Algebra worksheet — GCSE Foundation

1.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

2.Make x the subject of the formula y = 5x + 3.

3.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

4.Solve x² = 81.

5.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

6.Write down the first four terms of the sequence with nth term 6n − 5.

7.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

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

9.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

10.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

11.y = 3x − 2. Work out the value of y when x = 4.

12.Which expression means 'add 3 to n, then multiply the result by 4'?

13.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.

14.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

15.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?