Algebra worksheet — GCSE Foundation

1.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

2.Write down the expression that means the same as m × m × m × n.

3.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

4.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

5.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?

6.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

8.p = 4. Work out the value of 2p³.

9.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

10.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

11.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

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

13.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

14.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

15.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.