Algebra worksheet — GCSE Foundation

1.Simplify 2b − 1 + 2b − 4 + 2b

2.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

3.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

4.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.

5.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

6.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

7.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

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

9.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

10.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

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

12.Simplify x + x + 4

13.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

14.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

15.Make x the subject of the formula y = x/2 − 5.