Algebra worksheet — GCSE Foundation

1.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

2.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

3.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

4.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

5.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

6.Solve 4(x − 3) = 2x + 6.

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.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

9.Expand 2(x + 12)

10.A square tile has an area of 144 cm². Work out the side length of the tile.

11.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.

12.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

13.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

14.Make x the subject of the formula y = (x − 4)/5.

15.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.