Algebra worksheet — GCSE Higher

1.Which of these rules generates the sequence 6, 11, 16, 21, …?

2.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

3.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

4.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.

5.When a number is added to its square the result is 30. Work out the possible values of the number.

6.Solve the inequality 2(x − 1) ≤ 8.

7.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

8.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

9.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

10.The graph of y = sin x is reflected in the x-axis to give the graph of y = g(x). Work out the value of g(90), where x is measured in degrees.

11.Solve 4x² − 9 = 0.

12.Write down the gradient of the line with equation y = −x + 3.

13.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

14.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

15.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.