Algebra worksheet — GCSE Foundation

1.Solve x² − 6x = 0.

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

3.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

4.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

5.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.

6.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

7.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

8.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

9.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

10.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

11.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.

12.Which expression means 'triple c, then add double d'?

13.Simplify p + p + p.

14.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

15.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.