Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 3(2x − 5) + 4x?

2.Work out the gradient of the straight line with equation y = (2x/5) − 3.

3.Work out the value of 5m² + 3m when m = −2.4

4.Work out the y-intercept of the graph of y = x² + 3x − 10.

5.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

6.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

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

8.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

9.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?

10.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.

11.Write down the gradient of the line with equation y = 7x − 2.

12.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

13.Which expression is equivalent to 5x − (x + 3)?

14.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.

15.Simplify 2b − 1 + 2b − 4 + 2b