Algebra worksheet — GCSE Foundation

1.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

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

3.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

4.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

5.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.

6.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

7.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

8.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

9.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

10.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

11.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.

12.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.

13.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

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

15.Write down the gradient of the line with equation y = 6 + 4x.