Algebra worksheet — GCSE Foundation

1.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

2.Solve the inequality 3x − 1 ≤ 11.

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

4.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

5.Work out the value of 2(x + 2) when x = −5

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

7.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

8.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

9.Which expression is equivalent to 0.5(4x + 6) − x?

10.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

11.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

12.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

13.Factorise fully 12x² + 18x.

14.Solve 5(x + 3) = 40

15.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.