Algebra worksheet — GCSE Foundation

1.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

2.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.

3.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

4.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

5.Make x the subject of the formula y = 3(x + 2).

6.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

7.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

8.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.

9.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

10.Work out the value of 3x² − 4x when x = −2.

11.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

12.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.

13.Work out the value of n² − n when n = −3

14.Factorise fully 5x + 5y − 5

15.Solve x² = 49.