Algebra worksheet — GCSE Foundation

1.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

2.Which of these statements is an identity?

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

4.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

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

6.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

7.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.

8.Make x the subject of the formula y = 2x − 9.

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

10.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

11.Factorise fully 56x − 24

12.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

13.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

14.Solve 2x − 2 = 2

15.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.