Algebra worksheet — GCSE Foundation

1.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.

2.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

3.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

4.A number machine adds 6 to its input. Work out the output when the input is −4.

5.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

6.Which of these rules generates the sequence 6, 11, 16, 21, …?

7.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

8.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.

9.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

10.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

11.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

12.y = x + 10. Work out the value of y when x = 0.

13.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

14.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

15.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.