Algebra worksheet — GCSE Foundation

1.Write down the gradient of the line with equation y = 7x − 2.

2.Which of these is a formula?

3.Which expression means 'triple c, then add double d'?

4.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

5.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.

7.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

8.The point A is at (5, −3). In which quadrant does A lie?

9.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

10.Which expression is equivalent to 6x − (2x − 5)?

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

12.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

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

14.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.

15.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.