Algebra worksheet — GCSE Foundation

1.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

2.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

3.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

4.Solve 4(x − 3) = 2x + 6.

5.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.

6.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

7.Write down the gradient of the line with equation y = −x + 3.

8.Work out the gradient of the straight line with equation y = (2x/5) − 3.

9.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

10.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

11.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

12.Expand 2(x − 13)

13.y = 5 − 2x. Work out the value of x when y = 11.

14.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

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