Substitution into formulae worksheet — GCSE Foundation

1.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.

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

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

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

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

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

7.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.

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

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

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

11.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.

12.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

13.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.

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

15.Work out the value of 5m² + 3m when m = −2.4