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Algebra: equations and sequences

Some written Stage 2 maths papers (for example at schools that set their own second round) may expect confident algebra - check your target school's current admissions information: solving equations with brackets and unknowns on both sides, substituting into formulae, and finding the n-th term of a sequence.

What is tested

  • Solving linear equations, including brackets and unknowns on both sides
  • Substituting values into expressions and formulae
  • Finding the n-th term of a linear sequence
  • Forming an equation from a word problem

Worked example

Solve 5(x − 2) = 3x + 6.

  1. Expand the bracket: 5x − 10 = 3x + 6.
  2. Subtract 3x from both sides: 2x − 10 = 6.
  3. Add 10 to both sides: 2x = 16.
  4. Divide by 2: x = 8.
  5. Check: 5(8 − 2) = 30 and 3(8) + 6 = 30.

Answer: x = 8

Exam-day checklist

  • Expand brackets first, taking care with negative signs.
  • Collect the x terms on one side, numbers on the other.
  • Do the same thing to both sides, one step per line - on a written paper this can earn method marks.
  • Always substitute your answer back in to check.

Common mistakes

  • Only multiplying the first term inside a bracket.
  • Moving a term across without changing its sign.
  • For a sequence, using the common difference as the whole rule instead of 'difference × n + adjustment'.

Try it yourself

1. Find the n-th term of the sequence 5, 8, 11, 14, ...

Show answer

3n + 2

The common difference is 3, so the rule starts 3n. When n = 1, 3n = 3 but the term is 5, so add 2: 3n + 2.

2. Solve 4x − 9 = 2x + 5.

Show answer

x = 7

Subtract 2x: 2x − 9 = 5. Add 9: 2x = 14. Divide by 2: x = 7.

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More topic guides

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Practice materials are original and independently produced. They are not official school papers and do not guarantee admission. School arrangements can change; parents should check each school’s current admissions information.