Algebra worksheet — GCSE Higher

1.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

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

3.A market trader builds a display of oranges in a rectangular block. The block is n oranges wide and 4 oranges longer than it is wide. The number of oranges needed is 5 when n = 1, 12 when n = 2, 21 when n = 3, 32 when n = 4, and 45 when n = 5. Work out an expression, in terms of n, for the number of oranges needed for a display of width n.

4.Simplify (5x² + 3x − 2) − (2x² − x + 5)

5.A car accelerates uniformly from rest at 2.5 m/s² until it reaches a speed of 20 m/s, then travels at this constant speed for a further 30 seconds. Work out the total distance travelled.

6.Solve the inequality 3x + 6 ≤ 0.

7.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

8.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

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

11.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

12.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

13.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).

14.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

15.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.