Algebra worksheet — GCSE Foundation

1.Which of these numbers is a cube number?

2.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

3.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

4.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

5.Which expression means 'add 3 to n, then multiply the result by 4'?

6.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.

7.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

8.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

9.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

10.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

11.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

12.Write down the expression that means the same as m × m × m × n.

13.Solve 4(x − 3) = 2x + 6.

14.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

15.y = x + 10. Work out the value of y when x = 0.