Algebra worksheet — GCSE Foundation

1.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

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

3.Simplify 2a + 3b − a + 2b − b

4.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

5.Expand 7(a + 8)

6.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

7.Work out the value of 5y + 9 when y = 0

8.Work out the value of 3x² − 4x when x = −2.

9.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

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

11.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

12.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.

13.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

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

15.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.