Algebra worksheet — GCSE Foundation

1.Factorise fully 5x + 5y − 5

2.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

3.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.

4.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

5.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.

6.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

7.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

8.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

9.Solve 3(2x − 1) = 27

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

11.Which of these is a term, rather than a whole expression, an equation, or a formula?

12.Which expression means 'y squared, multiplied by 3'?

13.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

14.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

15.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.