AMO study guide
AMO · Work through your exam, one topic at a time.
The American Mathematics Olympiad (AMO) is a competition built around non-routine problems rather than routine computation. According to the organiser's page, AMO is an affiliate of Math Olympiads for Elementary and Middle Schools, USA (MOEMS), which the page describes as one of the oldest and most established primary and secondary school math competitions in the world, and the Singapore International Math Contest Centre (SIMCC) is the main organiser of AMO in ASEAN and Hong Kong, working with local Country and Territory Partners. The AMO study guide has 6 sections and about 1,903 words.
01Non-routine problem solving (Grade 3)
Grade 3 non-routine problems rarely need a formula. They test whether you can find a rule, keep track of information, and check your answer against the story.
300 words, about 2 min02Non-routine problem solving (Grade 4)
Grade 4 problems combine two ideas at once: a remainder condition with a list, a Venn diagram with a total, or a rectangle split into smaller rectangles. The arithmetic is still accessible; the challenge is organizing cases.
321 words, about 2 min03Non-routine problem solving (Grade 5)
Grade 5 problems often hide a fraction or ratio inside a story. The reliable method is to draw a unit bar or tape diagram, label the known part, and find what one unit represents.
338 words, about 2 min04Non-routine problem solving (Grade 6)
Grade 6 non-routine problems mix rates, proportional reasoning, and integer arithmetic. A rate problem is safe if you write the units: km/h, L/min, pages/day.
330 words, about 2 min05Non-routine problem solving (Grade 7)
Grade 7 problems usually require a translation step: words to an equation, a diagram to an angle equation, or a counting problem to cases. Once the equation is written, solve it systematically and check whether the answer makes sense in the original story.
327 words, about 2 min06Non-routine problem solving (Grade 8)
Grade 8 problems reward structure: cycles in powers, symmetry in counting, similarity ratios, and algebraic factoring. The calculation is rarely the hard part; recognizing the pattern is.
287 words, about 1 min