Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

2.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

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.Work out the value of a² − 2b when a = −3 and b = 4.

5.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

6.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

7.Which of these numbers is a cube number?

8.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

9.Work out the value of n² − n when n = −3

10.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

11.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

12.Which expression is equivalent to 0.5(4x + 6) − x?

13.Solve 4x − (2x − 6) = 18

14.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

15.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.