Algebra worksheet — GCSE Higher

1.A candidate solves the inequality x² > 9 and writes: "x² > 9, so x > 3." Which of these is a correct comment on the candidate's work?

2.Factorise 6x² − 7x − 3.

3.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.

4.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

5.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

6.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

7.Solve the inequality 3x − 1 ≤ 11.

8.Which of these equations is equivalent to 5x − 2 = 3x + 8?

9.Solve the inequality 5 − x ≤ 2.

10.Solve x² − 2x − 24 = 0.

11.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

12.The point (3, 6) lies on the circle x² + y² = 45. The tangent to the circle at (3, 6) crosses the x-axis at the point P. Work out the coordinates of P.

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

14.A tram sets off from a stop. Its velocity-time graph rises in a straight line from 0 m/s to 12 m/s over the first 8 seconds, then stays constant at 12 m/s for a further 10 seconds. Work out the total distance the tram travels in these 18 seconds, using the area under the graph.

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