Substitution into formulae worksheet — GCSE Higher

1.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.

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

3.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.

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

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 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.

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

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

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

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

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

12.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.

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

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

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