Algebra worksheet — GCSE Foundation

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

2.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?

3.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

4.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

5.Work out the value of 3b − 4 when b = 6

6.Which of these equations describes a vertical line?

7.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

8.Solve 2x + 7 = x + 13

9.Which expression is equivalent to 4(x − 2) + 10?

10.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

11.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

12.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.

13.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

14.Solve x − 4 = −9

15.In the expression 5x² − 3x + 7, which of these is a single term of the expression?