Algebra worksheet — GCSE Higher

1.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

2.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.

3.The first five terms of a quadratic sequence are 6, 11, 18, 27, 38. Work out an expression, in terms of n, for the nth term.

4.The point A(−6, 8) lies on the circle x² + y² = 100, whose centre is the origin O. The tangent to the circle at A crosses the y-axis at the point B. Work out the length of OB.

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.Solve x² − x − 12 = 0.

7.Expand and simplify (x − 3)²

8.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

9.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.

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

11.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

12.Which of these rules generates the sequence 6, 11, 16, 21, …?

13.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

14.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

15.An exponential model has equation y = A × bˣ, where b > 1. Its graph passes through the points (1, 135) and (2, 405). Work out the value of A.