Algebra worksheet — GCSE Foundation

1.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.

2.Make x the subject of the formula y = (x − 4)/5.

3.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

4.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

5.Write down the y-intercept of the line with equation y = 3x + 8.

6.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

7.Write down the gradient of the line with equation y = −x + 3.

8.Expand 7(a + 8)

9.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.

10.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

11.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

12.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

13.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

14.Write down the expression that means the same as (x + 7) ÷ 4.

15.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.