Algebra worksheet — GCSE Higher

1.Simplify 5a/6 − a/3

2.y = 5 − 2x. Work out the value of x when y = 11.

3.Factorise fully 56x − 24

4.Solve the inequality 3x − 1 ≤ 11.

5.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

6.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

7.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

8.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

9.An exponential model has equation y = A × bˣ, where b > 1. Its graph passes through the points (1, 135) and (2, 405). Work out the value of A.

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

11.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

12.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

13.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.

14.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.

15.Work out the equation of the straight line through the points (−2, 1) and (0, 7).