Algebra worksheet — GCSE Foundation

1.Work out the value of 3a − 2b when a = 5 and b = 4

2.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.

3.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?

4.Work out the gradient of the straight line with equation 3y = 12 − 6x.

5.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?

6.Which of these equations describes a vertical line?

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

8.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

9.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

10.Solve the inequality 3x + 6 ≤ 0.

11.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

12.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

13.Make x the subject of the formula y = 4x − 3.

14.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

15.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.