Algebra worksheet — GCSE Higher

1.Solve 5(x + 3) = 40

2.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).

3.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.

4.The graph of y = f(x) has x-intercepts at x = −1 and x = 4. Which statement correctly describes the x-intercepts of y = f(2 − x)?

5.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

6.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.

7.Work out the value of 3a − 2b when a = 5 and b = 4

8.An exponential model has equation y = A × bˣ, where b > 1. Its graph passes through the points (1, 135) and (2, 405). Work out the value of A.

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

10.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

11.The graph of y = f(x) passes through the point (2, 5). Write down the coordinates of the corresponding point on the graph of y = f(x − 4) + 1.

12.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

13.A market trader builds a display of oranges in a rectangular block. The block is n oranges wide and 4 oranges longer than it is wide. The number of oranges needed is 5 when n = 1, 12 when n = 2, 21 when n = 3, 32 when n = 4, and 45 when n = 5. Work out an expression, in terms of n, for the number of oranges needed for a display of width n.

14.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

15.Line L has equation y = 2x + 3. Work out the equation of the line perpendicular to L that passes through the point (4, 1), giving your answer in the form x + 2y = c.