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Tag: BMO Preparation
All BMO and UKMT Pathway Guide editorial articles matching this filter. Browse the full archive at News & Updates, or use the navigation to filter by stage, paper, or topic tag.
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BMO Combinatorics Recurrence: How to Build the State Before Counting
When direct counting fails in BMO-style problems, use a recurrence-first method. Define states, identify moves, and prove exhaustiveness with this teaching illustration. Read article
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BMO Extremal Principle: Choosing the Largest or Smallest Object to Start a Proof
Mastering the extremal principle is key for BMO proofs. Learn how selecting the largest or smallest object simplifies complex logic, with worked hypothetical teaching illustrations and common pitfalls. Read article
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BMO Equality Cases: Finishing an Inequality Proof Completely
Learn why BMO inequality problems demand explicit equality-case verification, with two worked hypothetical examples, a common shortcut mistake, and a practical diagnostic to check your own proofs. Read article
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BMO Induction: Choosing a Statement Strong Enough to Prove
A focused guide on selecting the correct induction hypothesis for BMO proofs, featuring worked hypothetical examples and diagnostic strategies. Read article
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BMO Infinite Descent: How to Write a Complete Proof
A guide to completing BMO-style infinite descent proofs by choosing a least positive solution, preserving integrality, and proving strict decrease. Read article
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Writing BMO Proofs in English: A Phrasebook and Style Guide for Second-Language Candidates
British markers read what you wrote, not what you meant. The connectives, notation conventions and rewriting habits that make an olympiad script legible in English. Read article
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BMO Algebra Decoded: Inequalities, Functional Equations and Polynomials (2026-27)
The fourth BMO problem area almost nobody drills: how to recognise, attack and actually finish inequality, functional equation and polynomial questions on Round 1. Read article
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The BMO1 Number Theory and Combinatorics Toolkit: Parity, Invariants, Pigeonhole and the Right Modulus
Parity, invariants, pigeonhole and choosing the right modulus: how to make BMO1 number theory and combinatorics systematic instead of a matter of luck. Read article
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BMO1 Geometry Decoded: The Configurations, Tools and Write-Up Habits That Earn Marks
Recognise the configuration, choose the right tool, then write it so a marker can follow: a practical geometry guide for the six-problem BMO1 paper. Read article