Algebra worksheet — GCSE Foundation

1.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

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

3.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

4.Which of these points lies in the first quadrant?

5.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

6.Solve the inequality 3x − 1 ≤ 11.

7.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

8.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

9.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

10.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

11.Solve x² + 7x = 0.

12.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

13.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

14.Solve 7x − 5 = 3x + 11

15.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.