Further Mathematics · AQA 7367 · Topic OT2

Mathematical problem solving

Solving unfamiliar, unstructured problems and explaining what the answer means. Applies to every paper.

  • 5 sub-topics
  • Taught in Year 13
  • 23 practice questions
  • 5 animated lessons
Practice questions (23) Lessons Worksheets All AQA Further Mathematics topics

What the specification says

Every sub-topic AQA can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. OT2.1Recognise the underlying structure of a problemY13
  2. OT2.2Extended arguments for unstructured problemsY13
  3. OT2.3Interpret solutions in contextY13
  4. OT2.6The problem-solving cycleY13
  5. OT2.7Diagrams in problem solvingY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 23 questions in this topic, free, no account needed.

Mathematical problem solving

Easy

'Hence' · Year 12 · 1 mark

  1. A part of a question begins 'Hence'. What does this require?
    (1)

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  1. A different method may earn no marks, even if the answer is right.BB: Use the result of the previous part

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Mathematical problem solving

Medium

Seeing the structure of an equation · Year 12 · 1 mark

  1. The equation z4+5z2+4=0z^4 + 5z^2 + 4 = 0 is a quadratic in which quantity?
    (1)

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  1. Look for one expression and its square.DD: z2z^2

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Mathematical problem solving

Hard

Extended argument · Year 12 · 3 marks

Show that n3−nn^{3} - n is divisible by 6 for every integer nn.
  1. Prove it.
    (3)
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  1. n3−n=(n−1)n(n+1)n^3 - n = (n-1)n(n+1)
  2. Three consecutive integers include a multiple of 2 and a multiple of 3.
  3. So the product is divisible by 6.

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