Algebra worksheet — GCSE Higher

1.f(x) = (x + 1)/2. Find f⁻¹(x).

2.Solve 2(x + 3) = 10

3.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.

4.Which expression is equivalent to 3(2x − 5) + 4x?

5.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

6.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

7.Four sequences are shown below. Sequence P: 3, 6, 12, 24, … Sequence Q: 1, 4, 9, 16, … Sequence R: 2, 4, 8, 14, … Sequence S: 5, 10, 15, 20, … Work out which of the sequences P, Q, R and S is geometric.

8.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

9.Factorise fully 56x − 24

10.Make x the subject of the formula y = 3(x + 2).

11.By completing the square, find the turning point of the curve y = x² − 4x + 9.

12.Solve the inequality 3x + 6 ≤ 0.

13.Subtract, giving your answer as a single fraction in its simplest form: 4/(x − 1) − 2/(x + 3)

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

15.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.