Algebra worksheet — GCSE Foundation

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

2.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

3.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

4.Solve the inequality 6x ≥ 18.

5.Work out the value of a² − 2b when a = −3 and b = 4.

6.Solve 5(x + 3) = 40

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

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

9.Solve 5x − 9 = 16

10.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

11.Write down the y-intercept of the line with equation y = 3x + 8.

12.A square has sides of length y cm. Write down an expression for the perimeter of the square.

13.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

14.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.

15.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?