Exam technique: “show that” questions – GCSE Maths

Foundation and Higher · Grade 5

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A 'show that' question prints the answer. Every mark is for the route. Start from what is given, write one operation per line, and stop when your last line is identical to the printed target. Then write 'as required'. Working backwards from the target, or writing the target on line 1, scores zero because you assumed what you had to prove.

Algebra show-thats need every expansion. Geometry ones need a named reason. Number ones need exact fractions, not a calculator decimal that 'looks like' $\frac{11}{6}$. Count the marks: 3 marks wants about three visible steps. If you do not land on the target, the slip is in your working — go back, do not fudge the last line.

The answer is printed — the marks are the steps. Start from what is given and work forwards until you match the printed line, then write 'as required'. Do not start from the result and work backwards.

Objectives

• Expand a single bracket and simplify with a subtracted x.
• Expand a pair and cancel an x squared term.
• Expand a square and cancel x squared, or expand a pair and stop.

Key points

• Recognise that 'show that' means the marks are for the working, not the answer — the answer is already on the page.
• Start from what you are given and work forwards in clear lines until you reach the printed result.
• Write every step a marker would need to see, including the expansion, the arithmetic and the units.
• End with a line that matches the printed statement exactly, then a short 'as required'.

Worked examples

Questions and answers

GCSE Maths exam technique: “show that” questions questions and answers. Try each one, then open the answer. Easy questions come first.

Common mistakes

Most lost marks on this topic are one slip.

1. Multiplying only the first term in a bracket (e.g. 3(x+4) = 3x+4)

   Distribute multiplier to every term inside the bracket

2. Forgetting to cancel x^2 when subtracting x^2

   x^2 - x^2 = 0; remove the quadratic term entirely

3. Expanding (x+a)^2 as x^2 + a^2 without the middle term

   (x+a)^2 = x^2 + 2ax + a^2

Exam tips

• This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
• If the question says “show that”, the result is given. The marks are for the steps that reach it.
• The method is the same on AQA-style and Edexcel-style papers.
• Count the marks: a 3-mark show-that needs about three visible steps — if you have one line, you have missed marks.
• Because the answer is given, you already know if you are right; use that to hunt down the slip before moving on.

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

Download worksheet (PDF)

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More on Exam technique: “show that” questions

• Exam technique: “show that” questions worked examples and method
  The method in order, key facts and the full lesson explanation
• Exam technique: “show that” questions practice questions
  A second set of questions with answers, plus quick checks

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Last updated 9 November 2026.