Algebra worksheet — GCSE Foundation

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.

2.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

3.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

4.Solve 5(x + 3) = 40

5.Solve 2x + 7 = x + 13

6.Write down the y-intercept of the line with equation y = 3x + 8.

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

8.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

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.Expand and simplify 2(a + 6) − 2(a − 7)

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

12.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

13.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

14.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

15.Write down the expression that means the same as p + p + p + q.