Algebra worksheet — GCSE Foundation

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

2.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

3.Make m the subject of the formula w = m − 8.

4.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

5.Write down the first four terms of the sequence with nth term 6n − 5.

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.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

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

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

10.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

11.Solve 4x² − 9 = 0.

12.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.

13.Solve 4(x − 3) = 2x + 6.

14.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

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