Algebra worksheet — GCSE Foundation

1.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

2.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

3.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

4.Solve x² + 3x − 10 = 0.

5.Factorise x² − 3x − 10.

6.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.

7.Which of these numbers is a cube number?

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.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

10.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

11.Solve the inequality 2(x − 1) ≤ 8.

12.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

13.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.

14.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

15.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.