Algebra worksheet — GCSE Foundation

1.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

2.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

3.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

4.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.

5.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.

6.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

7.Simplify 5x + 3y − 2x + y.

8.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

9.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

10.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

11.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

12.Simplify (5x² + 3x − 2) − (2x² − x + 5)

13.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

14.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

15.Work out the value of 5a + 2 when a = 3