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.Solve 4x² − 9 = 0.

3.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

4.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

5.Which of these is a factor of 15x + 20?

6.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

7.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

8.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.

9.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

10.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

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

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

13.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

14.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

15.In the expression 5x² − 3x + 7, which of these is a single term of the expression?