Algebra worksheet — GCSE Higher

1.Solve the inequality x² − 5x + 6 < 0.

2.f(x) = x + 3 and g(x) = 2x. Work out fg(x).

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

4.A cyclist's velocity increases from 3 m/s to 11 m/s over 5 seconds, at a constant rate. Work out the cyclist's acceleration, in m/s².

5.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

6.Solve the inequality 5 − x ≤ 2.

7.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

8.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

9.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

10.The iterative formula xₙ₊₁ = √(2xₙ + 15) is used repeatedly, starting from x₀ = 1. Work out the value that xₙ approaches, correct to 2 decimal places.

11.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

12.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

13.Solve 2x² = 18.

14.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

15.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.