Algebra worksheet — GCSE Higher

1.Solve the inequality 5 − x ≤ 2.

2.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.

3.n = 3. Work out the value of (2n)².

4.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).

5.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.

6.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

7.Solve the inequality 2(x − 1) ≤ 8.

8.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.

9.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

10.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

11.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

12.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

13.f(x) = 3x − 2. Find f⁻¹(x).

14.A tram travels between two stops. Its velocity-time graph consists of straight line segments joining the points (0, 0), (5, 20), (12, 20), (16, 4) and (20, 4), where time is in seconds and velocity is in m/s. Work out the average speed of the tram over the whole 20 seconds. Give your answer to 1 decimal place.

15.A region R satisfies y ≤ x + 1, x + y ≤ 5 and y ≥ 0. Which of these correctly describes R in words?