Algebra worksheet — GCSE Foundation

1.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

2.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

3.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

4.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

5.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

6.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

7.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

8.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.

9.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

10.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

11.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

12.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

13.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

14.Work out the value of 4p² − 3 when p = 2.5

15.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.