Algebra worksheet — GCSE Higher

1.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

2.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

3.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

4.The solution set of an inequality is described as: x is less than −3, or x is greater than or equal to 1. Write this solution set using set notation.

5.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

6.The nth term of a sequence is n² − 2n + 5. Work out the 10th term.

7.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

8.Work out the value of (x − 4)/2 + 3 when x = 10

9.The graph of y = sin x is transformed onto the graph of y = sin x + 1. Which statement correctly describes the transformation and the new range of the graph?

10.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

11.Solve the inequality 9 − 2x ≥ 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.Solve x² − 2x − 24 = 0.

14.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.

15.Which expression is equivalent to 0.5(4x + 6) − x?