Singapore Mathematical Olympiad (SMO) — IP-Friendly Parent & Student Guide
Download printable cheat-sheet (CC-BY 4.0)05 Sep 2025, 00:00 Z
> 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.
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## 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
- Awards: Gold / Silver / Bronze within fixed upper bands; Merit/Participation
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## 2 Why SMO matters for IP students
- 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
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## 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.
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## 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
- Cross‑training with CCA Olympiad groups
Helpful context
- IMO overview — https://eclatinstitute.sg/blog/International-Mathematical-Olympiad
- H3 Mathematics (2026) — https://eclatinstitute.sg/blog/H3-Mathematics-in-A-Level-2026
- H3 vs Further Math — https://eclatinstitute.sg/blog/H3-Mathematics-Versus-Further-Mathematics-in-A-Level
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## 5 Training playbook (8–12 weeks)
Week 1–2: Baseline & habits
- Sit one past paper (section‑balanced) under a realistic 1.5 h timer.
- Build an error log with four columns: concept, trigger, fix, similar Qs.
- Read 2 proof write‑ups (Senior/Open level) and rewrite them in your own words.
Week 3–6: Topic clusters (alternate days)
- Number Theory: residues, Euclid algorithm variants, order/period arguments.
- Combinatorics: invariants, Pigeonhole, constructive counting, recursion.
- Geometry (synthetic): angle‑chasing, homothety, power of a point; clean diagrams.
- Inequalities: AM‑GM variants, Cauchy–Schwarz in disguise, bounding by convexity.
- Drill 15–30 min “trigger reps” per cluster; finish with 1–2 mixed problems.
Week 7–8: Mixed sets and pacing
- 2–3 mixed papers under time.
- Post‑mortem within 24 h: classify miss as “knowledge”, “recognition”, or “execution”.
- Rewrite 1–2 solutions in contest‑style format; ensure line‑by‑line logic.
Week 9–12 (optional stretch): Simulation and polish
- Full simulation with buffer management; rehearse skip/return rules.
- Attempt a higher‑section problem (e.g., Senior/Open) even if targeting Junior/Senior—focus on set‑up, not perfection.
- Share one polished solution per week with a peer/coach for critique.
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## 6 Skill transfer to school math
- Pattern spotting → Binomial expansions and sequences in IP WAs.
- Invariants → Conservation arguments in mechanics word problems.
- Constructive counting → Casework in probability; careful inclusion–exclusion.
- Proof fluency → Clearer explanations in coordinate geometry and induction.
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## 7 Admin & logistics
- Registration windows, eligibility, conduct reminders, invigilation format
- Materials policy (confirm yearly with school/organiser; follow official circulars)
Useful references
- Singapore Mathematical Society — SMO info: https://sms.math.nus.edu.sg/SMO/index.html
- DSA math tests & portfolios: https://eclatinstitute.sg/blog/How-DSA-Math-Talent-Tests-Work
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## 8 Next steps and resources
- When to deepen Olympiad track vs pivot to syllabus mastery
- Book a focused clinic to calibrate a personalised drill plan
- Further reading:
- IMO overview — https://eclatinstitute.sg/blog/International-Mathematical-Olympiad
- SASMO guide — https://eclatinstitute.sg/blog/Singapore-and-Asian-Schools-Math-Olympiad-SASMO
- NMOS guide — https://eclatinstitute.sg/blog/National-Mathematical-Olympiad
- H3 Mathematics (2026) — https://eclatinstitute.sg/blog/H3-Mathematics-in-A-Level-2026
- H3 vs Further Math — https://eclatinstitute.sg/blog/H3-Mathematics-Versus-Further-Mathematics-in-A-Level
- Bridging IPY4 → JC1 — https://eclatinstitute.sg/blog/Bridging-the-Gap-From-IP-Year-4-(IPY4)-to-JC1
> 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.
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## 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.
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### 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”).
