Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

2.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

3.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

4.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.

5.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

6.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

7.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

8.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

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

10.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

11.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

12.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

13.Work out the gradient of the straight line with equation 2x + y = 8.

14.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.

15.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.