Algebra worksheet — GCSE Foundation

1.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

2.The point A lies on the x-axis. Which statement about A must be true?

3.Simplify p + p + p.

4.Work out the value of 5m² + 3m when m = −2.4

5.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.

6.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

7.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

8.Write down the expression that means the same as 3 × y × y.

9.Expand 7(a + 8)

10.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

11.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?

12.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

13.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

14.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

15.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.