Algebra worksheet — GCSE Higher

1.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

2.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

3.How many turning points does the graph of y = x² − 7x + 10 have?

4.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

5.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

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

7.The curve y = −x² + 6x − 5 has a maximum point. Use completing the square to find its coordinates.

8.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.

9.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

10.Factorise 6x² − 7x − 3.

11.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

12.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

13.By completing the square, find the turning point of the curve y = x² + 8x − 3.

14.Work out the coordinates of the reflection of (6, −3) in the y-axis.

15.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?