Algebra worksheet — GCSE Foundation

1.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

2.In which quadrant does the point (−3, 0.5) lie?

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

4.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

5.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

6.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

7.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

8.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

9.Which expression is equivalent to 0.5(4x + 6) − x?

10.A number machine adds 6 to its input. Work out the output when the input is −4.

11.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.

12.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

13.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

14.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

15.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.