Algebra worksheet — GCSE Foundation

1.Make b the subject of the formula a = 5b.

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

3.Solve x² + 7x = 0.

4.Solve x² − 5x + 6 = 0 by factorising.

5.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

6.Simplify 5x + 3y − 2x + y.

7.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

8.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

9.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

10.a = 2 and b = 5. Work out the value of ab².

11.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

12.Make x the subject of the formula y = x/2 − 5.

13.A number machine adds 5 to its input. Work out the output when the input is 0.

14.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

15.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.