Algebra worksheet — GCSE Higher

1.a = 2 and b = 5. Work out the value of a²b.

2.Solve the inequality 9 − 2x ≥ 1.

3.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.

4.Which of these pairs of lines are perpendicular to each other?

5.Work out the gradient of the straight line with equation 2x + y = 8.

6.Make x the subject of the formula y = (x − 4)/5.

7.f(x) = (x + 1)/2. Find f⁻¹(x).

8.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

9.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

10.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

11.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

12.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

13.Solve 2x² − 7x + 3 = 0.

14.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

15.Points A(−1, 2) and B(5, 8) are the endpoints of a line segment. Work out the equation of the perpendicular bisector of AB.