Algebra worksheet — GCSE Higher

1.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.

2.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

3.Solve the inequality 2(x − 1) ≤ 8.

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

5.The graph of y = cos x is transformed onto the graph of y = cos(x − 90°). State the direction of the translation and which standard graph the image is.

6.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

7.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = −f(x) + 5 crosses the y-axis.

8.Work out the value of (x − 4)/2 + 3 when x = 10

9.Solve 4(x − 3) = 2x + 6.

10.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

11.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

12.Solve the inequality 5 − x ≤ 2.

13.A region S consists of every point that lies on or above the line y = 2, on or below the line y = x, and on or to the left of the line x = 6. Which of these is the system of inequalities that defines S?

14.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

15.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.