Algebra worksheet — GCSE Foundation

1.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

2.Solve 5x − 9 = 16

3.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.

4.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

5.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

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

7.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

8.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

9.Work out the value of 3n − 2 when n = 1

10.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

11.Which of these values of x is a solution of x² + 2x − 15 = 0?

12.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

13.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

14.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

15.Solve the inequality 6x ≥ 18.