Algebra worksheet — GCSE Foundation

1.Which of these is an inequality?

2.A number machine multiplies its input by 3. The output is 15. Work out the input.

3.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

4.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

5.Which of these numbers is a cube number?

6.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.

7.Solve x² − 6x = 0.

8.Solve (2x + 1)/3 = 5

9.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

10.Work out the value of 5a + 2 when a = 3

11.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

12.Solve 4x² − 9 = 0.

13.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

14.Solve x² + 7x = 0.

15.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.