Algebra worksheet — GCSE Foundation

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

2.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

3.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

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

5.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

6.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

7.y = 5 − 2x. Work out the value of x when y = 11.

8.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

9.Make m the subject of the formula w = m − 8.

10.Which expression means the same as a × a × a?

11.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.

12.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

13.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

14.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

15.Factorise fully 56x − 24