Algebra worksheet — GCSE Foundation

1.Solve x − 4 = −9

2.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

3.A number machine adds 5 to its input. Work out the output when the input is 0.

4.Which expression means the same as a × a × a?

5.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

6.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.

7.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

8.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

9.Which expression means 'y squared, multiplied by 3'?

10.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

11.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

12.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.

13.Which expression is equivalent to 7x − 3(2x − 6)?

14.Write down the expression that means 5 more than half of n.

15.Make x the subject of the formula y = 3(x + 2).