Algebra worksheet — GCSE Foundation

1.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

2.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

3.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

4.Solve the inequality 2(3x − 1) ≥ 4x + 8.

5.Solve 4x + 3 = 19

6.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

7.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

8.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

9.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

10.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

11.Solve 5x + 2 = 17.

12.Which of these equations is equivalent to 5x − 2 = 3x + 8?

13.Write down 0.2x with its coefficient written as a fraction in its simplest form.

14.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.

15.A vertical line passes through the point (4, 7). Write down the equation of this line.