Preparing for the American Mathematics Competition 12 (AMC 12) can feel different from preparing for a school mathematics test. Knowing a formula is useful, but unfamiliar problems also ask you to choose an approach, interpret conditions and check your reasoning under time pressure.
Whether you are planning a first attempt or reviewing a previous result, start with three questions: What are the rules for your entry? Which skills need attention? How will you turn practice into independent problem solving?
Need help planning your AMC 12 preparation? Tell Hanlin your school grade, mathematics curriculum and previous competition experience. Send AMC12 START so we know you came from this guide.
1. Confirm the format and entry requirements
The Mathematical Association of America's official AMC overview describes AMC 12 as a 25-question, 75-minute multiple-choice competition. It has two versions, AMC 12A and AMC 12B. The overview lists Grade 12 or below and an age under 19.5 on competition day among the participation requirements.
If you participate outside the United States and Canada, consult the MAA's international participation information and the relevant International Group Leader for your country or region. The MAA directs international students to register through that local route.
Before entering, confirm the deadline, local date and time zone, exam location, identity requirements and permitted equipment. Read the instructions for your actual paper, including scoring and how unanswered questions are treated. Our registration information and competition rules can help you organise those questions.
2. Understand what AMC 12 adds to your preparation
The MAA overview includes trigonometry, advanced algebra and advanced geometry within AMC 12's high school mathematics scope, while excluding calculus. Its AMC 10 description excludes those advanced topics. If you are moving from AMC 10 to AMC 12, review the additional material alongside the problem-solving habits you have already developed.
Use the following prompts to assess your foundations:
- Algebra: Can you rearrange expressions, recognise useful identities and check restrictions before accepting a solution?
- Geometry and trigonometry: Can you draw a clear diagram and explain why the relationships you use apply?
- Number reasoning: Can you use divisibility, remainders or parity to reduce the possibilities?
- Counting and probability: Can you define the cases, avoid overlap and justify how you count outcomes?
These are study prompts, rather than an exhaustive official syllabus. Our exam content page offers another starting point. Use suitable published problems to check understanding; recognising a topic name is not the same as applying it independently.
3. Try a problem that rewards choosing an efficient method
An illustrative algebra question
A positive real number x satisfies x + 1/x = 3. What is x2 + 1/x2?
You could first solve a quadratic equation for x, but the requested expression suggests a shorter route. Square the given relationship:
(x + 1/x)2 = x2 + 2 + 1/x2 = 9.
Subtract 2 to obtain x2 + 1/x2 = 7.
This example was written for this guide. It is not an official AMC 12 question or a measure of competition difficulty.
The useful habit is to look at what the question asks before committing to a calculation. Here, finding the individual value of x is unnecessary. After solving a practice problem, ask whether your method found more information than you needed.
Check the reasoning as well as the answer. The reciprocal requires x to be nonzero, which is satisfied by the stated condition. The middle term when squaring is 2, not 1; omitting it changes the result. A short explanation helps expose such mistakes.
4. Separate knowledge gaps from time-management gaps
Begin with a short mixed set without a timer. Record whether you solved each question independently, needed a hint or could not find a starting point. Before reading the solution, write down what stopped you.
Next, attempt a suitable published paper under the correct time limit and current exam conditions. Revisit unfinished problems without the timer before opening the solutions. If you can now solve them, review method selection and time allocation. If you still cannot begin, return to the underlying concept.
Keep an error log with a specific action. "Check the cross term when squaring a sum" is more useful than "avoid careless errors." Reattempt selected questions several days later without looking at your notes. That helps you distinguish remembering a solution from understanding the method.
When practising multiple-choice questions, justify why an option is impossible instead of simply crossing it out. Track which answers came from a complete argument and which came from uncertainty, then review them separately.
5. Build a manageable four-week starting routine
Adapt this outline to your current level and time available. It is a way to establish priorities, rather than a promise of a particular score.
- Week 1: Diagnose. Confirm your entry arrangements, attempt a mixed set and choose two areas for focused review.
- Week 2: Strengthen methods. Work on those areas in short sessions. Explain each solution and compare alternative approaches where useful.
- Week 3: Mix topics. Practise choosing a method without a topic label. Revisit earlier errors and check whether you can solve the problems independently.
- Week 4: Add timed practice. Use the correct time limit and equipment rules. Review unfinished questions, inefficient calculations and answer-recording mistakes.
The MAA's student and parent resource page provides preparation resource links. Our preparation materials page is another place to begin. Work with publicly released materials and reserve some suitable papers for later timed practice.
6. If AIME is your goal, check the current pathway
The MAA's current invitational competition guidance gives an AMC 12 score of 85 or above as the AIME qualification threshold for its 2027 arrangements, subject to other eligibility requirements. It also introduces a minimum age of 13 for AIME participation. International participants are instructed to follow their International Group Leader's policies.
For a U.S. or Canadian entry, check the complete current MAA requirements. For an international entry, confirm the applicable qualification and administration arrangements locally. Do not assume a historical cutoff or another region's process determines your invitation.
Discuss your AMC 12 preparation with Hanlin
Planning your first AMC 12 attempt, moving up from AMC 10 or working towards AIME? Scan the QR code to contact Hanlin on WeChat and send AMC12 START.
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References: the MAA's AMC overview, international participation information, student and parent resources, and invitational competition guidance linked above. Information checked in October 2026. Confirm the current rules for your region and competition season.
