Abstract

The American Invitational Mathematics Examination (AIME) is an important milestone in the mathematical development of talented students. Its traditional scoring system is straightforward: each correct answer earns one point, regardless of the difficulty of the problem, for a maximum score of 15.

Although this system is transparent and easy to administer, it raises a fundamental question: Does awarding equal points to every correct answer adequately reflect differences in the mathematical achievement demonstrated by students?

This article argues that the AIME scoring system deserves serious, systematic investigation. It examines the strengths of equal-weight scoring, considers the potential advantages and limitations of difficulty-sensitive scoring, compares the AIME with other mathematics competitions, and proposes an empirical framework for evaluating alternative scoring models.

The purpose is not to assume that weighted scoring is necessarily better. Rather, it is to encourage a careful examination of whether the current system measures mathematical achievement as effectively as it could.

1. Introduction: Does Every Correct Answer Deserve the Same Number of Points?

The AIME consists of 15 problems, each requiring an integer answer from 000 to 999. Under the traditional scoring system, every correct answer earns one point, regardless of the problem’s difficulty. A perfect score is 15.

This arrangement is straightforward. However, it raises an important question about measurement.

In a typical AIME examination, earlier problems are generally intended to be more accessible than later ones, although individual problems do not always follow this pattern. A student may solve an early problem in one or two minutes, while a particularly challenging final problem may require 15–20 minutes of sustained reasoning—or may remain unsolved despite substantial effort.

Under the current system, both solutions earn exactly one point.

Is this necessarily the best way to measure mathematical achievement?

The question is not whether easier problems are valuable. They are essential to a well-designed examination. Nor is it whether difficult problems should automatically receive more points. That conclusion requires evidence.

The more fundamental question is whether a scoring system should recognize meaningful differences in problem difficulty and mathematical accomplishment, and, if so, how those differences should be measured.

This question deserves serious consideration, particularly because AIME results can influence students’ perceptions of their mathematical abilities and their subsequent educational opportunities.

2. Counting Correct Answers Versus Measuring Mathematical Achievement

A scoring system necessarily simplifies a student’s performance into a numerical result. The challenge is deciding what that number should represent.

Under equal-weight scoring, the AIME measures the number of problems answered correctly. This is an objective and readily understandable measure of performance.

However, counting correct answers and measuring mathematical achievement are not necessarily identical objectives.

Consider two hypothetical students:

• Student A correctly solves five relatively accessible problems.

• Student B correctly solves five problems, including several that require substantially more advanced reasoning.

If both students receive the same score, the scoring system does not distinguish between these two patterns of achievement.

That does not automatically mean Student B should receive a higher score. We would first need reliable evidence about problem difficulty, the mathematical skills being assessed, and the extent to which those skills align with the competition’s objectives.

Nevertheless, the example illustrates a legitimate question: Should the scoring system consider only the number of correct answers, or should it also consider the demonstrated level of mathematical accomplishment?

A familiar workplace analogy helps illustrate the issue. Imagine an organization in which all 100 employees receive exactly the same salary, regardless of their responsibilities, expertise, or contributions. Many people would question whether such a system adequately recognizes differences in performance.

Of course, an examination is not an employment system, and mathematical achievement cannot be equated directly with workplace contribution. The analogy simply illustrates a general principle: equal numerical rewards do not always represent equal levels of achievement.

The appropriate scoring policy depends on what the examination is intended to measure.

3. The Case for Equal-Weight Scoring

Before considering alternatives, it is important to acknowledge the strengths of the current AIME system.

First, it is transparent. Students know exactly how their scores are calculated. Every correct answer contributes one point.

Second, it is easy to administer. The system requires no additional calculations based on estimated difficulty, discrimination, or other statistical characteristics of individual problems.

Third, it minimizes disputes about point allocation. Because every problem has the same nominal value, students do not need to understand or challenge a more complicated weighting formula.

Fourth, it rewards efficient problem selection and time management. A student who identifies and solves several accessible problems can earn a respectable score without solving the most difficult problems.

Fifth, equal weighting avoids the need to establish a potentially controversial hierarchy of problem values. Problem difficulty can vary among students depending on their mathematical backgrounds, strengths, and experience.

These are substantial advantages. Any proposed alternative should demonstrate that its benefits justify the additional complexity and potential disadvantages.

Equal-weight scoring should not be discarded merely because other scoring systems are possible.

However, simplicity alone does not establish that the current system is the most effective way to measure mathematical achievement. That question requires further investigation.

4. Why Difficulty-Sensitive Scoring Deserves Serious Consideration

The central concern is that the 15 AIME problems can differ considerably in their mathematical demands, yet the current system assigns each of them the same point value.

A problem requiring a short calculation and a problem requiring several layers of insight, sophisticated transformations, or an original line of reasoning may both contribute one point.

If the competition aims primarily to count correct answers, this arrangement is entirely consistent with its objective.

If the competition also aims to distinguish levels of mathematical accomplishment, however, it is reasonable to ask whether equal weighting is the most appropriate design.

A difficulty-sensitive system might assign different point values to problems based on a defensible assessment of their mathematical demands.

Such a system could potentially recognize differences in achievement more effectively. It might also change the incentives students face when deciding how to allocate their time during the examination.

But several important qualifications are necessary.

Problem difficulty should not be inferred solely from question number. Nor should it be determined exclusively by the percentage of students answering a problem correctly. A problem’s empirical difficulty can depend on the population taking the examination, and a low success rate does not, by itself, establish that a problem measures a more valuable mathematical ability.

Furthermore, spending more time on a problem does not automatically make a solution more mathematically significant.

The case for reform therefore rests not on the assumption that difficult problems must receive more points, but on the proposition that the relationship between problem difficulty, mathematical achievement, and scoring deserves systematic examination.

5. What Other Mathematics Competitions Can Teach Us

The AIME is not the only mathematics competition that must decide how to assign points to problems of varying difficulty.

Other competitions demonstrate that alternative scoring structures are possible. These examples do not prove that the AIME should adopt a different system, but they show that equal weighting is not the only practical approach.

5.1. Australian Intermediate Mathematics Olympiad (AIMO)

According to the Australian Maths Trust’s published AIMO information, the competition contains 10 questions. Eight require integer answers, while two require written solutions that may include proofs.

The published scoring structure assigns:

• Questions 1–4: 2 points each

• Question 5: 3 points

• Question 6: 4 points

• Questions 7–10: 5 points each

The standard questions therefore account for 35 points, with an investigation offering up to four additional bonus points.

Official source: Australian Maths Trust — AIMO

This system assigns different values to questions within the same competition. It also combines integer-answer questions with written mathematical reasoning.

The AIMO example is relevant because it demonstrates that a mathematics competition can use a differentiated point structure without abandoning a clear, published scoring framework.

However, AIMO is not identical to the AIME. The two competitions have different formats, purposes, and assessment requirements. Its scoring structure should therefore be treated as an example of an alternative design, not evidence that the same structure would improve AIME results.

5.2. Canadian Open Mathematics Challenge (COMC)

The Canadian Open Mathematics Challenge provides another example.

According to the Canadian Mathematical Society’s 2026 student FAQ, the COMC has 12 questions divided into three groups:

• Questions 1–4: 4 points each, introductory

• Questions 5–8: 6 points each, intermediate

• Questions 9–12: 10 points each, advanced

The maximum score is 80 points. The introductory and intermediate sections allow students to earn full marks for correct answers without showing their work, with partial credit possible under specified conditions. The advanced questions require fully developed solutions.

Official source: Canadian Mathematical Society — COMC 2026 Student FAQ

The COMC thus uses different point values for different groups of questions and also distinguishes between answer-based scoring and the evaluation of written solutions.

This arrangement recognizes that questions can serve different roles within an examination.

Once again, the comparison should be interpreted cautiously. The COMC and AIME differ in their formats and scoring objectives. The COMC does not establish that a weighted AIME would be more valid, reliable, or fair.

Nevertheless, the two examples demonstrate that differentiated scoring is a workable option in mathematics competitions. The AIME’s existing system should therefore be evaluated on its merits rather than treated as the only possible design.

6. A Possible Alternative: Difficulty-Sensitive Scoring

To make the discussion more concrete, consider a hypothetical scoring model for the AIME.

Under this illustrative model, the maximum score would be 30 points rather than 15.

The model is intended only to demonstrate how differentiated scoring could work. It is not a recommendation to adopt these particular weights.

There are several reasons for caution.

First, question number is not a validated measure of difficulty. An early problem may be unexpectedly challenging, while a later problem may be relatively accessible to a particular student.

Second, the proposed groups would need to be evaluated against actual problem characteristics and student performance data.

Third, a different weighting system could change student rankings. That change would not, by itself, demonstrate that the new rankings were more accurate or more meaningful.

Fourth, changing the scale from 15 to 30 points would not automatically improve measurement. The important issue is not the numerical range of the score, but whether the scoring method better serves the examination’s stated objectives.

The value of this example is that it makes the underlying question concrete: Would a carefully designed system that accounts for meaningful differences among problems provide a better measure of mathematical achievement than the current system?

That question should be answered through research rather than intuition.

7. How Could a Scoring Reform Be Evaluated Empirically?

If the Mathematical Association of America (MAA) were to examine the AIME scoring system, a systematic research program could help determine whether alternative models offer meaningful advantages.

The following approaches would provide a useful starting point.

7.1. Analyze Historical Questions and Student Performance

The first step would be to examine historical AIME examinations and available student-response data.

Researchers could investigate:

• The percentage of students answering each problem correctly.

• The relationship between problem difficulty and question position.

• How problem performance varies among students at different overall achievement levels.

• Whether particular problems distinguish consistently between different levels of mathematical preparation.

• Whether the observed patterns remain stable across different years and student populations.

Such analyses could help identify problems that are empirically more challenging and investigate what those differences mean.

However, the percentage of correct answers should not be treated as a complete measure of mathematical significance. It is one useful indicator among several.

7.2. Simulate Alternative Scoring Systems

Researchers could calculate hypothetical scores for historical participants under several scoring models, including:

1. The current equal-weight system.

2. Systems assigning different weights to empirically calibrated difficulty groups.

3. Systems using other defensible item characteristics, provided those characteristics align with the competition’s objectives.

The resulting scores could be compared to determine how much the different models alter score distributions and individual results.

Researchers could also examine whether a proposed model creates unintended incentives, such as encouraging students to ignore accessible problems in favor of higher-value problems.

The purpose would be to understand the consequences of each model before considering implementation.

7.3. Examine Ranking Stability

One important question is whether a new scoring system would substantially change the ordering of students.

Researchers could examine:

• How often student rankings change.

• Which groups of students gain or lose relative standing.

• Whether changes are concentrated among students with particular patterns of correct answers.

• Whether the new rankings remain stable when the model is tested on different years of data.

A change in rankings is neither inherently good nor inherently bad.

If a new model produces different rankings, researchers must determine whether those changes better reflect the mathematical achievement the AIME intends to recognize.

Ranking stability is therefore an important diagnostic measure, but it is not a sufficient criterion for deciding whether a scoring system is better.

7.4. Use Independent Measures of Mathematical Achievement

The most important question is whether an alternative scoring system measures the intended construct more effectively.

Researchers could compare AIME scores under different models with independent measures of mathematical achievement, where appropriate data are available.

Potential sources might include performance on other well-designed mathematical assessments, carefully evaluated written solutions, or other relevant measures of mathematical reasoning.

These comparisons would require careful design. No single external measure should automatically be treated as a definitive standard of mathematical ability.

Nevertheless, independent evidence could help determine whether a weighted score reflects meaningful differences in achievement rather than simply rewarding a particular pattern of answers.

7.5. Consider Reliability, Validity, and Practical Consequences

Research on test scoring provides useful context, but it does not settle the AIME question.

Kılıç and Doğan (2019), in reviewing earlier research, report a finding attributed to Ghiselli (1964) that differential item weighting may have relatively little effect when a test contains 10–20 items. Since the AIME contains 15 questions, this reported finding is relevant to the present discussion. However, it is not direct evidence about the AIME.

Kılıç and Doğan’s own simulation study examined a different weighting procedure under simulated conditions involving tests of 20, 30, and 40 items. The AIME’s 15 questions fall below the range simulated by Kılıç and Doğan, while lying within the 10–20-item range attributed to Ghiselli. This difference in the evidence base makes direct extrapolation uncertain. Neither the earlier finding as reported by Kılıç and Doğan nor their own simulations establishes whether difficulty-sensitive scoring would improve AIME scores.

The appropriate conclusion is that the effects of weighting should be investigated empirically, with particular attention to the AIME’s scoring objectives, historical performance data, and independent measures of mathematical achievement.

Reference:

Kılıç, A. F., & Doğan, N. (2019). The effect of item weighting on reliability and validity. Journal of Measurement and Evaluation in Education and Psychology, 10(2), 149–164. https://doi.org/10.21031/epod.516057

Any evaluation should consider several distinct questions:

• Reliability: Does the scoring model produce sufficiently consistent results?

• Validity: Do the scores support the interpretations and uses intended by the competition?

• Discrimination: Does the model meaningfully distinguish among levels of mathematical achievement?

• Fairness: Does the model introduce unintended disadvantages for particular groups of students?

• Practicality: Can the system be explained, implemented, and administered transparently?

These considerations are related but not interchangeable. A model might improve one aspect of measurement while creating problems in another.

A credible reform should therefore be judged by the overall quality of the evidence, not by a single statistical result.

8. Important Risks of Difficulty-Weighted Scoring

Difficulty-sensitive scoring has potential advantages, but it also introduces significant risks.

The definition of difficulty may be disputed. A problem that is difficult for one group of students may be accessible to another. Empirical difficulty can also change as curricula and preparation practices evolve.

Weights can create unintended incentives. If students know that certain questions are worth substantially more points, they may change their problem-selection strategies in ways that do not align with the examination’s broader objectives.

A more complicated system can reduce transparency. Students and parents should be able to understand how scores are calculated and why the scoring rules are used.

Historical comparisons may become more difficult. If the scoring system changes, a score under the new system may not be directly comparable to a score under the old one. The MAA would need to explain the implications for historical results and any uses of those results.

Statistical sophistication does not guarantee educational validity. A model can be mathematically complex without measuring mathematical achievement more effectively.

These risks are reasons to conduct careful research, not reasons to avoid asking the question.

The goal should not be to make scoring more complicated for its own sake. It should be to determine whether a better-supported system can improve the interpretation and use of AIME results.

9. A Constructive Proposal: Study the Scoring System Before Changing It

The AIME’s scoring system deserves a formal, evidence-based review.

The first step need not be immediate implementation of a new model. Instead, the MAA could commission or conduct a structured study involving assessment researchers, mathematics educators, competition problem writers, and other relevant experts.

Such a study could:

1. Define the mathematical achievements the AIME is intended to recognize.

2. Analyze historical problem and student-performance data.

3. Identify plausible alternative scoring models.

4. Simulate the effects of those models on historical results.

5. Evaluate reliability, validity, ranking changes, fairness, and practical consequences.

6. Publish the findings and explain whether the evidence supports retaining or modifying the current system.

This approach would permit a serious evaluation without prejudging its outcome.

The distinction between examination administration and examination scoring is important here.

Changes to the testing format, security arrangements, or delivery procedures may address genuine operational concerns. Those changes deserve attention in their own right.

However, improving the administration of an examination does not necessarily resolve questions about what its scores measure.

A competition can be administered securely and consistently while still having a scoring system worth evaluating. Conversely, a scoring system can be simple and transparent while still requiring evidence that it serves its intended purpose well.

The two issues should be examined separately.

If scoring reform is intended to improve the measurement of mathematical achievement, it should be treated as a substantive assessment question—not merely as a secondary consideration after changes to the examination format.

A formal review would not require the MAA to commit to weighted scoring. It would require the organization to investigate whether the current system remains the most appropriate choice.

That is a reasonable and constructive first step.

10. Conclusion: The Goal Is Better Measurement, Not More Complicated Scoring

The AIME’s equal-weight scoring system has important advantages. It is simple, transparent, and easy to administer. Those qualities should not be underestimated.

Nevertheless, the fact that every correct answer earns one point raises a legitimate question about how the examination recognizes differences in mathematical achievement.

Other mathematics competitions demonstrate that differentiated point values are feasible. Measurement research offers useful principles for evaluating alternative approaches, although the existing literature does not establish that a weighted system would improve AIME results.

The next step should therefore be neither automatic acceptance of the current system nor immediate adoption of a new one. It should be a systematic investigation of the alternatives.

The MAA could examine historical data, simulate different scoring models, assess changes in student rankings, and compare the results with independent measures of mathematical achievement. The findings could then inform a transparent decision about whether the existing system should be retained or revised.

A scoring system should be judged not simply by how long it has been used or how easy it is to administer, but by how well it measures what the competition is intended to recognize.

The objective is not to make the AIME more complicated. It is to ensure that its scores provide the most meaningful and defensible representation of students’ mathematical achievement that the available evidence can support.

References and Further Reading

1. Australian Maths Trust. Australian Intermediate Mathematics Olympiad (AIMO). Official competition information, including question format and scoring system. https://amt.edu.au/aimo

2. Canadian Mathematical Society. FAQs for Students — COMC 2026. Official information on examination structure and grading. https://cms.math.ca/competitions/comc/comc2026/faq/students/

3. Kılıç, A. F., & Doğan, N. (2019). The effect of item weighting on reliability and validity. Journal of Measurement and Evaluation in Education and Psychology, 10(2), 149–164. https://doi.org/10.21031/epod.516057

4. Mathematical Association of America. MAA AMC and AIME Competitions. https://maa.org/maa-invitational-competitions/

Join the Discussion

Editorial Note

This article advocates a systematic evaluation of the AIME scoring system. It does not claim that difficulty-weighted scoring has already been demonstrated to be superior to equal-weight scoring, nor does it endorse any particular weighting formula.

The examples from AIMO and COMC demonstrate that alternative scoring structures exist; they do not establish that those structures would be appropriate for the AIME. Similarly, the cited measurement research provides background for the discussion but does not constitute direct evidence about the AIME.

Any decision to change the AIME scoring system should be based on transparent empirical analysis, a clearly defined assessment objective, and careful consideration of the consequences for students.

Abstract

The 2027 American Invitational Mathematics Examination (AIME) will introduce a new testing format featuring professional testing centers, electronic administration, two separately timed sections, and a ten-minute break. While protecting competition integrity is an important objective, these changes also raise questions about assessment quality, student experience, accessibility, and administrative complexity. This commentary examines the implications of the new format, distinguishing the MAA’s stated security objectives from questions that warrant further evidence and evaluation. It argues for clear examination-day guidance, careful consideration of practical burdens, and systematic assessment of the new arrangements after implementation. The goal is not to oppose enhanced security, but to ensure that examination procedures remain proportionate to their purposes and support the accurate measurement of mathematical achievement.

The Mathematical Association of America (MAA) has announced significant changes to the American Invitational Mathematics Examination (AIME) for 2027. These changes affect AIME qualification, eligibility requirements, exam format, and the pathway to the USAMO and USAJMO.

For official information, visit the MAA Invitational Competitions website.

Key Updates

• Fixed qualifying scores: Students must score at least 100 on the AMC 10 or 85 on the AMC 12 to qualify for the AIME.

• Minimum age requirement: Students must be at least 13 years old to be eligible.

• Pearson testing centers: The AIME will be administered at Pearson testing centers.

• Computer-based testing: The examination will be delivered electronically.

• New two-part format: The three-hour examination will consist of two 90-minute sections. Part 1 covers Questions 1–8, while Part 2 covers Questions 9–15, with a short break between sections. Once Part 1 ends, students cannot return to its questions.

• Single AIME administration: The separate AIME I and AIME II examinations will be replaced by one examination offered during the February 5–6, 2027, testing window.

• Changes to USAMO/USAJMO qualification: AMC scores will no longer contribute to the qualification index for the USAMO or USAJMO. AIME performance will therefore play a more important role in advancement.

• Registration fee: $85.

What These Changes Mean for Students

These changes make AIME preparation more important than ever for students aspiring to qualify for the USAMO or USAJMO. Students should prepare not only to achieve the required AMC qualifying score but also to develop the advanced problem-solving skills needed to perform well on the AIME.

For students pursuing higher levels of mathematical competition, consistent AIME preparation is an increasingly important part of a long-term competition strategy. For more guidance, read How to Prepare for the AIME

• MAA Invitational Competitions: 2027 USAMO/USAJMO Qualification Changes
• MAA: 2027 AIME Administration and Qualification Thresholds
• MAA: 2026–2027 Competition Dates

A New Qualification System Requires a New Preparation Strategy

For students aspiring to qualify for the USA Junior Mathematical Olympiad (USAJMO) or the USA Mathematical Olympiad (USAMO), the 2026–2027 competition season brings a significant change that should influence how they prepare for mathematics competitions.

Beginning with the 2027 USAMO and USAJMO, AMC scores will no longer be a factor in qualification. According to the Mathematical Association of America (MAA), qualification will be based primarily on AIME scores. This marks a major departure from the previous system, in which AMC and AIME scores both contributed to a student’s qualification index.

For students and parents, the practical implication is clear:

If your goal is USAJMO or USAMO, AIME preparation should begin well before the AMC 10/12 examinations—not after they are over.

Waiting until November to begin serious AIME preparation may leave students with too little time to develop the advanced problem-solving skills needed to compete at the next level.

1. Understanding the Change: From AMC + AIME to an AIME-Focused System

Under the previous qualification system, both AMC and AIME scores contributed to a student’s USAMO/USAJMO qualification index.

For example, the 2025 qualification formulas were:

• USAMO Index: AMC 12 Score + 10 × AIME Score

• USAJMO Index: AMC 10 Score + 10 × AIME Score

These formulas were documented in the MAA’s official announcement of the 2025 qualification thresholds. For details, see:

• 2025 USAMO and USAJMO Qualifying Thresholds
• USAMO and USAJMO Qualification Indices from 2010 to 2025

Under this system, a very high AMC score could partly compensate for a comparatively modest AIME score.

Beginning in 2027, however, AMC scores will no longer contribute to USAMO/USAJMO qualification. Students can no longer rely on an exceptionally high AMC score to offset a lower AIME score.

The strategic emphasis must therefore shift. Students who aspire to USAJMO or USAMO need to focus much more directly on their AIME performance.

The AMC remains essential for AIME qualification and for developing strong mathematical foundations. But for students whose ultimate goal is USAJMO or USAMO, AIME preparation deserves attention much earlier in the competition season.

2. A Real Student Example: Why the Old System Could Be Misleading

Consider a student from one of our previous classes who earned the following scores in 2023:

Under the 2023 USAJMO qualification system, the qualification index cutoff for AMC 10B and AIME II was 180. The student’s qualification index was calculated as follows:

138+10×5=188>180.

Therefore, the student successfully qualified for the USAJMO with an AIME score of just 5.

Similarly, another student scored 133.5 on the AMC 12B and 7 on the AIME II in 2022.

Under the 2022 USAMO qualification system, the corresponding qualification index cutoff was 203. The student’s qualification index was

133.5+10×7=203.5>203.

Therefore, this student also successfully qualified for the USAMO, with an AIME score of just 7.

These examples illustrate an important feature of the former qualification system: a high AMC score could compensate for a relatively low AIME score, allowing students to qualify for the USAJMO or USAMO without achieving an exceptionally high AIME score.

Under the new system, however, AMC scores no longer count toward USAJMO or USAMO qualification. The first student’s AMC 10B score of 138, for example, would no longer provide any advantage in the qualification process. An AIME score of 5 that was sufficient under the former system would no longer be enough to qualify this student under the new system.

This does not necessarily mean that an AIME score of 7 or 8 will be insufficient. The official 2027 qualification cutoff has not yet been announced. The key point is that a high AMC score can no longer compensate for a lower AIME score.

Students and parents should therefore reconsider any preparation strategy based on the assumption that an outstanding AMC result can make up for a comparatively low AIME score. Under the new system, students aspiring to qualify for the USAJMO or USAMO need to place greater emphasis on developing strong AIME problem-solving skills well before the AMC examinations.

3. What AIME Score Should Students Target?

As of October 2026, the MAA has announced the qualification-system change but has not published the final numerical AIME cutoffs for 2027 USAMO and USAJMO.

Nevertheless, based on historical qualification patterns and my experience teaching AMC and AIME students, I recommend setting ambitious AIME goals.

My current projections are:

USAJMO: Aim for approximately 9–11 or higher on the AIME.

USAMO: Aim for approximately 11–13 or higher on the AIME.

These are my educational projections and recommended preparation targets, not official MAA qualification cutoffs. Actual qualification thresholds may differ.

For students seriously pursuing USAJMO, I encourage them to treat 10 AIME points as a meaningful preparation goal rather than assuming that an AMC score of 140 or higher will compensate for a lower AIME score.

Students aiming for USAMO should set an even more ambitious goal, targeting approximately 11–12 or higher.

These targets are not guarantees of qualification. They are planning benchmarks designed to help students and families recognize the level of AIME performance they may need to pursue under the new system.

4. Why Waiting Until After the AMC May Be Too Late

The 2026 AMC 10/12 examinations are scheduled for November 5 and November 13, 2026. The 2027 AIME will be administered on February 5 or 6, 2027, according to the official MAA competition schedule.

That leaves approximately three months between the AMC and the AIME.

For students who already have strong mathematical foundations and need only limited refinement, three months may be productive. For students hoping to make a substantial improvement in AIME performance, however, this can be a very short preparation window.

The AIME is not simply a more difficult version of the AMC. It demands deeper reasoning, more sophisticated strategies, and greater flexibility when approaching unfamiliar problems.

Successful AIME preparation often requires students to develop:

• Advanced problem-solving strategies: Recognizing hidden structures, choosing productive approaches, and combining ideas in unfamiliar ways.

• Stronger number theory skills: Divisibility, modular arithmetic, Diophantine equations, and related techniques.

• Deeper combinatorial reasoning: Systematic counting, case analysis, and clever arguments.

• More sophisticated geometry: Geometric relationships, auxiliary constructions, and multiple solution approaches.

• Greater algebraic flexibility: Manipulating expressions, identifying patterns, and connecting different representations.

• Better problem-solving judgment: Deciding which problems to pursue, when to change approaches, and how to use limited time effectively.

These skills require sustained practice, reflection, and exposure to challenging problems. They cannot reliably be developed through a last-minute review of AIME questions.

The earlier students begin developing these skills, the more time they have to build the mathematical maturity required for AIME success.

5. AMC Preparation Is Not Less Important—It Is the Foundation for AIME Success

There is an equally important point that I want students and parents to understand.

Recommending early AIME preparation does not mean abandoning AMC preparation or treating the AMC as unimportant.

Quite the opposite.

In our experience teaching mathematics competition students, strong AMC preparation provides an essential foundation for AIME success.

Why?

Because the advanced strategies and deeper problem-solving skills required by the AIME build upon mathematical knowledge and habits developed through rigorous training at the AMC level.

Students who have mastered algebraic manipulation, number theory fundamentals, geometry, counting, probability, and systematic problem-solving are better equipped to tackle the more demanding problems on the AIME.

Students who lack these foundations may find advanced AIME problems unnecessarily difficult, even if they have practiced some AIME problems before.

This leads to an important educational principle:

AMC preparation builds the foundation; AIME preparation develops that foundation into more advanced problem-solving ability.

The two should not be viewed as competing priorities. They are complementary stages of mathematical development.

Students do not need to wait until AMC preparation is completely finished before beginning more advanced techniques. In fact, appropriately structured AIME preparation can deepen their understanding of the same mathematical concepts they are learning through AMC training.

This is why I advocate a continuous approach to competition preparation, in which strong AMC foundations and AIME-level reasoning reinforce each other.

6. Why We Recommend Starting AIME Preparation Before the AMC

For students whose immediate goal is simply to qualify for the AIME, the priority is to achieve the required AMC score.

For the 2027 competition cycle, the announced AMC qualification thresholds are:

• AMC 10: 100 or above

• AMC 12: 85 or above

Students who meet the applicable eligibility and qualification requirements can register for the AIME, subject to MAA rules. For details, see: Major Changes to the AIME Rules for 2027 

However, students who aspire to go beyond AIME qualification and reach USAJMO or USAMO need to plan further ahead.

Rather than following this sequence—

1. Finish AMC preparation.

2. Take the AMC in November.

3. Wait for the AIME invitation.

4. Begin AIME preparation.

5. Attempt to develop advanced skills in the remaining time.

—I recommend a more effective approach:

1. Build a strong AMC foundation while beginning appropriate AIME-level training.

2. Develop advanced problem-solving strategies before the AMC examination.

3. Continue strengthening AIME-specific skills throughout the fall.

4. After the AMC, refine those skills and focus increasingly on AIME practice and timed problem-solving.

This approach allows students to use the fall semester more effectively. It also reduces the risk of reaching December or January with insufficient experience in the advanced techniques that AIME problems demand.

For students with serious USAJMO or USAMO ambitions, preparation should be guided by the ultimate goal, not merely by the next examination on the calendar.

7. A New Qualification System Calls for a New Preparation Strategy

The 2027 change is more than a technical adjustment to a qualification formula. It should influence how students plan their mathematical development.

Under the old system, an outstanding AMC score could sometimes strengthen an otherwise borderline qualification index.

Under the new system, that option disappears: AMC scores will no longer be a factor in USAMO/USAJMO qualification.

The overall path is therefore best understood as:

Strong AMC foundation → AIME qualification → Strong AIME performance → USAJMO/USAMO qualification

Each stage matters, but the transition from AMC to AIME deserves particular attention.

Students who begin advanced preparation early have more opportunities to develop essential skills, identify weaknesses, and improve their problem-solving methods before the AIME arrives.

Students who postpone AIME preparation until after the AMC may find themselves competing against students who have already spent months building those skills.

The difference is not simply how many problems a student completes. It is how much time the student has to develop the mathematical insight and flexibility needed to solve challenging problems independently.

8. Start Preparing Now—Not After the November AMC

If your child is aiming for USAJMO or USAMO, this is the time to think seriously about AIME preparation.

Do not assume that a high AMC score alone will be enough.

Do not wait until the AMC results arrive before deciding whether to prepare for the AIME.

And do not underestimate the time required to develop advanced mathematical problem-solving skills.

Our approach emphasizes both strong AMC foundations and early, structured AIME preparation. The goal is not simply to prepare students for the next test, but to help them develop the depth of understanding and problem-solving ability needed to progress toward higher-level mathematical competitions.

For students who aspire to USAJMO or USAMO, the fall is an important opportunity to begin that process.

If USAJMO or USAMO is the destination, AIME preparation should not be the plan for after the AMC. It should be part of the plan for the AMC.

The 2027 qualification system has changed. Students’ preparation strategies should change accordingly.

Start early. Build strong foundations. Develop advanced problem-solving skills. Give yourself the time needed to reach your goals.

Our AIME Fall Geometry Course: Start Building Your AIME Skills Now

To help students strengthen their mathematical foundations and begin developing advanced problem-solving skills, we offer the Online Intensive AIME Prep Fall Weekend Course (Geometry) for students entering Grades 7–12.

The course combines systematic instruction, challenging problems, and advanced strategies to strengthen students’ geometric reasoning. These skills are valuable not only for the AIME, but also for tackling difficult geometry problems on the AMC 10 and AMC 12.

Online Intensive AIME Prep Fall Weekend Course — Geometry

Why Start Now?

Strong AMC preparation and advanced AIME preparation should reinforce each other.

AIME-level geometry develops deeper reasoning, more sophisticated strategies, and greater flexibility in solving unfamiliar problems. At the same time, this training strengthens students’ ability to tackle challenging geometry questions on the AMC 10 and AMC 12.

For students aiming for USAJMO or USAMO, early preparation is especially important under the new 2027 qualification system. Developing advanced problem-solving skills takes time, and students benefit from building these skills well before the AMC examinations are over.

Don’t wait until the AMC is over to start preparing for the AIME. Start building the skills now. For more guidance, read How to Prepare for the AIME

Summary

Knowing when to guess on the AMC 10/12 can help you earn a higher score. If you can eliminate two or more answer choices, guessing is usually a good idea. If you have no idea which answer is correct and all five choices seem equally likely, leaving the question blank is better. When four choices remain, guessing and leaving the question blank are equally good in terms of points on average. The key is to use what you know, eliminate choices whenever possible, and avoid spending too much time on a single difficult problem.

Leaving the question unanswered earns 1.5 points. Therefore, guessing is better when

or equivalently,

In other words, guessing is worthwhile when your chance of being correct is greater than 25%.

If n answer choices remain and each is equally likely to be correct, your chance of guessing correctly is 1/n. Your average score from guessing is therefore

The table below shows how this works in practice.

Note: Guessing gives you a chance to earn 6 points, while leaving the question blank guarantees 1.5 points.

These calculations assume that all remaining choices are equally likely to be correct. In practice, your reasoning and how confidently you eliminate choices also matter.

3. What Is an Educated Guess?

An educated guess is not simply picking an answer at random. It means using what you know to eliminate incorrect choices, even if you cannot solve the entire problem.

On the AMC 10 and AMC 12, you can often eliminate answer choices by using the following techniques:

• Check signs, parity, and size. Determine whether an answer must be positive or negative, even or odd, or within a certain range.

• Try the answer choices. For some algebra problems, substituting the choices directly is faster than solving the equation from scratch.

• Use divisibility and modular arithmetic. Number-theoretic properties can rule out choices that do not satisfy necessary conditions.

• Estimate the answer. Approximation and simple upper or lower bounds can help eliminate unreasonable choices.

• Look for necessary conditions. Even if you cannot finish a proof, you may be able to identify properties that the correct answer must satisfy.

These techniques help you make better guesses and become a more efficient problem solver.

Keep in mind that eliminating an answer choice only helps if you have a good reason to believe it is incorrect. A guess based on shaky reasoning may not be as reliable as you think.

4. When Should You Guess on the AMC 10/12?

Here is a practical guide for contest day.

• Five choices remaining: If you have no useful information and all choices seem equally likely, leave the question blank. Random guessing gives you a lower average score.

• Four choices remaining: If all four choices seem equally likely, guessing and leaving the question blank give you the same points on average. If you have a good reason to favor one choice, guessing may be better.

• Three choices remaining: If you have reliably eliminated two choices, guessing is worthwhile.

• Two choices remaining: If you have narrowed the answer down to two plausible choices, guessing is generally a good idea.

• One choice remaining: If your elimination is logically sound, select the remaining answer.

The main point is that you should decide whether to guess based on how likely you are to be correct, not just how many choices you have eliminated.

For example, if you eliminate two choices and the remaining three are equally likely to be correct, guessing gives you an average of 2 points, compared with 1.5 points for leaving the question blank. But if your reasoning is unreliable, your actual chance of being correct may be lower.

5. Time Management: The Most Important Strategy

Guessing is only one part of a good contest strategy. You have 75 minutes to solve 25 problems of varying difficulty. Spending too much time on one difficult problem can prevent you from earning points on other problems you could solve.

A practical approach is to:

1. Solve the problems you know first. Secure the points available on questions you can solve confidently.

2. Move on when a problem takes too long. Mark it for review instead of letting it consume too much time.

3. Return to difficult problems when time permits. Try a different approach and look for opportunities to eliminate answer choices.

4. Make educated guesses when appropriate. Use mathematical reasoning to decide whether guessing makes sense.

5. Save time for checking. Review your calculations, verify your answers, and make sure you have not overlooked any solvable problems.

During practice, aim to solve as many problems correctly as possible within the 75-minute time limit. Ideally, work toward solving all 25 problems accurately. This will help you build the mathematical skills and speed needed for stronger contest performance.

On contest day, however, your goal is to earn the highest score possible by combining accuracy, smart problem selection, effective time management, and educated guessing.

6. Final Takeaway

The AMC 10 and AMC 12 reward strong mathematical skills, but a good guessing strategy can also make a difference.

Remember these simple rules:

• Three or fewer choices remaining: Guess, assuming the remaining choices are equally likely to be correct.

• Four choices remaining: Guessing and leaving the question blank give you the same points on average if all four choices are equally likely.

• All five choices remaining: Leave the question blank if you have no useful information and must guess randomly.

Eliminating answer choices is helpful, but only when your reasoning is reliable. Do not spend too much time trying to eliminate choices on a difficult problem.

Ultimately, the best strategy is to build strong mathematical skills, solve the problems you know how to handle, manage your time wisely, and use educated guesses when they give you a reasonable chance to earn more points.