Algebra worksheet — GCSE Foundation

1.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

2.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

3.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

4.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.

5.Work out the value of a² − 2b when a = −3 and b = 4.

6.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

7.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

8.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

9.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

10.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

11.A curve has equation y = x² − 9. Which statement about its graph is correct?

12.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

13.x = 5. Work out the value of 3x² − 4.

14.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

15.Simplify k + k + k + k + k.