Algebra worksheet — GCSE Foundation

1.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

2.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.

3.Solve the inequality 5x − 3 > 2x + 9.

4.a = 2 and b = 5. Work out the value of ab².

5.Solve 5x² − 15x = 0.

6.Write down 0.2x with its coefficient written as a fraction in its simplest form.

7.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

8.Solve x² = 81.

9.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

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

11.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.

12.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

13.Solve 2x − 2 = 2

14.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

15.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.