Australian Mathematical Olympiad (AMO) Preparation
To prepare for the Australian Mathematical Olympiad, master writing rigorous proofs — not just finding answers — across number theory, combinatorics, geometry and inequalities, and work through past problems and Australian Maths Trust training materials with your full solutions critiqued. The AMO is an invitation-only, proof-based olympiad near the top of the Australian mathematics pathway, and from 2026 it runs as three linked competitions rather than one.
Key facts at a glance
- 2026 restructure: from 1 January 2026, three competitions — AMO Summer, AMO Winter and AMO Finals.
- Invitations: about 250 students to each of Summer and Winter; about 60 to Finals at state exam centres.
- AMO Summer: six challenging problems requiring sound mathematical proofs.
- Associated 2026 dates: 25 February, 29 July and 1–2 September 2026 (confirm with AMT).
- Entry: invitation-only, via strong results in earlier AMT competitions.
- Official source: Australian Maths Trust.
- Dates & format: see the AMO dates and format page.
What makes the AMO different
Up to and including the Australian Intermediate Mathematics Olympiad, most Australian maths competitions are answer-based. The AMO is the point where that changes: it requires full, rigorous written proofs. A correct final number earns little without a watertight argument, and a wrong final number can still earn substantial marks if the reasoning is sound and well-presented. This single shift — from answers to arguments — defines how preparation must work, and it is the biggest adjustment for students arriving from the AMC and AIMO.
Where to go next
AMO sits above AIMO, which sits above AMC. These are the steps.
- Already scoring Credit or Distinction
- Targeting HD and the hardest questions
- Already at AMC Distinction or HD
- Moving from competition maths into olympiad
- Knows the content, loses marks to timing
- Wants exam-day rehearsal
The 2026 structure
The Australian Maths Trust restructured the AMO from 1 January 2026 into three competitions. AMO Summer and AMO Winter each invite around 250 students and serve as the main proof exams, with AMO Summer consisting of six demanding proof problems. AMO Finals invites roughly 60 students to sit at exam centres in each state. The pathway then continues toward the selection of Australia’s International Mathematical Olympiad team. Because the format is new, students and parents should confirm the exact rules and dates directly with the AMT.
The core olympiad topics
| Topic | What to develop |
|---|---|
| Number theory | Divisibility, modular arithmetic, primes, Diophantine reasoning |
| Combinatorics | Counting, pigeonhole, invariants, constructions and bounds |
| Geometry | Angle chasing, similarity, circles, rigorous diagrams and proof |
| Algebra & inequalities | Functional equations, classic inequalities, algebraic manipulation |
How to prepare for proof problems
- Learn to write proofs. Practise full written solutions and have a teacher or experienced student mark them for rigour and clarity, not just the final answer.
- Build the four toolkits. Work systematically through number theory, combinatorics, geometry and inequalities using AMT olympiad materials.
- Study past AMO problems. Attempt each fully before reading the solution, then compare your argument with the official write-up.
- Train partial credit. Even on a problem you cannot finish, write down what you can prove — lemmas and cases earn marks.
Where the AMO sits, and how to reach it
Because the AMO is invitation-only, the practical question for most families is how to qualify. The route runs through earlier competitions: a strong Australian Mathematics Competition result, then the Australian Intermediate Mathematics Olympiad, which is where invitations to the senior olympiad pathway begin. See our AIMO qualification and pathway guide for the step just below the AMO, and our AMC vs AIMO comparison for how the early stages fit together. To build the foundations, the Ace Achievers AIMO preparation course (A$499) targets exactly the extension and early-proof skills the pathway needs; a free diagnostic shows current readiness.
Structure and dates last verified June 2026 against the Australian Maths Trust. The AMO was newly restructured for 2026 and details may change — always confirm with the AMT before relying on a date or format.
Frequently asked questions
How do I prepare for the Australian Mathematical Olympiad?
Master writing rigorous proofs, not just finding answers. Study the standard olympiad topics — number theory, combinatorics, geometry and inequalities — and work through past AMO problems and AMT training materials, writing full solutions and having them critiqued. Proof-writing is the decisive skill.
How is the Australian Mathematical Olympiad structured in 2026?
From 1 January 2026 the AMO was restructured into three competitions: AMO Summer, AMO Winter and AMO Finals. Roughly 250 students are invited to each of Summer and Winter, and about 60 to Finals at state exam centres. AMO Summer consists of six challenging proof problems.
Who can sit the Australian Mathematical Olympiad?
The AMO is invitation-only. Students qualify through strong performance in earlier Australian Maths Trust competitions such as the AMC and the Australian Intermediate Mathematics Olympiad, with school notification of invitations.
When is the Australian Mathematical Olympiad in 2026?
The 2026 AMO competitions are associated with dates including 25 February, 29 July and 1–2 September 2026. Because it is invitation-based and newly restructured, confirm exact dates with the Australian Maths Trust.
What is the difference between the AMO and the AMC?
The AMC is an open, multiple-choice entry competition. The AMO is an invitation-only, proof-based olympiad several steps further along the pathway, requiring full written mathematical arguments rather than answers.