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Tag: BMO
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 Trigonometry: When a Geometry Proof Needs Sine Rule Before an Auxiliary Line
For BMO geometry proofs involving side ratios in adjacent triangles, apply the sine rule before adding auxiliary lines. This guide explains when to use metric trigonometry versus circle or line constructions. Read article
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BMO Graph Theory: When to Model a Problem with Vertices and Edges
For the 2026-27 BMO preparation season (BMO1 on 19 November 2026, BMO2 on 21 January 2027 in the China region), a BMO1 or BMO2 candidate who sees a combinatorics problem about people, pairs, connections or forbidden configurations should ask three questions before reaching for casework: is the relation binary, is the target a triangle or… Read article
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BMO Pigeonhole Principle: Define the Boxes Before Counting the Objects
Learn why BMO pigeonhole proofs fail when students count objects before locking down the partition. A checked worked case, a deliberate misfire, and a diagnostic to fix your combinatorial proof structure. Read article
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BMO Modular Arithmetic: Choose a Modulus That Rules Out an Integer Solution
A worked guide to selecting the right modulus in BMO number theory problems: when modular arithmetic proves no integer solution exists, with checked examples, a contrasting case where the wrong modulus fails, and diagnostic steps for your next practice session. Read article
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SMC to BMO Proof Writing: Replace a Plausible Pattern With a Complete Argument
Transitioning from the Senior Mathematical Challenge (SMC) to the British Mathematical Olympiad (BMO) requires replacing pattern-matching intuition with rigorous, complete written arguments. This guide explains the shift in reasoning demands and provides worked teaching illustrations with checked steps. 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