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Tag: BMO Proof Writing
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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BMO1 Diophantine equations: factor or bound? A decision table for two-variable proofs
BMO1 Diophantine equations need a structural decision: factor a product form or bound a variable. This guide gives a decision table, a complete positive-integer factor-pair audit, and a finite-range bound check. Read article
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BMO1 angle chasing: a configuration audit before you add an auxiliary circle
Before adding an auxiliary circle in a BMO1 angle chase, record which side of each chord the key points lie on, the order of points on each line, and whether the quadrilateral is convex or crossed. Equal angles alone are not enough: same-side equal angles support concyclicity; opposite-side equal angles generally do not. Read article
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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 Geometry Auxiliary Construction: Choosing Between Circle and Line
Stuck on a BMO1 geometry proof? Learn when to introduce an auxiliary circle for angle chasing versus an auxiliary line for ratios and similarity. Read article
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BMO Functional Equations Substitution: Systematic Checks for Complete Proofs
Spotting one solution is not enough. This guide provides systematic substitution checks to turn lucky guesses into complete ‘determine all functions’ proofs for BMO candidates. 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