Algebra worksheet — GCSE Foundation

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

2.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.

3.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

4.A square tile has an area of 144 cm². Work out the side length of the tile.

5.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

6.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

7.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

8.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

9.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

10.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

11.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

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 geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

14.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

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