Algebra worksheet — GCSE Foundation

1.y = 3x − 2. Work out the value of y when x = 4.

2.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

3.Solve x/4 + 1 = 3

4.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

5.Write down the gradient of the line with equation y = −x + 3.

6.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

7.a = 2 and b = 5. Work out the value of a²b.

8.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

9.Expand 2(x + 12)

10.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

11.Which of these is a factor of 15x + 20?

12.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

13.a = 3 and b = 5. Work out the value of a²b.

14.The graph of y = (x − 4)(x + 1) crosses the x-axis. Which pair gives the correct roots and reasoning?

15.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.