Algebra worksheet — GCSE Higher

1.Simplify (5x² + 3x − 2) − (2x² − x + 5)

2.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

3.Solve 2(x + 3) = 10

4.The trapezium rule is used to estimate the area under a curve between x = 2 and x = 6. The curve is concave up (it curves upwards, like the inside of a bowl) throughout this interval. Which statement about the estimate is correct?

5.Solve the inequality x² ≥ 16, giving your answer using set notation.

6.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

7.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

8.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

9.a = 2 and b = 5. Work out the value of a²b.

10.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.

11.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.

12.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

13.Line P has equation y = −2x + 5 and line Q has equation 2y = x + 6. Are lines P and Q perpendicular to each other?

14.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

15.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.