Mastering Pattern Recognition for IB Maths AA & AI
Paper 3 opens with an unfamiliar context and asks you to find a general rule. Examiners are testing whether you can turn a few numeric cases into a formula you can defend. This is the single most common skill gap between a 5 and a 7 in IB Maths.
Why it matters
- Paper 3 (HL AA and HL AI) always leads with a small-case investigation — usually 2–4 marks purely for spotting the pattern.
- "Show that" and "prove that" questions in Papers 1 and 2 hinge on the same skill: conjecture from cases → generalise → verify.
- This is where marker's mark schemes reward the method, even when the algebra later goes wrong. Don't skip it because you can't finish the whole proof.
Examiner signals
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General term / n-th term prompts“Find un”, “in terms of n”, “write a formula for …” — these are the flags. Always compute the first 3 explicit values first.
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“Show that” and “prove by induction”These questions give you the answer — you're being marked on the working. Never re-derive; use the given form as the target.
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Conjecture-then-justifyPaper 3 will often ask “based on your results above, conjecture …” and then “show your conjecture holds …”. Two separate marks, two separate skills.
Interactive fluency practice for Mastering Pattern Recognition for IB Maths AA & AI
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FAQ
How do I approach an unfamiliar Paper 3 pattern-recognition question?
Always work out the first three explicit cases before generalising. Write u1, u2, u3 out, spot the difference / ratio, and then write down your conjecture before attempting to prove it. IB examiners award marks for the conjecture on its own — even if you never manage the proof.
What's the difference between “show that” and “find” questions?
“Show that X = Y” gives you the target. You cannot lose the mark for a wrong answer — only for missing method. “Find” expects the numeric answer to be correct. Treat “show that” as an invitation to write the method out slowly.
Do I need to memorise proof-by-induction wording?
Yes — the four ritual steps (basis, assumption, inductive step, conclusion) are worth around 4 of the 6 marks. The maths inside the inductive step is often only 2 marks. Learn the wording verbatim from the sample answers on the IB Maths Analysis & Approaches HL specimen paper.