Algebra worksheet — GCSE Foundation

1.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.

2.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

3.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

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

5.The point A is at (5, −3). In which quadrant does A lie?

6.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

7.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

8.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.

9.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

10.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

11.Which expression is equivalent to 7x − 3(2x − 6)?

12.p = 4. Work out the value of 2p³.

13.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

14.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.

15.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.