Algebra worksheet — GCSE Foundation

1.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.

2.Work out the value of 5m² + 3m when m = −2.4

3.Solve 2x² − 32 = 0.

4.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.

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

6.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.

7.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

8.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

9.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

10.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

11.Which expression is equivalent to 0.5(4x + 6) − x?

12.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

13.Which expression means the same as a × a × a?

14.Solve 5x² − 15x = 0.

15.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.