Algebra worksheet — GCSE Foundation

1.Solve x² − 2x − 24 = 0.

2.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

3.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

4.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

5.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

6.Simplify 5x + 3y − 2x + y.

7.Which of these rules generates the sequence 6, 11, 16, 21, …?

8.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

9.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

10.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

11.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?

12.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

13.Which expression means 'add 3 to n, then multiply the result by 4'?

14.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

15.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.