Algebra worksheet — GCSE Foundation

1.A square tile has an area of 144 cm². Work out the side length of the tile.

2.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

3.Solve 4(x − 3) = 2x + 6.

4.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.

5.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

6.Simplify 5a/6 − a/3

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

8.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

9.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

10.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

11.a = 3 and b = 5. Work out the value of a²b.

12.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

13.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

14.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

15.Write down the gradient of the line with equation y = 6 + 4x.