Algebra worksheet — GCSE Foundation

1.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

2.Expand 7(a + 8)

3.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

4.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

5.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

6.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

7.A straight line has equation y = 5x. Work out the value of y when x = 3.

8.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

9.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

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.Which expression means 'y squared, multiplied by 3'?

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

13.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

14.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

15.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.