Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

2.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

3.Factorise x² − 3x − 10.

4.Which of these equations describes a vertical line?

5.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

6.Simplify k + k + k + k + k.

7.Work out the value of 5a + 2 when a = 3

8.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

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

10.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

11.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

12.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

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

14.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

15.A vertical line passes through the point (4, 7). Write down the equation of this line.