Algebra worksheet — GCSE Higher

1.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

2.Which of these is an identity?

3.The table shows the velocity, in m/s, of a train at various times, in seconds: 0 at t = 0, 20 at t = 4, 35 at t = 10, 27 at t = 14. Assuming the velocity changes at a constant rate between each pair of readings, estimate the distance the train travels between t = 0 and t = 12, using the trapezium rule.

4.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.

5.Work out the value of 2(x + 2) when x = −5

6.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

7.Solve 2x + 7 = x + 13

8.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.

9.Solve 4(x − 3) = 2x + 6.

10.Simplify 2/(x + 1) + 3/(x − 2), giving your answer as a single fraction.

11.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

12.n is an integer. Which of these expressions is always an even number?

13.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

14.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

15.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.