AMC 10 · AMC 12 · AIME
AMC 10 & AMC 12 Preparation: A Practical Path to AIME
Preparing for the AMC 10 or AMC 12 takes more than collecting practice tests. Build reliable skills across the main contest topics, learn to manage a 75-minute multiple-choice exam, and turn every missed problem into a specific next step. If AIME qualification is your goal, add short-answer problem solving without neglecting the AMC skills that come first.
What to study for AMC 10 and AMC 12
Both contests reward clear reasoning across algebra, geometry, number theory, and combinatorics. Make a topic inventory from a recent timed paper: label each question by topic, difficulty, and whether you solved it confidently, guessed, or ran out of time. Your pattern of misses is more useful than a single total score.
- Algebra: equations, inequalities, functions, sequences, and smart substitutions.
- Geometry: triangles, circles, similarity, coordinate geometry, and area.
- Number theory: divisibility, remainders, prime factors, and modular patterns.
- Combinatorics: organized counting, casework, probability, and avoiding overcounting.
A repeatable weekly study cycle
Use a cycle you can sustain: two focused topic sessions, one mixed set, one timed section, and one review session. In each topic session, learn or refresh a method, solve a small set without rushing, and explain why each step works. In mixed practice, decide which tool fits before looking at any hint.
Practice test strategy, not just content
On a 75-minute AMC paper, protect time for questions you can solve accurately. If an approach stalls, mark the problem and move on; return with fresh attention. After a timed set, separate knowledge gaps from execution errors such as misreading, arithmetic slips, or spending too long on one path.
Review mistakes so they do not repeat
For each missed, guessed, or slow question, write down the topic, your first approach, the step where it broke down, and one useful reminder. Then close the solution and solve it again from a blank page a few days later. The delayed re-solve shows whether you learned the idea or only recognized the explanation.
Use the free math error log template to organize review, or browse topic-based practice problems when you find a skill to strengthen.
Bridge from AMC preparation to AIME
AMC problems are multiple choice; AIME problems require a three-digit integer answer and usually demand a longer chain of reasoning. Before your AMC, sample a harder problem now and then to build depth, but keep most sessions focused on the contest you are taking. Afterward, spend more time writing out a complete argument, checking edge cases, and verifying the final integer answer independently.
AIME progress still depends on strong fundamentals. Review the idea behind a solution, not just the trick that happened to work once. The AIME qualification guide includes an eight-week structure and review advice.
AMC 10, AMC 12, and AIME preparation questions
How should I prepare for both the AMC 10 and AMC 12?
Build shared foundations in algebra, geometry, number theory, and combinatorics, then practice with the format and difficulty of the contest you plan to take. Use timed sets and review every missed, guessed, or unusually slow problem.
When should AMC students start practicing AIME problems?
Start with occasional AIME problems once core AMC topics feel familiar, especially if you can explain your reasoning after solving. Keep most practice aligned with your upcoming AMC until that contest is over, then shift more time to AIME's short-answer format.
What is the best way to review an AMC practice test?
For each miss, guess, or slow solution, record the topic, the first point your approach stalled, the key idea, and a cue for next time. Re-solve it later without looking at the solution and check whether the same error returns.