Q: What does Singapore Mathematical Olympiad (SMO): IP-Friendly Parent & Student Guide cover? A: One-page evergreen reference for SMO (Junior, Senior, Open) format, scoring, timelines and training strategy.
TL;DR SMO is Singapore's flagship Olympiad for secondary and JC students. Use an 8-12 week drill plan, prioritise error-minimisation in MCQ sections, and align practice with IP WA/Promo calendars. Strong SMO performance feeds the national pipeline (NTST → NTTP → IMO) and signals readiness for H3/Further Math.
Registration quick answer (Singapore): Schools typically coordinate SMO entries with the Singapore Mathematical Society; students register through their teacher‑in‑charge. Independent entry may be announced by SMS for some years — always follow the official SMO page for current instructions and dates: https://sgmathsociety.org/singapore-mathematical-olympiad-smo/
1 What is SMO?
Organiser: Singapore Mathematical Society (SMS)
Sections: Junior, Senior, Open; individual contest, written format
Typical cadence: registration in Term 2, paper in mid-year; awards thereafter
DSA leverage: valued under “Mathematics & Computational Thinking” achievements
Curriculum bridge: number theory, inequalities, functional equations reinforce IPY3/Y4 depth
JC readiness: habits transfer to H2 proofs and H3/Further Math rigour
3 Paper structure and scoring
Expect a progression from routine to non-routine questions. Early problems check algebra and pattern recognition; later ones need deeper structure (invariants, bounding, extremal).
Scoring policies and section splits update periodically. Always check the official circulars from the organiser/school before relying on online summaries.
Practical pacing (works for most candidates):
Bank all certain questions within the first 25-35 % of time.
Enforce a 60-90 s “decision gate”: either commit or skip and return.
Leave a 10-15 min buffer for re-checks and tidy write-ups.
Common traps
Over-algebra: search for invariants/symmetry first; expand second.
Guessing under time pressure: only when you can eliminate ≥2 options reliably (if applicable).
Unjustified leaps in Senior/Open write-ups: state lemmas, label constructions, keep diagrams clean.
4 Pipeline: SMO → NTST → NTTP → IMO
How strong SMO results lead to NTST invites
What NTTP training looks like; realistic timelines around WAs and Promos
Author note: Formats and cut-offs change from year to year. Treat all structure/scoring remarks here as orientation; defer to official school/organiser memos for the exact rules that apply to your cohort.
9 Worked examples (with solutions)
9.1 Number Theory — Pigeonhole on residues
Problem. Show that among any 10 integers, two differ by a multiple of 9.
Solution. Reduce each integer modulo 9. There are only 9 residue classes {0,1,2,3,4,5,6,7,8}. Placing 10 numbers into 9 boxes forces at least one box to contain ≥2 numbers (Pigeonhole Principle). Those two numbers share the same residue r, so their difference is divisible by 9. ∎
Why this matters. The same idea underlies many SMO combinatorics/NT puzzles: map objects to a small set of “types”, then apply pigeonhole to force a collision.
9.2 Combinatorics — Binary strings without consecutive ones
Problem. Let f(n) be the number of length-n binary strings with no consecutive ones. Find a recurrence for f(n) with f(1), f(2), and express f(n) in terms of Fibonacci numbers.
Solution. Consider the first symbol.
If it is 0, the remaining n-1 symbols form any valid string: f(n-1) choices.
If it is 1, the second must be 0; the remaining n-2 symbols form any valid string: f(n-2) choices. Thus f(n) = f(n-1) + f(n-2).
Base counts: f(1) = 2 (“0”, “1”), f(2) = 3 (“00”, “01”, “10”). With F1=1, F2=1 as the Fibonacci seed, it follows by induction that f(n) = F_{n+2}. ∎
Exam habit. After writing a recurrence, always state base cases clearly and justify each branch condition (“no 11”).
