Algebra worksheet — GCSE Foundation

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

2.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

3.Make x the subject of the formula y = x + 7.

4.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

5.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

6.Which of these is an expression?

7.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

8.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

9.Work out the value of n² − n when n = −3

10.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

11.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

12.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

13.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.

14.Which of these numbers is a cube number?

15.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.