Q: Can a student prepare for maths or science competitions without specialist tuition? A: A student can start with organiser-published samples, school support, library materials and a consistent review routine. However, not every organiser publishes full past papers for free, and no resource guarantees an award. Check the verified access notes below before building a plan.
19 July 2026 audit result: Free official access varies substantially. APMOPS and RMO currently publish useful question-and-answer sets. NMOS and SPSO publish selected material. SMO's full solution books are paid publications. Recent SASMO papers are tied to its LMS and registration routes. No current public SJPO or SPhO preparation library was verified from the cited modern NUS pages.
Verified official resource map
This table records what was visible on current organiser-controlled pages during the audit. A page labelled "limited" can still be useful, but should not be described as a complete free archive.
No current public preparation library verified in this audit
Ask the school coordinator for the current circular and permitted resources
This is not evidence that one competition is better than another. It only describes current public preparation access.
Direct organiser links
NMOS
NUS High's Special Round solution page currently links solutions from selected years. Use them to study written reasoning, but do not assume they reproduce the current Main Round format.
APMOPS
Hwa Chong Institution has a dedicated APMOPS sample page with sample questions and answers for Round 1 and samples for the Invitation Round. The 2026 competition has already concluded, but the samples remain useful for understanding its published problem style.
RMO
RI's current RMO page offers the previous two Round 1 question sets and solutions. It also publishes 2026 teacher and student user guides. RMO registration is school-only, so preparation access does not create an individual registration route.
SMO
The Singapore Mathematical Society's SMO page links sample questions. Its solution-book page describes detailed yearly and multi-year books and marks recent issues as available for purchase. Do not describe the full solutions archive as free.
SASMO
The current SASMO registration page says its 2026 school fee included LMS access to 2023, 2024 and 2025 contest papers and answer keys. It gives the same recent-paper benefit for the higher-priced private-candidate route. Teachers are also directed to a free SIMCC membership login for information about past papers.
That is account or registration-linked access, not an unrestricted public archive. The domain sasmo.sg currently labels its main page an unofficial guide, so it should not be used as the authority for current rules even though old sample PDFs remain indexed there.
SMKC
The dedicated SMKC site publishes the current format and syllabus. It also confirms that wrong answers lose one point, which matters when practising. The reviewed page did not expose a current public set of free sample papers.
SPSO
NUS High's SPSO sample page includes a syllabus outline and worked samples for Sections A and B. It is a useful official starting point, but it is not a promise that every current competition question comes from the displayed examples.
SJPO and SPhO
Search results still surface an old SJPO general-round sample and 2013 or 2015 syllabus files on an IPS-hosted NUS domain. The current NUS Physics URLs previously cited by this page did not provide a usable current resource page during the audit. Use archived files only as historical practice and obtain the current rules from the student's school coordinator.
What can the school provide?
MOE says all primary schools have programmes beyond the curriculum for students with particular strengths and interests, giving E2K Mathematics and Science as examples. That statement does not mean every student is entitled to E2K, that every school uses the same selection process, or that every school provides competition coaching.
Ask the school's Mathematics or Science department:
Which competitions will the school enter this year?
Who is eligible, and is nomination required?
Does the school provide preparation sessions or materials?
Can students access organiser resources through a teacher account?
What fees, devices or transport must families provide?
Do not assume a teacher can create an unpaid club or supervise a new study group. Ask what the school currently offers.
Use NLB without assuming every title is available
The NLB catalogue can be searched by title, author, subject or keyword, with item availability shown by branch. Useful search terms include mathematical olympiad, problem solving, combinatorics, number theory and physics problems.
Catalogue discovery does not prove that NLB holds a specific recommended book or that a copy is immediately available. Borrowing depends on membership and item status. Reservations can also carry a per-item fee, so check the current account terms before reserving multiple books.
A low-cost workflow is:
Search the catalogue from home.
Check the branch and item status.
Use an available copy on the shelf when practical.
Reserve only after checking the current fee.
Record the edition because problems and solutions can differ across editions.
Free general learning support
Khan Academy says its learning library is free. It can help a student repair a curriculum gap in algebra, geometry, probability or physics.
It is not aligned to NMOS, RMO, SMO, SPSO or another Singapore competition. Use it for a named knowledge gap, then return to the organiser's sample format. This page no longer labels Brilliant's changing access model or AoPS account features as a verified free tier.
A resource-first practice loop
Free material becomes useful only when the student reviews it carefully. Try this loop:
Check the current format. Confirm time, question types, calculator rule and scoring on the organiser page.
Attempt a small official set. Start without timing if the format is unfamiliar.
Mark from an official answer or solution. Do not copy a third-party answer without checking it.
Classify each error. Separate missing knowledge, misunderstood wording, invalid reasoning, calculation mistakes and time pressure.
Repair one gap. Use a school text, library book or general learning platform.
Retry later. Solve the same problem without looking at the old working.
Add timing gradually. A complete timed paper is useful only after the student understands the question types.
There is no official rule that every student needs one or two sessions weekly, ten to fifteen questions per session, or a fixed number of preparation months. Set the workload from the confirmed date, available material and the student's current needs.
Build an honest budget
The old claim that serious preparation always costs less than S$50 per month was not evidence-backed. A family may spend nothing on preparation material, but competition entry, account access, books, printing, devices or transport can still cost money.
Create a route-specific budget:
current competition fee from the organiser or school notice;
required platform or payment-processing charges;
optional book or reservation costs;
printing and stationery;
travel; and
any optional paid coaching.
Do not average costs across a year to make an arbitrary monthly ceiling appear true. Also do not buy old papers until you have checked whether the organiser already provides the same material.
What this guide cannot promise
Official samples, library books, school support and self-study can provide a credible starting path. They do not establish that:
every competition can be prepared for entirely free;
free preparation is equal to paid coaching for every learner;
a particular routine will produce a medal;
competition participation improves school results or admissions outcomes; or
a student who self-studies will outperform one receiving coaching.
The right support depends on the student's foundation, independence, feedback access and wellbeing. If a student is repeatedly stuck, seek feedback from a teacher or another qualified adult before simply adding more papers.
No. Current access ranges from free samples and selected solutions to paid books, registration-linked LMS access or no verified public archive. Use the resource map above.
Which free resource should a student start with?
Start with the current organiser's format or syllabus, then attempt the closest official sample that is actually available. For RMO and APMOPS, useful free question sets are currently public. Other competitions have more limited access.
Is NLB borrowing completely free for everyone?
Do not assume so. Membership eligibility, borrowing privileges and reservation charges vary. Search availability first and check the current NLB account terms before placing a reservation.
Are old SJPO resources still useful?
They may be useful as historical physics problems, but they are not evidence of the current syllabus or paper rules. Confirm the current circular through the school.
Does a student need tuition?
There is no universal answer. Begin with current official material and school support. If the student cannot diagnose errors or lacks prerequisite knowledge, targeted feedback may be more useful than adding more papers.
Can free preparation guarantee an award?
No. Resource access does not guarantee performance, awards, DSA selection or another admissions outcome.
Last reviewed: 19 July 2026. Resource access, fees and account rules can change. Check the organiser, school and NLB pages before relying on a resource or paying.
