Algebra worksheet — GCSE Foundation

1.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

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

3.a = 2 and b = 5. Work out the value of a²b.

4.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

5.Which of these equations describes a vertical line?

6.Solve 5(x + 3) = 40

7.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

8.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

9.y = 3x − 2. Work out the value of y when x = 4.

10.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

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

12.Which expression means 'add 3 to n, then multiply the result by 4'?

13.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

14.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

15.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?