Substitution into formulae worksheet — GCSE Higher

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

2.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.

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

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

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.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.

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

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

9.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.

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

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

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

13.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.

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

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