Algebra worksheet — GCSE Foundation

1.Write down the gradient of the line with equation y = −x + 3.

2.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

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.Work out the coordinates of the reflection of (6, −3) in the y-axis.

5.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

6.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

7.Which of these equations gives a straight-line graph when plotted?

8.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

9.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.

10.Which of these points lies in the first quadrant?

11.Write down the expression that means the same as w ÷ 6.

12.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

13.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

14.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

15.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.