Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

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

3.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

4.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

5.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

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

7.Solve the inequality 2(3x − 1) ≥ 4x + 8.

8.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

9.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.

10.Solve 3x − 1 = 8

11.Which expression is equivalent to 3(2x − 5) + 4x?

12.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.

13.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

14.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

15.Work out the value of n² − n when n = −3