Algebra worksheet — GCSE Foundation

1.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

2.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

3.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

4.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

5.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

6.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

7.How many turning points does the graph of y = x² − 7x + 10 have?

8.Solve x² = 81.

9.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

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

11.Solve 5(x + 3) = 40

12.Work out the distance of the point (−6, 4) from the x-axis.

13.Solve the inequality x − 10 < −3.

14.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

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.