Algebra worksheet — GCSE Higher

1.A circle has centre (0, 0) and equation x² + y² = 8. Work out the radius of the circle, giving your answer as a surd in its simplest form.

2.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.

3.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

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

5.Make x the subject of the formula y = x/2 − 5.

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

7.Which expression is equivalent to 6x − (2x − 5)?

8.A bacteria colony doubles every 4 hours and its size is recorded only every 4 hours. The recorded population 20 hours after the start is 9,600. After how many hours did the recorded population first exceed 1,000?

9.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

10.The graph of y = f(x) passes through the point (2, 5). Write down the coordinates of the corresponding point on the graph of y = f(x − 4) + 1.

11.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.

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

13.The graph of y = f(x) has a minimum turning point at (4, −5). The graph of y = f(x) + a has a minimum turning point whose minimum VALUE is 2. Work out the value of a, and state the coordinates of the minimum turning point of y = f(x) + a.

14.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

15.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?