Algebra worksheet — GCSE Foundation

1.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

2.Which expression is equivalent to 7x − 3(2x − 6)?

3.Which expression is equivalent to 6x − (2x − 5)?

4.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

5.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

6.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

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

8.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

9.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

10.Solve 6x + 4 = 28

11.Which of these statements is an equation with exactly one solution?

12.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.

13.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

14.Work out the coordinates of the reflection of (6, −3) in the y-axis.

15.Solve 5x − 9 = 16