Algebra worksheet — GCSE Higher

1.Points A(8, 15) and B(−8, 15) both lie on the circle x² + y² = 289, which has centre (0, 0). Work out the length of the chord AB.

2.Solve 2(x + 3) = 10

3.Solve the inequality x² + 6x + 9 > 0.

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

5.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

6.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).

7.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

8.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

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

10.Which of these quadratic graphs does NOT cross the x-axis at all?

11.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

12.A car's journey is represented by a velocity-time graph. The total distance travelled, found from the area under the graph, is 350 metres, and the total time for the journey is 25 seconds. Work out the car's average speed for the whole journey, in m/s.

13.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

14.The equation x² − 6x + k = 0 has exactly one solution. Work out the value of k.

15.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.