Algebra worksheet — GCSE Foundation

1.Factorise x² − 3x − 10.

2.Write down the expression that means the same as w ÷ 6.

3.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.

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

5.Make x the subject of the formula y = (x − 4)/5.

6.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

7.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

8.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

9.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

10.Which expression means the same as a × a × a?

11.Solve 5x − 9 = 16

12.Solve 4(x − 3) = 2x + 6.

13.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

14.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

15.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?