Algebra worksheet — GCSE Foundation

1.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

2.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.

3.Make m the subject of the formula w = m − 8.

4.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

5.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

6.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

7.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

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.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

10.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

11.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

12.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.

13.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

14.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

15.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.