Algebra worksheet — GCSE Foundation

1.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

2.Simplify 5a/6 − a/3

3.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

4.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

5.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

6.y = 3x − 2. Work out the value of y when x = 4.

7.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

8.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

9.Solve the inequality x + 5 < 12.

10.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

11.Make x the subject of the formula y = 2x − 9.

12.Which of these equations gives a straight-line graph when plotted?

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

14.Solve 4x − (2x − 6) = 18

15.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.