Algebra worksheet — GCSE Foundation

1.Simplify k + k + k + k + k.

2.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

3.Solve the inequality 4x + 1 > 2x + 9.

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

5.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

6.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

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

8.Solve x² − 2x − 24 = 0.

9.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

10.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

11.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

12.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

13.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

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

15.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?