Algebra worksheet — GCSE Higher

1.Make x the subject of the formula y = 4(x − 6).

2.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.

3.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

4.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.

5.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.

6.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

7.A speed-time graph shows a constant speed of 15 m/s for 20 seconds. Work out the distance travelled, using the area under the graph.

8.Write down the first four terms of the sequence with nth term 6n − 5.

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

10.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.

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

12.By completing the square, find the turning point of the curve y = 3x² + 12x + 7.

13.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

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

15.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.