Algebra worksheet — GCSE Foundation

1.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

2.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

3.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

4.Expand 2(x + 12)

5.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

6.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.

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

8.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

9.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

10.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

11.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.

12.Work out the gradient of the straight line with equation y = (2x/5) − 3.

13.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

14.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

15.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.