Algebra worksheet — GCSE Higher

1.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

2.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.

3.The graph of y = f(x) passes through the point (2, 7). The graph of y = f(x) + a passes through the point (2, 3). Work out the value of a.

4.f(x) = (x + 1)/2. Find f⁻¹(x).

5.Work out the value of 3x² − 4x when x = −2.

6.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

7.A square tile has an area of 144 cm². Work out the side length of the tile.

8.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

9.Which expression means 'triple c, then add double d'?

10.Solve the inequality x² + 6x + 9 > 0.

11.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.

12.Make x the subject of the formula y = 4x − 3.

13.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

14.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

15.Expand and simplify (x + 1)(x + 2)(x + 3).