Substitution into formulae worksheet — GCSE Foundation

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

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

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

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

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

6.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.

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

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

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

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

11.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

12.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

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

14.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.

15.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.