Algebra worksheet — GCSE Foundation

1.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

2.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

3.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

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

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

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

7.Make x the subject of the formula y = 5x + 3.

8.Which of these is an equation, rather than an expression, a formula or an identity?

9.Solve x/4 + 1 = 3

10.A number machine adds 6 to its input. Work out the output when the input is −4.

11.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

12.Solve 7x − 5 = 3x + 11

13.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

14.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?

15.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.