Algebra worksheet — GCSE Foundation

1.Solve 6x − 5 = 3x + 13.

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

3.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

4.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

5.Simplify k + k + k + k + k.

6.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

7.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

8.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

9.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

10.Expand and simplify 2(a + 6) − 2(a − 7)

11.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

12.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

13.Which expression is equivalent to 6x − (2x − 5)?

14.Make m the subject of the formula w = m − 8.

15.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.