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Why this page exists
Free official resources by competition
Free online platforms
Q: Do I need expensive tuition for my child to do well in maths and science competitions? A: No. Every major competition organiser in Singapore publishes free sample papers, past questions or syllabi. Combined with library books, school-based enrichment and free online platforms, a motivated child can prepare effectively without paid tuition. This guide lists every free and low-cost resource we could find - so that family income is not the deciding factor.
TL;DR Most competition organisers (NUS High, HCI, RI, SMS, SIMCC, IPS, NUS Physics) publish free materials on their official websites. NLB public libraries stock olympiad and problem-solving books at no cost. Online platforms like Art of Problem Solving, Khan Academy and Brilliant offer free tiers. School-based programmes (MOE E2K, olympiad CCAs) are free and under-utilised. You can prepare seriously for under 50/month−orfor0 with library access and official resources. This page links to every competition guide and resource page on our site so you can plan a pathway from one place.
One weekly loop: learn, attempt, mark, log, retry.
Turn free resources into steady progress.
Concrete example: A Primary 5 student preparing for NMOS can download official sample questions, borrow one olympiad problem-solving book from NLB, and keep a notebook with three columns: question type, mistake, and next retry date.
Why this page exists
On parent forums, a recurring theme stands out: the sense that competition preparation is only available to families who can afford specialist tuition centres. One parent described spending thousands per month on enrichment across multiple children. Others noted that official preparation materials are hard to find, with only a handful of books stocked at major bookshops.
The reality is that most competition organisers in Singapore publish free resources. The challenge is knowing where to look. This guide consolidates those sources in one place.
Every child who is curious about maths or science deserves a fair chance to explore competitions - regardless of family budget.
Free official resources by competition
The table below lists where each major competition has historically published free preparation materials. Availability changes between cycles - always check the organiser's official website for the most current resources.
For detailed guides on each competition (format, eligibility, difficulty, DSA value), see our individual competition pages linked below.
Not every organiser publishes full solutions for every year. Some release only selected problems or sample papers.
Older papers may be removed from websites when organisers update their sites. If a link no longer works, check whether the organiser has migrated to a new domain.
Do not rely on third-party sites hosting papers without permission - always start from the official source.
For a side-by-side comparison of all these competitions (difficulty, eligibility, format), see:
These platforms offer free access to problem-solving content that develops the kind of thinking competitions test. None of them are Singapore-specific, but the skills transfer directly.
Art of Problem Solving (AoPS) community
The AoPS online community forums host thousands of competition problems from olympiads worldwide, with student-written solutions and discussions. The forums are completely free. AoPS also offers free resources including Alcumus (an adaptive problem-solving tool) and past AMC/AIME problems with solutions.
Best for: Students at the intermediate to advanced level (P5 and above) who want exposure to problems beyond the Singapore syllabus.
Brilliant offers interactive courses in maths and science with a problem-solving focus. The free tier provides access to a limited set of daily challenges and introductory courses. The interactive format builds intuition rather than drilling procedures.
Best for: Students who learn well through guided exploration and visual explanations. The free tier is limited but still useful for building problem-solving instincts.
Khan Academy is entirely free and covers maths from primary through university level. While it follows the US curriculum rather than Singapore's, the underlying maths is the same. Topics like number theory, combinatorics and geometry are covered in ways that support competition preparation.
Best for: Filling specific knowledge gaps (e.g. a student who needs to learn modular arithmetic or basic probability before attempting certain competition problems).
The National Library Board (NLB) is one of the most under-utilised resources for competition preparation. Public libraries across Singapore stock:
Olympiad and problem-solving books - titles covering competition mathematics at primary and secondary levels. Use the NLB catalogue to search for terms like "mathematical olympiad", "problem solving" or specific competition names.
International competition collections - books compiling problems from AMC, IMAS, and other international competitions.
Popular science and maths books - titles that build curiosity and deeper understanding (the kind of reading that develops a genuine love of the subject rather than pure exam technique).
How to make the most of NLB:
Search the NLB catalogue online before visiting - check if the book you want is available and at which branch.
Use the reservation system to have books sent to your nearest branch.
Borrow multiple books and rotate - you do not need to buy every title.
Check the "New Arrivals" section periodically, as NLB does acquire new competition-related titles.
NLB membership is free for Singapore citizens and permanent residents.
Many schools offer free enrichment and competition training - but parents need to know what to ask for. Here are the main programmes to enquire about:
MOE E2K Programme (Excellence 2000)
E2K is an MOE-developed enrichment programme for high-ability primary school students in mathematics and science. It focuses on developing higher-order thinking through investigative tasks - not drilling competition techniques, but building the kind of reasoning that competitions reward.
Available at selected primary schools.
Run by trained school teachers using MOE-developed materials.
Free - no cost to parents.
Ask your child's form teacher or HOD (Maths/Science) whether your school offers E2K and what the selection criteria are.
School olympiad CCAs and training
Many primary and secondary schools run maths and/or science olympiad training as a CCA or ad-hoc enrichment programme. These are typically:
Led by teachers with competition experience.
Free (part of the school's CCA programme).
Available to students who are nominated or who express interest.
If your school does not currently offer competition training, it is still worth asking. Some schools will organise training if there is enough student interest, and teachers may be willing to supervise a small study group.
IP school enrichment
Students in Integrated Programme (IP) schools often have access to structured enrichment in maths and science, including competition preparation. Check with your school's talent development department about what is available.
Low-cost options (under $50/month)
If you are willing to spend a small amount, these options offer good value:
Past paper compilations
Bookshops like Popular and Kinokuniya stock competition preparation books, typically priced between 10and30 each. While the selection for some competitions (particularly SPSO) can be limited, you can often find:
SASMO practice papers by level
General olympiad problem-solving workbooks
Books aligned to NMOS or SMO difficulty
One or two well-chosen books, combined with the free official resources above, can provide months of practice material.
Competition entry fees
Most competitions in Singapore have modest entry fees:
SASMO and SMKC entry fees are typically in the range of 15−−25 per student.
Some school-registered competitions (NMOS, RMO, SMO) may have lower or waived fees when schools register students in bulk.
These fees give your child access to a real competition experience - including official results and certificates - which is valuable preparation in itself.
Structured self-study approach
For the cost of a few books and competition entries (well under $50/month averaged across the year), a student can follow this approach:
Use official past papers from the organiser websites listed above.
Supplement with one or two books from NLB or a bookshop.
Practise on AoPS or Khan Academy for specific topic gaps.
Enter one or two competitions per year for real-test experience.
This approach is not inferior to expensive tuition. Many competition medallists - including students who have represented Singapore internationally - began with self-study and school-based support.
Building strong foundations
Competition success starts with solid foundations in school-level maths and science. If your child is finding competition problems overwhelming, it may help to strengthen their core understanding first before layering on olympiad techniques.
We offer structured tuition in mathematics and physics for IP and JC students:
Can my child really prepare for competitions for free?
Yes. Every major maths and science competition organiser in Singapore publishes free sample papers or past questions on their official website. Combined with NLB library books (free to borrow) and free online platforms like AoPS and Khan Academy, a determined student has access to more practice material than they can realistically complete. The bottleneck is not money - it is consistent effort and guidance on what to practise.
Are paid resources better than free ones?
Not necessarily. The official past papers published by organisers like SMS, NUS High and RI are the single most useful preparation resource - and they are free. Paid books and tuition can add structure and coaching, but they are not required. A student who works through official past papers methodically, with an error log and timed practice, will outperform a student who passively attends classes without doing independent work.
What if my school does not offer competition training?
Start by asking - many schools have informal training that is not widely publicised. If your school genuinely does not offer anything, you can:
Use the free official resources listed on this page for self-study.
Form a small study group with classmates and work through problems together.
Ask a maths or science teacher if they would be willing to supervise a weekly problem-solving session.
Use AoPS forums to discuss problems and learn from other students' solutions.
Which free resource should I start with?
Start with the official past papers from the competition your child plans to enter. There is no better preparation than practising the exact format and difficulty your child will face. Once your child has worked through available official material, supplement with AoPS (for maths) or the relevant physics resources (for science competitions). See our competition comparison guide to choose the right starting competition.
How do I structure self-study without a tutor?
A practical weekly routine:
Timed practice (1--2 sessions per week): Attempt one full past paper or a set of 10--15 problems under timed conditions matching the real competition.
Review and error log (after each session): For every problem you got wrong or could not solve, write down the solution method and what you missed. This is the most important step.
Topic study (1 session per week): If the error log reveals a recurring weak area (e.g. number theory, combinatorics), spend one session studying that topic using a book or online resource.
Free exploration (optional): Let your child explore problems that interest them on AoPS or Brilliant - this builds the intrinsic motivation that sustains long-term effort.
Are online resources enough, or does my child need books too?
Online resources alone can take a student a long way, especially for maths competitions where AoPS and official past papers cover most needs. Books add value when your child needs structured topic coverage (e.g. a systematic introduction to number theory) rather than scattered problem practice. The good news is that NLB libraries stock many of these books for free.
My child loves maths but does not enjoy competition pressure. What should I do?
That is perfectly fine - and actually common among strong students. Competitions are one pathway, not the only one. Focus on resources that develop your child's love of the subject: puzzle books, recreational mathematics, science exploration kits, and platforms like Brilliant that emphasise discovery over performance. If your child later becomes curious about competitions, the foundation will already be there.
Where can I find a full list of competitions and dates?
