AMC 10:
small problems.
Big mathematical thinking.

The right starting point

Who is the AMC 10 for?

Formal eligibility and practical readiness are different questions. MAA permits students in grade 10 and below who satisfy the age limit, so an eligible middle-school student can take the AMC 10; it is not reserved for tenth graders. MAA eligibility Our recommendation is to choose the challenge that stretches the student without making every problem inaccessible.

A useful readiness conversation starts with fractions, ratios, signed numbers, exponents, equations, and familiar geometry. Can the student explain a solution, not merely produce an answer? Can they draw a diagram from words, test a small case, and recover after an approach fails? These are our placement questions, not additional official entry requirements.

A student who earns excellent classroom grades may still need time to adjust to unfamiliar problems. Conversely, a student who is not the fastest calculator may enjoy discovering patterns and elegant arguments. We recommend a short diagnostic followed by discussion: which questions sparked curiosity, where did the reasoning break down, and what would make the next attempt more productive?

Parents should also ask whether the interest belongs to the child. Competition preparation works best as an invitation to think deeply, not as a permanent comparison with classmates. A first season can reasonably aim for a consistent practice habit and more independent solutions. Qualification can be a later goal, rather than the only definition of success.

AMC 8, AMC 10, or AMC 12?

Age is evaluated on the relevant competition day. All table entries: MAA competition overview.

The AMC 8 can be a useful developmental starting point, but it is not a required prerequisite for the AMC 10. The invitational route described by MAA begins with qualifying performance on the AMC 10 or AMC 12. MAA invitational sequence We recommend selecting an exam using both eligibility and mathematical readiness, not simply choosing the highest number.

Inside the examination

What does the AMC 10 actually test?

The official AMC 10 description includes elementary algebra, basic geometry, area and volume, elementary number theory, and probability; it excludes trigonometry, advanced algebra, and advanced geometry. MAA curriculum scope The important distinction for preparation is between having encountered a topic and recognizing how to use it in an unfamiliar setting.

For example, a school exercise might name the formula and ask for substitution. Our competition-style practice might instead ask students to compare two areas, discover a hidden equation, or count arrangements without listing every possibility. These examples illustrate our teaching approach, not a promise about the exact distribution of topics on a future paper.

• Algebra: We practice translating conditions into equations, recognizing structure, working with ratios, and checking whether an answer is reasonable.
• Geometry: We emphasize accurate diagrams, area relationships, angle facts, and choosing a useful representation before calculating.
• Number theory: We develop fluency with divisibility, prime factors, remainders, parity, and the consequences of an integer condition.
• Counting and probability: We teach organized cases, complementary counting, and the difference between counting outcomes and assuming they are equally likely.

Do not interpret those categories as a fixed percentage blueprint. This guide does not assign invented topic weights to the AMC 10. Instead, use several practice papers to identify recurring gaps in the individual student's work, then alternate targeted study with mixed problems that require choosing a method independently.

Why the format changes your preparation

Twenty-five questions in 75 minutes gives an average of three minutes per question, but equal time per question is not a sensible requirement. Official question count and timing Our suggested approach is flexible: secure accessible problems, mark uncertain ones, and revisit them with a fresh perspective.

Written reasoning still matters even when the final response is multiple choice. In practice, ask students to record why a method works and how they eliminated an answer. That record makes mistakes diagnosable. A correct guess and a fully understood solution should not receive the same treatment in the next lesson.

A small example of competition-style thinking

Consider this original SOMATH example: how many positive integers from 1 through 100 are divisible by 3 or by 5? It is not a reproduced AMC question. Its purpose is to show how a familiar arithmetic skill becomes a reasoning task when two groups overlap.

There are 33 multiples of 3 and 20 multiples of 5 in the interval. Adding gives 53, but that counts multiples of 15 twice. There are six such numbers: 15, 30, 45, 60, 75, and 90. Subtracting those six duplicate counts gives 47.

The theory is inclusion-exclusion: count the members of each group, then correct the overlap. A student who remembers only “add and subtract something” has not yet secured the idea. Ask why 15, rather than 8, describes the overlap, and why 100 itself contributes to one group but not the other.

Then change the question. How many numbers are divisible by exactly one of 3 and 5? Now the six overlapping numbers must be excluded entirely, giving 33 + 20 − 2 × 6 = 41. Finally, how many are divisible by neither? Subtract the original union from 100 to get 53.

This sequence illustrates our recommended teaching method: one accessible problem, a named principle, and a nearby variation that checks understanding. The student learns to notice the meaning of “or,” “exactly one,” and “neither,” rather than treating every counting question as the same template.

Know the arithmetic

How is the AMC 10 scored?

The scoring system awards 6 points for a correct answer, 1.5 points for a blank answer, and 0 points for an incorrect answer, with a maximum of 150. AMC 10 scoring reference In the formula below, C means correct answers and B means blank answers.

Correct, blank, and wrong answers must total 25. From this rule, an entirely blank paper scores 37.5, while 15 correct answers and 10 blanks score 105. These are arithmetic examples, not performance targets or predictions. A score of 75 is not equivalent to a 50% classroom grade because the scoring system rewards blanks differently.

The calculator uses the scoring rule above and the current MAA 2027 AIME score requirement. It is not an official score report or an invitation.

Accuracy, blanks, and guessing

Replacing one blank with a correct answer adds 4.5 points; replacing it with a wrong answer loses 1.5 points. That makes the decision more subtle than “answer everything.” Our recommendation is to distinguish a reasoned attempt from a guess and to reserve time for checking work that is already close to a reliable solution.

Expected value provides a useful mathematical model. If a guess is correct with probability p, its expected score is 6p, while leaving it blank gives 1.5. Guessing has a higher expected value only when p exceeds 25%. With five equally likely choices the expected score is 1.2; with three equally likely remaining choices it is 2.

Those calculations assume the probability estimates are justified. Eliminating an option through faulty reasoning does not actually improve the situation. Nor does a favorable expected value guarantee points on one question. Use this discussion to teach decision-making under uncertainty, not as a substitute for learning the mathematics or following the host's current exam instructions.

Read the data carefully

AMC 10 statistics: what the numbers do and do not mean

Historical results help families understand the scale of the examination, but they should not become labels for children. The Art of Problem Solving historical archive reports a 2025 AMC 10A mean of 57.13 and a 2025 AMC 10B mean of 57.00. AoPS historical results A mean is a summary of that reported group, not a readiness requirement or a forecast for a particular student.

The same archive reports 31,617 students for 2025 AMC 10A and 25,195 for 2025 AMC 10B. AoPS reported exam counts We present these as the archive's per-exam counts, not a verified worldwide census. They should not be added and described as unique participants, because students can take both versions. MAA A/B participation rules

For the 2025 examinations, the reported AIME cutoffs were 105 on AMC 10A and 99 on AMC 10B; the distinction thresholds were 112.5 and 105, respectively, and the Honor Roll of Distinction thresholds were 136.5 and 133.5. 2025 cutoff and awards summary These describe the previous exam cycle, not the newly announced 2027 AIME score rule.

Table sources: AoPS means and Areteem thresholds and award labels. No percentile is inferred from the means.

Historical cutoffs were not constant

From 2022 through 2025, the historical AMC 10A AIME cutoffs shown below ranged from 93 to 105, while the AMC 10B cutoffs ranged from 94.5 to 105. Historical AIME cutoffs The point is not to predict next year's threshold from a line: MAA has since announced fixed qualifying scores for the 2027 AIME. MAA current policy

Use statistics to set context, then return to the student's work. For planning, we recommend tracking accuracy on accessible questions, the number of problems solved without hints, and whether previously learned methods transfer to new situations. Those observations tell a teacher what to teach next; a single ranking does not.

What comes next

How AMC 10 connects to AIME and olympiads

MAA's invitational sequence moves from the AMC 10 or AMC 12 to AIME, then to the USA Junior Mathematical Olympiad or USA Mathematical Olympiad, with further selection opportunities beyond those competitions. Official invitational sequence This is a series of distinct selection stages, not an automatic promotion through a single course.

Flowchart summarizes MAA's current invitational information. It does not replace detailed eligibility, residency, citizenship, age, or selection policies.

The important 2026–27 changes

MAA's current page says qualifying scores for the 2027 AIME are fixed at 100 for AMC 10 and 85 for AMC 12, with a minimum AIME age of 13. MAA AIME eligibility update This means an otherwise AMC-eligible younger child should not be promised an AIME seat merely for crossing the score threshold.

MAA also says AIME will be administered at Pearson testing centers on February 5 and 6, 2027, with one attempt during the window. The exam has 15 integer-answer questions in two 90-minute parts, with eight questions in the first part and seven in the second. MAA AIME administration details

For USAJMO and USAMO, the current MAA update says selection is primarily based on AIME scores and AMC scores are no longer a factor. MAA olympiad qualification update Consequently, an older blog's weighted AMC-plus-AIME index formula should not be presented as the current rule.

The practical advice is simple: check the official invitation and policies for the relevant cycle, then prepare for the next exam's actual format. Developing deeper reasoning remains useful even when administration or selection rules change. Our guide separates dated historical statistics from current policy precisely because families need both context and accurate instructions.

From interest to exam day

AMC 10 dates, A versus B, and registration

The scheduled 2026 dates are November 5 for AMC 10A and November 13 for AMC 10B. MAA registration calendar A and B are different versions offered on different dates; eligible students may participate on both dates, but may not take AMC 10 and AMC 12 on the same day. MAA participation guidance

Do not choose B on the assumption that it is always easier, or A because a friend says its cutoff is lower. The historical values above do not support a permanent ordering. Our recommendation is to consider availability, preparation, and whether a second contest would be an enjoyable additional opportunity rather than an exhausting obligation.

Students and parents do not register directly with MAA; they arrange participation through a school or an approved competition host. MAA registration guidance Start with your school, then consult the public host list linked by MAA. Ask whether the host accepts outside students before making plans.

Confirm the student's name, grade, date of birth, exam version, location, arrival time, host deadline, and any fee directly with the organizer. Competition-manager registration deadlines are not the same thing as guaranteed student registration availability. MAA's calendar lists institutional registration windows, so a family's usable deadline depends on the chosen host. MAA registration windows

Keep preparation and official registration separate

Enrollment in a preparation class should not be mistaken for an official competition seat. SOMATH's Tao Titans page describes a preparation program, and this guide does not represent SOMATH as a confirmed AMC 10 examination host. SOMATH program description Obtain a separate confirmation from the actual organizer.

For exam-day equipment and conduct, follow the host's current instructions and MAA policies rather than a generic packing list. The 2025 teacher manual prohibited calculators, phones, smartwatches, and other computing devices, and required in-person administration. MAA 2025 teacher manual MAA says AMC 10/12 are unchanged from 2025 in its current update, but hosts should still confirm current arrangements. MAA current announcement

The SOMATH approach

How to prepare without turning every evening into a test

Our recommended preparation cycle is diagnose, learn, practice, explain, and revisit. Start with a paper that has not already been studied. Then distinguish missing knowledge from an execution error, a misunderstood condition, or an inefficient strategy. Each category suggests a different next lesson; simply assigning another full paper may repeat the same problem.

We recommend protecting fresh papers for timed practice and using other problems for untimed exploration. Timed work measures current execution; untimed work builds new understanding. A useful week includes both, plus a short return to earlier mistakes after the solution is no longer fresh in memory.

This is SOMATH's recommended learning cycle, not an official MAA preparation requirement.

An adaptable eight-week plan

• Weeks 1–2, establish the baseline: Try a diagnostic, review prerequisite arithmetic and algebra, and begin an error notebook. Select two manageable priorities rather than attempting to repair every weakness at once.
• Weeks 3–4, strengthen core reasoning: Alternate geometry, number theory, counting, and algebra. Require diagrams or organized cases when they clarify the problem. End each session with a short explanation in the student's own words.
• Weeks 5–6, mix topics and methods: Use mixed sets so students must identify the relevant idea without a chapter heading. Add short timed blocks, then allow untimed completion to separate speed from understanding.
• Week 7, rehearse the full format: Complete a fresh paper under the official time limit. Review every uncertain answer, including correct ones reached through guessing. Practice marking questions for a second pass.
• Week 8, consolidate: Revisit recurring mistakes, confirm logistics, and maintain a sustainable sleep and study routine. Avoid introducing a large collection of advanced tricks immediately before the contest.

This is an illustrative plan, not a promise of a particular score in eight weeks. Adjust the starting point and workload to the child's age, existing commitments, and response to practice. If the contest is close, focus on accessible improvements rather than compressing months of learning into a few stressful days.

What belongs in an error notebook?

For each selected problem, record the original obstacle, the key mathematical idea, and a short explanation of the corrected method. Add a related problem later to test transfer. Copying a polished solution is not enough: the student should eventually be able to reconstruct the reasoning without looking.

We suggest labels such as “misread condition,” “missing concept,” “unorganized cases,” “algebra slip,” and “ran out of time.” Avoid the unhelpful blanket label “careless.” Ask what specific habit would prevent the mistake next time: defining a variable, labeling units, checking parity, or substituting a proposed answer into the original condition.

How parents can help without taking over

Agree on a small, sustainable routine with the student before increasing the workload. For example, a family might reserve two short independent sessions and one longer review period each week. This is an optional planning example, not a required schedule. The appropriate amount depends on the student's age, confidence, and other responsibilities.

During independent work, resist giving the key step immediately. Offer a neutral prompt: “What do you know?”, “Could a diagram help?”, or “Can you test a smaller case?” If frustration rises, pause and return later. The objective is not to prove that the child can tolerate unlimited difficulty; it is to create productive opportunities for thinking.

At review time, let the student choose one solution to explain. Ask a genuine question about the reasoning, even if you already understand it. If neither of you can resolve a problem, record the exact point of confusion for the teacher. That is more useful than searching for a solution and declaring the topic finished.

We also recommend separating the debrief from the emotional moment after a timed test. First acknowledge the effort. Later, examine a few representative problems and decide on one actionable change. Keep the conversation specific enough that the student leaves knowing what to try next, not merely that a larger score would have been preferable.

When should the plan change?

Review the plan when practice becomes consistently inaccessible, when the student finishes everything without meaningful effort, or when the workload crowds out essential school learning. A useful adjustment may be a different problem level, a foundational lesson, or more time discussing solutions. More questions are not automatically the right answer.

If a student repeatedly makes the same error, ask whether the explanation has actually been understood. Have them teach the idea back, use a new representation, and solve a fresh example. Our recommended measure of progress is not how many solution pages were read, but what the student can now do independently.

Use the SOMATH practice papers actively

Our published 2025 AMC 10A problems and solutions and 2025 AMC 10B problems and solutions pair questions with theory notes and hidden explanations. Try the problem before revealing the answer, then ask what clue suggested the method and how the solution would change if a condition changed.

For school-math foundations that need attention first, review functions, domain, range, and notation or ask for a placement recommendation. Competition preparation and foundational learning can support each other, but there is no advantage in hiding a basic gap behind increasingly difficult worksheets.

Achievement in context

Does AMC 10 matter for college applications?

AMC achievement can be meaningful evidence of mathematical interest and accomplishment, but it is not an admissions guarantee. Caltech explicitly includes mathematics competitions among ways students may demonstrate STEM preparedness, while explaining that students can show preparation in multiple ways. Caltech STEM preparedness guidance MIT says there is no admissions formula and that it cannot estimate chances without reviewing the application in context. MIT admissions guidance

The sensible parent question is therefore not “What score gets my child into college?” It is “Would sustained mathematical exploration be a genuine and worthwhile part of this student's education?” Our recommendation is to pursue competition work when the student values it, then describe the resulting work honestly if it becomes relevant to an application.

Participation, distinction, and qualification are different claims

Taking an exam demonstrates participation. Earning a named award demonstrates that specific recognition. Receiving an AIME invitation demonstrates qualifying for a further examination under that cycle's rules. The MAA sequence distinguishes the AMC, AIME, and olympiad stages, so those labels should not be used interchangeably. MAA competition sequence

For applications, we recommend reporting the exact examination year and version, the verified score when useful, and the exact award or invitation received. Do not call an AMC participant an olympiad qualifier unless the student actually qualified for the named olympiad. Do not describe a historical percentile as the student's percentile unless an official report supports it.

A useful record might have fields for “exam,” “year,” “score,” “award wording,” and “verification document.” Keep the source report rather than relying on memory when application season arrives. This is an administrative recommendation, not a claim that any particular college requires a specific AMC score or documentation format.

Depth matters more than collecting labels

Competition preparation can be connected to a broader story: an interest in a particular mathematical topic, a school math club, collaborative problem-solving, or helping younger students understand a difficult idea. Our advice is to describe what the student actually did and learned. Avoid embellishing ordinary participation into a research project or inventing leadership responsibilities.

For example, a student might keep a portfolio of original explanations comparing two methods for the same problem. Another might organize a small discussion group and document the problems explored. These are suggested educational activities, not guaranteed application advantages. They are worthwhile when the student enjoys the work and can explain it authentically.

MIT emphasizes rigorous academics and genuine interests rather than an admissions formula, while Caltech presents competitions alongside other ways to demonstrate STEM preparation. MIT; Caltech Our interpretation is that AMC preparation should complement a strong education, not displace necessary coursework, sleep, or other meaningful interests.

What about students who never qualify for AIME?

A student can still learn a great deal from the preparation process without earning an invitation. In our recommended approach, progress includes more precise reasoning, better explanations, and greater independence with unfamiliar problems. Those are learning goals, not admissions promises, and they remain valid even when a score disappoints.

Families should be cautious about claims that a certain result increases admission probability by a precise percentage. The official admissions guidance cited here does not provide such a causal estimate, and MIT explicitly rejects a simple formula for chances. MIT on admissions chances This guide therefore includes no fabricated admissions chart, acceptance-rate multiplier, or guaranteed outcome.

If a student dislikes competition mathematics, explore other ways to develop the underlying interest. That might mean deeper school coursework, mathematical writing, coding with genuine mathematical content, or collaborative exploration. The right educational choice is the one the student can sustain meaningfully, not the one that merely sounds impressive in a short activity description.

Learn on the Upper West Side

AMC 10 preparation at SOMATH

Tao Titans Math Competition Prep serves grades 6–12 with placement by readiness and includes AMC 8, AMC 10, AMC 12, and other suitable competitions. The published schedule is Fridays, 4–6 PM, with a maximum of six students. SOMATH course information The course's grade range does not override the eligibility limits of any specific contest.

Our recommendation is to begin with a free evaluation rather than choosing a class solely from a grade label. Bring recent work if available and tell us which competition interests the student. We can discuss prerequisite gaps, an appropriate level of challenge, and whether a competition group or foundational course is the better starting point.

At home, we suggest asking “What did you notice?” before asking “Did you get it right?” In a lesson, the corresponding priority is to make reasoning visible: draw, explain, compare methods, and check. A promising solution is something a student can defend and adapt, not just repeat after seeing an answer.

Clear answers

AMC 10 frequently asked questions