Substitution into formulae worksheet — GCSE Foundation

1.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

2.Work out the value of n² − n when n = −3

3.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

4.Work out the value of 5a + 2 when a = 3

5.Work out the value of m² + 3m when m = −2

6.Work out the value of 4p² − 3 when p = 2.5

7.Work out the value of 3b − 4 when b = 6

8.Work out the value of 2x² when x = −3

9.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

10.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

11.Work out the value of 3x² − 4x when x = −2.

12.Work out the value of a² − 2b when a = −3 and b = 4.

13.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.

14.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

15.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.