Algebra worksheet — GCSE Foundation

1.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

2.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

3.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

4.A number machine multiplies its input by 5. Work out the output when the input is −1.

5.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

6.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

7.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

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

9.Work out the value of (x − 4)/2 + 3 when x = 10

10.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

11.Simplify p + p + p.

12.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

13.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

14.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.

15.Work out the value of 2x² when x = −3