Algebra worksheet — GCSE Foundation

1.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

2.Which expression means 'triple c, then add double d'?

3.x = 5. Work out the value of 3x² − 4.

4.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

5.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

6.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

7.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

8.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

9.Write down the expression that means the same as (x + 7) ÷ 4.

10.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

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

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

13.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.

14.Write down the gradient of the line with equation y = 7x − 2.

15.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.