Algebra worksheet — GCSE Foundation

1.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.

2.Solve 3x − 5 = 4.

3.Write down the expression that means the same as m² × m × 3.

4.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.

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

6.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

7.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

8.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

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

10.Work out the gradient of the straight line with equation y = (2x/5) − 3.

11.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

12.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

13.Solve 5x² − 15x = 0.

14.Solve x² − 2x − 24 = 0.

15.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.