Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as p + p + p + q.

2.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

3.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

4.Make a the subject of the formula b = 20 − a.

5.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

6.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

7.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

8.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

9.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.

10.Factorise x² − 64.

11.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.

12.The point A is at (5, −3). In which quadrant does A lie?

13.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

14.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

15.Solve the inequality x − 10 < −3.