Printable · GCSE Foundation · ages 14-16
Algebra worksheet — GCSE Foundation
Fifteen questions across the algebra statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Algebra worksheet — GCSE Foundation
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- 1.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.y = x² − 6x + 5
- 2.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.
- 3.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.
- 4.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?
- 5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
- 6.Simplify 2a + 3b − a + 2b − b
- 7.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.
- 8.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.y = x² + 2x − 15
- 9.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.y = 2x + 4
- 10.Solve the inequality 3x − 1 ≤ 11.
- 11.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.
- 12.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.
- 13.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.
- 14.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.
- 15.Solve the simultaneous equations 2x + y = 7 and x − y = 2.
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