How to prepare for AMC 10 and AMC 12

Where the points actually are

The AMC rewards pattern recognition under time pressure far more than it rewards advanced content. Everything on the AMC 10 is reachable with strong algebra, geometry, counting and number theory. The gap between a 90 and a 120 is almost entirely about having seen the problem type before and not losing minutes on the first five easy questions.

Topic breakdown

01Algebra

Systems, quadratics and Vieta's formulas, sequences and series, logarithms, functional equations at a basic level, clever substitution.

02Counting and probability

Casework, complementary counting, stars and bars, the pigeonhole principle, expected value, binomial coefficients.

03Number theory

Modular arithmetic, divisibility, greatest common divisor, base representation, last-digit and remainder tricks.

04Geometry

Similar triangles, power of a point, cyclic quadrilaterals, area ratios, coordinate geometry, the standard trigonometric identities for AMC 12.

05Test strategy

Scoring rules make an informed blank better than a wild guess. Learn to recognise a problem you cannot finish in three minutes and leave it.

A study plan that works backwards from the date

1. Twelve weeks out Take a full past AMC under exam conditions to get a baseline. Do not study first. You need to know which of the four content areas is actually costing you points.
2. Weeks 1 to 6 Work through one content area per week using AoPS Introduction to Algebra, Counting and Probability, and Number Theory. Do 15 to 20 problems a day from the AoPS Contest Collections filtered to your weakest area.
3. Weeks 7 to 10 Switch to full past papers, one every three days, timed. Score them the same day. Keep a single error log: for every miss, write whether it was content, arithmetic, or clock.
4. Weeks 11 to 12 Drill questions 1 to 15 for speed only. Most students lose more points to careless errors early than to hard problems late. Target 25 minutes for the first 15 questions.
5. Final week One paper, light review of your error log, and stop. Sleep matters more than one extra problem set.

Tips that come from the format itself

• Answer choices are data. Estimating, plugging in options, and eliminating by parity or magnitude solves a surprising fraction of mid-range problems faster than solving properly.
• Track your score on questions 1 to 10 separately. If you are not near perfect there, harder content will not help you.
• Sit both A and B if you can. The two exams have independent difficulty swings and only your best score counts for AIME.
• The 1.5 points for a blank is real. If you can eliminate fewer than two options, leaving it blank is mathematically the better play.
• Write neatly on the exam booklet. A large share of missed problems are arithmetic slips on cramped scratch work.

Practice resources

• AoPS AMC problem archive with community solutions Past problems · free

  Every AMC problem since 1950 with multiple solutions per problem. This is the single most valuable free resource in competition maths.

• MAA AMC official page Official · free

  Dates, rules, eligibility and the list of registered testing sites.

• AoPS Introduction series textbooks Book · paid

  Introduction to Algebra, Counting and Probability, Number Theory and Geometry map almost exactly onto the AMC 10 syllabus.

• Alcumus adaptive practice Practice platform · free

  Free adaptive problem generator from AoPS. Set the difficulty to AMC 10 level and work by topic.

• Khan Academy algebra and geometry Course · free

  Use this to fill genuine content gaps, not for contest practice. It is not pitched at competition difficulty.

Past papers and official materials

• AMC 10 problems and solutions, all years

  Published openly by AoPS with permission arrangements. Includes official answer keys.

• AMC 12 problems and solutions, all years

  Same archive, AMC 12 papers.

Videos worth your time

• AoPS official YouTube channelArt of Problem Solving

  Walkthroughs of AMC and AIME problems by the people who write the standard textbooks.

• 3Blue1Brown3Blue1Brown

  Not contest prep, but the geometry and probability intuition transfers directly.

Skills this builds

• Algebra
• Counting and probability
• Number theory
• Plane geometry
• Speed and time management
• Strategic guessing

Read what other students said about preparing