cm and w = 3 cm.
  • 10 cm²
  • 21 cm²
  • 20 cm²
  • 28 cm²

Substitution practice

Write down the substitution and calculation for each question.

3.Calculate p when p = 6q − 5 and q = 4.
4.Evaluate 4a + 3b when a = 2 and b = 5.
5.A rectangle has perimeter P = 2l + 2w. Find its perimeter when l = 8 m and w = 5 m.
6.Find z when z = x² − 3 and x = 6.
7.A club charges £4 to join and £3 for each session. Use C = 4 + 3n to find the total cost for 7 sessions.

Formulas in context

Substitute the given values into each formula. Remember to include the correct units.

8.Convert 12 miles to kilometres using K = 1.6M, where M is the distance in miles.
9.A delivery costs £2.50 plus £0.80 for each kilometre. Use C = 2.50 + 0.80d to find the cost of a 15 km delivery.
10.A triangle has area A = ½bh. Find its area when the base b is 14 cm and the height h is 9 cm.
11.Use s = ut + ½at² to calculate s when u = 3, t = 5 and a = 2.

Match each formula

Match each formula to the calculation it represents when the values are substituted.

12.Match each formula on the left with its correct substituted calculation on the right.
  • A = lw, with l = 9 and w = 4
  • P = 2l + 2w, with l = 9 and w = 4
  • y = 3x + 1, with x = 6
  • C = 5 + 2n, with n = 8
  • 5 + 2 × 8
  • 2 × 9 + 2 × 4
  • 3 × 6 + 1
  • 9 × 4

3 printable pages

  • Substitution and Formulas Worksheet, page 1 of 3: Substitution and formulas, Choose and calculate, Substitution practice

    Page 1

  • Substitution and Formulas Worksheet, page 2 of 3: Formulas in context

    Page 2

  • Substitution and Formulas Worksheet, page 3 of 3: Match each formula

    Page 3

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