Algebra worksheet — GCSE Foundation

1.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

2.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

3.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.

4.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

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

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

7.Which of these statements is an equation with exactly one solution?

8.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

9.a = 2 and b = 5. Work out the value of ab².

10.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

11.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

12.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

13.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

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

15.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.