Algebra worksheet — GCSE Foundation

1.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

2.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

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

4.Simplify 5a/6 − a/3

5.Make c the subject of the formula k = 6c.

6.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

7.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

8.Solve the inequality 5 − x ≤ 2.

9.Which expression means 'triple c, then add double d'?

10.Simplify k + k + k + k + k.

11.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

12.Work out the value of 3a − 2b when a = 5 and b = 4

13.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

14.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

15.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.