Q: Where can I find math olympiad books and past papers for Singapore competitions? A: The best starting point is official organiser websites - NUS High (NMOS), Hwa Chong (APMOPS), RI (RMO), SASMO, SMS (SMO), and SIMCC (SMKC) have all historically published sample questions or past papers. Beyond official sources, look for problem-solving books that match your competition level: puzzle-style workbooks for primary, topic-based problem collections for secondary, and proof-oriented texts for JC-level olympiads.
TL;DR Start with official past papers from each competition's organiser site. Match your book choices to your competition level - problem-solving puzzles for P3--P4, topic-based collections for P5--P6, and proof-writing guides for secondary and above. Free online resources include organiser archives, international problem databases, and community forums. Past papers are most effective when used under timed conditions with an error log.
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Official papers
Official Past Papers & Sample Questions
Book types by level
What Books to Look For by Level
Free practice
Free Online Resources
A study method
How to Use Past Papers Effectively
Concrete example: choosing resources
A P5 student preparing for NMOS or APMOPS should not start with proof-heavy secondary olympiad books. Begin with official samples, topic-based counting and geometry practice, and a timed error log so weak problem types are visible.
Official Past Papers & Sample Questions
The table below lists where each major Singapore maths competition has historically published official practice material. Availability may change between cycles - always check the official site for current resources.
Not every organiser publishes full solutions for every year. Some release only selected problems or sample papers.
Older papers may be removed from websites over time. If a link no longer works, check whether the organiser has migrated to a new site.
Do not rely on third-party sites hosting papers without permission - always start from the official source.
What Books to Look For by Level
We deliberately avoid naming specific commercial titles. Instead, here is what to look for at each stage so you can evaluate options yourself.
P3--P4 (Beginner / SASMO Early Divisions)
At this level, the goal is to build comfort with non-routine problems rather than drilling advanced techniques.
Problem-solving puzzle books - look for books that present word problems, logic puzzles, and pattern-recognition tasks designed for upper-primary students.
Competition-style workbooks - some publishers produce workbooks aligned to SASMO or NMOS difficulty. These typically include graded problems with worked solutions.
Heuristics-focused books - books that teach systematic problem-solving strategies (working backwards, drawing diagrams, making a table) are especially useful at this stage.
P5--P6 (Intermediate / NMOS, APMOPS, RMO Round 1)
Students preparing for NMOS, APMOPS, or RMO Round 1 benefit from books that introduce competition topics more formally.
Number theory basics - divisibility, primes, factors, LCM/HCF problems.
Combinatorics and counting - systematic counting, permutations and combinations at an introductory level.
Geometry - angle chasing, area computations, properties of triangles and circles beyond the school syllabus.
Algebra - setting up and solving equations, algebraic manipulation for problem-solving.
Look for books that provide graded difficulty within each topic, ideally with full solutions (not just answers).
Secondary and JC (SMO, APMO-Prep, IMO-Prep)
At the secondary and JC level, the jump in difficulty is significant. Useful resource categories include:
Competition problem collections - books that compile problems from national and international olympiads (AMC, MATHCOUNTS, BMO, APMO, etc.) with solutions.
Topic-specific problem books - dedicated volumes on number theory, combinatorics, geometry, or algebra at the olympiad level.
Proof-writing guides - books that teach mathematical proof techniques (induction, contradiction, construction) are essential for SMO Open, APMO, and beyond.
University-level introductory texts - for ambitious students, introductory university textbooks in discrete mathematics or abstract algebra can provide useful background.
Free Online Resources
Official organiser websites
The organiser sites listed in the table above are the most authoritative free sources. Many publish sample papers, syllabi, and - in some cases - full past-paper archives with solutions.
International problem databases
Several well-known international platforms host large collections of competition problems from around the world. The Art of Problem Solving (AoPS) community, for example, maintains an extensive problem wiki and discussion forums where students can find problems at every level. These platforms are useful for practice but should supplement - not replace - official Singapore competition papers, since the syllabus emphasis and problem style differ between countries.
Past-paper archives
Some school maths departments and teacher-run sites compile past-paper collections for local competitions. When using these, verify that the papers are legitimately shared and that solutions are reliable. Unofficial solutions can contain errors.
YouTube and video explanations
A growing number of educators post worked solutions to competition problems on YouTube. These can be helpful for understanding solution techniques, but quality varies widely. Prioritise channels that show clear working and explain the reasoning behind each step.
How to Use Past Papers Effectively
Having access to past papers is only useful if you practise with them strategically.
Timed practice - Simulate competition conditions. Set a timer matching the actual exam duration and work through the full paper without interruption. This builds stamina and time-management skills that cannot be developed through untimed practice.
Error logging - After marking a paper, record every mistake in a dedicated notebook or spreadsheet. For each error, note: the topic, the type of mistake (careless, conceptual, or never-seen-before), and the correct approach. Review this log before your next practice session.
Topic-based drilling - If your error log shows a cluster of mistakes in a particular area (e.g., combinatorics or geometry), pause full-paper practice and drill that topic intensively using a book or problem set focused on it. Return to full papers once the gap is addressed.
Spaced repetition - Revisit problems you got wrong after a gap of one to two weeks. If you can solve them cleanly without referring to the solution, the concept has stuck. If not, drill the underlying technique again.
Build Strong Foundations First
Competition mathematics builds on - and extends - the school curriculum. Students who struggle with school-level topics will find competition problems frustrating rather than productive. If your child needs to strengthen their core maths foundations before tackling competition work, structured tuition can help close gaps efficiently.
IP Maths Tuition - for IP-track students in lower and upper secondary
Note: Eclat Institute does not offer olympiad-specific tuition or competition coaching. Our tuition programmes focus on the school and national exam curriculum. For dedicated olympiad training, look into programmes run by competition organisers or specialist coaches.
NUS High School has historically published sample questions and past-year papers on their official website. Check nushigh.edu.sg for current availability. Availability may change between competition cycles.
Are SASMO past papers available online?
SASMO publishes sample papers for each division on sasmo.sg. These give a reliable sense of question style and difficulty. Full past-year papers may not always be freely available - check the official site for the latest resources.
What is the best book for a Primary 5 student preparing for NMOS?
Rather than recommending a single title, look for workbooks that cover number theory basics, combinatorics, and geometry at the upper-primary level, with graded difficulty and worked solutions. Books specifically aligned to Singapore maths competitions or the NMOS syllabus will be most directly useful.
How is SMO different from NMOS in terms of preparation?
NMOS targets Primary 5 students and focuses on non-routine problem-solving within a broadly primary-level scope. SMO covers Secondary and JC levels, with significantly harder problems that may require proof-writing skills (especially in the Open category). The jump from NMOS to SMO Junior is substantial - students typically need a few years of continued competition exposure and topic-deepening in between.
Should my child use international competition papers (like AMC) for practice?
International papers can be useful for broadening problem-solving exposure, but they differ in syllabus emphasis and style from Singapore competitions. Use them as supplementary practice rather than primary preparation material. For example, AMC problems tend to be multiple-choice and emphasise speed, while SMO Open problems require written proofs.
How many past papers should my child do before the actual competition?
There is no fixed number. A reasonable approach is to start with two or three papers under timed conditions to identify weak topics, then focus on targeted topic drilling, and return to full papers as the competition date approaches. Quality of review matters more than quantity of papers completed.
Does Eclat Institute offer maths olympiad coaching?
No. Eclat Institute does not offer olympiad-specific tuition or competition coaching. Our tuition programmes focus on the school and national exam curriculum - IP Maths and A-Level H2 Maths. For dedicated olympiad training, look into programmes run by competition organisers, university maths departments, or specialist coaches.
