Algebra worksheet — GCSE Foundation

1.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

2.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

3.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.

4.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

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

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

7.The point A is at (5, −3). In which quadrant does A lie?

8.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

9.Solve 2x + 1 = 9

10.Which of these is a factor of 15x + 20?

11.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

12.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

13.Write down the expression that means the same as m² × m × 3.

14.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

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