Algebra worksheet — GCSE Foundation

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

2.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

3.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

4.Simplify 5a/6 − a/3

5.Make p the subject of the formula n = p/3.

6.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

7.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

8.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

9.a = 3 and b = 5. Work out the value of a²b.

10.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

11.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

12.Work out the value of 3n − 2 when n = 1

13.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

14.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

15.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.