Algebra worksheet — GCSE Foundation

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

2.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

3.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

4.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

5.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

6.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

7.Which of these is a formula?

8.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

9.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

10.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

11.Expand and simplify (x − 3)²

12.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

13.Make x the subject of the formula y = 5x + 3.

14.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

15.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.