Algebra worksheet — GCSE Foundation

1.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

2.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

3.Expand 2(x − 13)

4.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.

5.Write down the gradient of the line with equation y = 6 + 4x.

6.Simplify 5a/6 − a/3

7.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

8.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

9.Solve x − 4 = −9

10.Which of these is an identity?

11.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

13.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

14.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

15.Which of these equations describes a vertical line?