Algebra worksheet — GCSE Higher

1.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

2.Solve 3x + 14 = 8x − 6

3.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)?

4.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = −f(x) + 5 crosses the y-axis.

5.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

6.A geometric sequence has first term 4 and common ratio √2. Work out the sum of the first three terms of the sequence, giving your answer in the form a + b√2.

7.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

8.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

9.Expand and simplify 2(a + 6) − 2(a − 7)

10.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.

11.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

12.The equation x² − 4x + k = 0 has two different real solutions. Work out the range of values of k.

13.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

14.When a number is added to its square the result is 30. Work out the possible values of the number.

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