Algebra worksheet — GCSE Foundation

1.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

2.Make x the subject of the formula y = 5x + 3.

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

4.A curve has equation y = x² − 9. Which statement about its graph is correct?

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 plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

7.a = 2 and b = 5. Work out the value of ab².

8.Write down the expression that means the same as m × m × m × n.

9.Simplify p + p + p.

10.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

11.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

12.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

13.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

14.Write down the gradient of the line with equation y = 6 + 4x.

15.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.