Algebra worksheet — GCSE Higher

1.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

2.Solve 2(x + 3) = 10

3.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.

4.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

5.The point (3, 6) lies on the circle x² + y² = 45. The tangent to the circle at (3, 6) crosses the x-axis at the point P. Work out the coordinates of P.

6.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

7.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

8.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

9.The equation x² − 4x + k = 0 has two different real solutions. Work out the range of values of k.

10.Which of these pairs of lines are perpendicular to each other?

11.The solution set of an inequality is described as: x is less than −3, or x is greater than or equal to 1. Write this solution set using set notation.

12.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

13.Factorise x² − 3x − 10.

14.Expand and simplify (x − 3)²

15.f(x) = x³ − 3x − 5. Given that f(2.2) = −0.952 and f(2.3) = 0.267, work out what this shows about the equation x³ − 3x − 5 = 0.