Substitution into formulae worksheet — GCSE Foundation

1.Work out the value of 3n − 2 when n = 1

2.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

3.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

4.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.

5.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.

6.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.

7.Work out the value of (x − 4)/2 + 3 when x = 10

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

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

10.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.

11.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

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

13.Work out the value of 2(x + 2) when x = −5

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

15.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.