Algebra worksheet — GCSE Foundation

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

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

3.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

4.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

5.Factorise fully 5x + 5y − 5

6.The point B has coordinates (−2, −2). In which quadrant is B?

7.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

8.Simplify 2b − 1 + 2b − 4 + 2b

9.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

10.Which of these is an inequality?

11.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

12.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

13.Simplify 2a + 3b − a + 2b − b

14.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

15.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.