Algebra worksheet — GCSE Foundation

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

2.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.

3.Write down the expression that means the same as m × m × m × n.

4.Write down 0.2x with its coefficient written as a fraction in its simplest form.

5.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

6.Make x the subject of the formula y = (x − 4)/5.

7.Which of these equations gives a straight-line graph when plotted?

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

9.Make x the subject of the formula y = 4(x − 6).

10.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.

11.Make x the subject of the formula y = 4x − 3.

12.Work out the value of 5y + 9 when y = 0

13.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

14.y = 5 − 2x. Work out the value of x when y = 11.

15.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.