Algebra worksheet — GCSE Foundation

1.Which of these is an identity?

2.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

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

4.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

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

6.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

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

8.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

9.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

10.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

11.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

12.Expand 7(a + 8)

13.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

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

15.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.