Algebra worksheet — GCSE Foundation

1.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

2.Work out the gradient of the straight line with equation 3y = 12 − 6x.

3.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

4.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

5.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

6.In which quadrant does the point (−3, 0.5) lie?

7.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

8.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

9.Make x the subject of the formula y = (x − 4)/5.

10.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.

11.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

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

13.Solve 5x + 2 = 17.

14.Work out the value of a² − 2b when a = −3 and b = 4.

15.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.