Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 3. The output is 15. Work out the input.

2.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

3.Which of these numbers is a cube number?

4.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

5.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

6.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.

7.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

8.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

9.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

10.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

11.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

12.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

13.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.

14.Solve the inequality 3x − 1 ≤ 11.

15.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.