Algebra worksheet — GCSE Foundation

1.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.

2.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

3.Solve the inequality 3x + 6 ≤ 0.

4.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

5.Solve 2x + 1 = 9

6.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

7.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

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

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

10.Write down the expression that means the same as 3 × y × y.

11.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

12.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

13.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

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

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