Algebra worksheet — GCSE Foundation

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

2.Expand 4(2x − 3).

3.Simplify 5x + 3y − 2x + y.

4.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

5.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

6.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

7.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

8.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

9.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

10.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

11.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

12.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

13.A number machine adds 6 to its input. Work out the output when the input is −4.

14.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.

15.Make p the subject of the formula n = p/3.