Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

2.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

3.Work out the gradient of the straight line with equation y = (2x/5) − 3.

4.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.

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

6.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

7.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

8.Work out the value of 5a + 2 when a = 3

9.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

10.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.

11.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

12.Which of these statements is an equation with exactly one solution?

13.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

14.a = 3 and b = 5. Work out the value of a²b.

15.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.