Substitution into formulae worksheet — GCSE Foundation

1.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.

2.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.

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

4.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.

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

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.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

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

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

10.Work out the value of 5y + 9 when y = 0

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

12.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.

13.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.

14.Work out the value of 3a − 2b when a = 5 and b = 4

15.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.