Algebra worksheet — GCSE Higher

1.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.

2.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.

3.By completing the square, find the turning point of the curve y = x² − 10x + 30.

4.Work out the value of 2(x + 2) when x = −5

5.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.

6.Make x the subject of the formula y = 4x − 3.

7.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.

8.A circle has centre (0, 0) and passes through the point (5, 12). Work out the equation of the circle.

9.Make x the subject of the formula y = 2x − 9.

10.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

11.n is an integer. Which of these expressions is always an even number?

12.Factorise 3x² + 10x − 8.

13.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.

14.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

15.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.