Algebra worksheet — GCSE Foundation

1.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

2.Work out the value of 4p² − 3 when p = 2.5

3.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

4.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

5.Solve x² + 3x − 10 = 0.

6.p = 4. Work out the value of 2p³.

7.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

8.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

9.Simplify x + x + 4

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

11.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

12.Which of these is a formula, rather than an expression, an equation, or an identity?

13.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

14.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

15.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.