Algebra worksheet — GCSE Higher

1.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

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

3.A circle has centre (0, 0) and equation x² + y² = 36. Work out the coordinates of the two points where the circle crosses the y-axis.

4.a = 2 and b = 5. Work out the value of a²b.

5.Work out the value of 3a − 2b when a = 5 and b = 4

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

7.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

8.Which of these values of x is a solution of x² + 2x − 15 = 0?

9.A machine bought for £2,400 loses 12% of its value every year. After how many complete years does its value first fall below £1,500?

10.Write down the first four terms of the sequence with nth term 6n − 5.

11.The equation x² − 7 = 0 has a positive root. Let f(x) = x² − 7. Given that x₁ = 2.6 and x₂ = 2.65, work out which of these is correct.

12.The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at (6, 8).

13.The curve y = 2x² − 12x + 7 has a minimum point. By completing the square, find the value of x at which the minimum occurs.

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

15.A company's weekly profit, in £, is modelled by y = f(x), where x is the number of weeks since launch. The graph of y = f(x) has a maximum at (10, 45000). A rival company uses the same marketing strategy but starts trading 6 weeks later and has fixed costs £8000 higher every week, so its profit is modelled by y = f(x − 6) − 8000. In which week does the rival's maximum weekly profit occur, and what is it?