Algebra worksheet — GCSE Higher

1.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

2.Solve x² − 6x = 0.

3.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

4.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.

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

6.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

7.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

8.The point (18, 24) lies on the circle x² + y² = 900, which has centre (0, 0). The tangent to the circle at (18, 24) crosses the y-axis at the point Q. Work out the y-coordinate of Q.

9.Factorise 3x² + 10x − 8.

10.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

11.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

12.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

13.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

14.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.

15.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.