Algebra worksheet — GCSE Higher

1.By completing the square, find the turning point of the curve y = x² − 4x + 9.

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

3.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).

4.A proof sets out to show that the sum of the squares of two consecutive odd numbers, written as 2n + 1 and 2n + 3, is always 2 more than a multiple of 8. Four attempts to expand (2n + 1)² + (2n + 3)² and reach a conclusion are shown below. Which attempt correctly proves this claim?

5.The nth term of a sequence is n² + 4n. Work out the term number, n, for which the term equals 45.

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

7.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

8.Factorise fully 12x² + 18x.

9.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

10.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

11.Which of these equations is equivalent to 5x − 2 = 3x + 8?

12.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?

13.Solve x² − 6x = 0.

14.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.

15.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.