Algebra worksheet — GCSE Foundation

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

2.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

3.Solve (2x + 1)/3 = 5

4.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

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

6.Which of these statements is an identity?

7.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

8.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

9.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

10.Which expression means 'add 3 to n, then multiply the result by 4'?

11.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

12.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

13.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.

14.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

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