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.

1. Introduction: A Major Change Deserves Careful Evaluation

The Mathematical Association of America (MAA) has announced substantial changes to the administration of the American Invitational Mathematics Examination (AIME) beginning in 2027. In the United States and Canada, the examination will move to Pearson Professional Centers and be administered electronically. Instead of one uninterrupted three-hour session, students will complete two separately timed parts: eight questions in the first 90 minutes, followed by seven questions in the second 90 minutes, with a ten-minute break between them. Once students move to Part 2, they cannot return to Part 1. The MAA has explained that the move to professional testing centers is intended to protect the integrity of its competitions and provide a secure testing environment.

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Protecting the integrity of a mathematics competition is a legitimate and important objective. Students, parents, educators, and institutions all have a strong interest in ensuring that examination results reflect students’ own mathematical abilities under fair and consistent conditions.

Nevertheless, a major change in examination administration deserves careful evaluation. It is reasonable to ask not only whether the new arrangements are intended to improve security, but also whether each additional restriction produces a demonstrable benefit, whether the benefits justify the associated burdens, and whether the resulting examination continues to serve its educational and selection purposes effectively.

These questions are particularly important because the AIME is more than an isolated mathematics examination. It is a significant milestone in the American Mathematics Competitions pathway, and its results have implications for students pursuing further mathematical opportunities. Beginning with the 2027 USAMO and USAJMO qualification cycle, the MAA has also announced that qualification will be based primarily on AIME scores, with AMC scores no longer serving as a factor in qualification.

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This commentary does not dispute the MAA’s authority to establish examination policies, nor does it assume that the new format will necessarily undermine security or fairness. Instead, it asks a more specific question: How should the benefits and costs of the new examination arrangements be evaluated, and what evidence would help determine whether the changes best serve students and the mathematical community?

2. Does the Two-Part Format Improve the Measurement of Mathematical Ability?

The 2027 AIME’s two-part structure introduces a consequential change in how students must manage their time and solve problems.

Under the new arrangement, students have 90 minutes to complete Questions 1–8 and another 90 minutes to complete Questions 9–15. After the first part ends, students cannot return to their earlier work.

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This restriction changes more than the logistics of the examination. In a conventional continuous session, a student can move among problems, revisit an earlier question after making progress elsewhere, and use the remaining time to reconsider an uncertain answer. Under the new format, the first 90 minutes create a firm boundary: any question left unresolved when Part 1 ends is no longer available for further work.

That boundary may affect students differently. Some may benefit from a clear division of the examination into two stages. Others may lose valuable opportunities to revisit problems, especially when a promising approach emerges only after they have worked on later questions. A student who has spent substantial time on a difficult problem may also face a strategic decision about whether to continue or move on, knowing that the decision cannot be reversed after the section closes.

None of these observations establishes that the new format is inherently unfair or that it will produce lower scores. They do, however, identify a change in what the examination rewards. In addition to mathematical knowledge, insight, and problem-solving ability, performance may depend more heavily on managing a fixed block of questions and making irreversible decisions about time allocation.

The central question is whether this additional constraint improves the measurement of mathematical achievement or primarily changes the conditions under which that achievement is demonstrated.

A rigorous evaluation could compare the new format with previous administrations using available performance data, examine how students perform across the two parts, and investigate whether the format affects groups of students differently. Such evidence would help distinguish a meaningful improvement in assessment from a procedural change whose educational consequences remain uncertain.

3. Does the Ten-Minute Break Have a Demonstrable Security Benefit?

The ten-minute break between the two parts deserves separate consideration.

The MAA’s stated rationale for moving the AIME to professional testing centers is to protect competition integrity and establish a secure testing environment. That objective is understandable. However, the general rationale for using secure testing centers does not, by itself, establish the additional security benefit of every feature of the new format.

A short break between separately timed parts may serve legitimate administrative purposes. It may help testing personnel manage the transition between sections, and the associated rules may be designed to limit opportunities for unauthorized communication. Yet these possible benefits should be distinguished from demonstrated outcomes.

The relevant questions include:

• What specific security risks is the ten-minute break intended to address?

• How does separating the examination into two parts reduce those risks?

• What procedures are used during the break to prevent prohibited communication or access to unauthorized materials?

• Is there evidence that this arrangement improves examination security beyond the protections already provided by professional testing centers?

These questions do not imply that the break is unnecessary or that the MAA lacks internal evidence supporting its decision. An organization may have legitimate operational or security reasons that have not been fully explained in a public announcement. The point is that a public rationale for the overall testing-center policy should not automatically be treated as a complete explanation for every additional restriction.

Clear communication would help students and educators understand not only what they must do, but also why the rules are structured as they are. It would also allow the mathematical community to evaluate the policy on the basis of its stated objectives rather than speculation.

4. Written Security Rules and Practical Enforcement

Written rules are essential to a secure examination, but their effectiveness also depends on how they are implemented.

The AIME’s new arrangements include restrictions on electronic-device use and communication during the break. Students are not permitted to use electronic devices or communicate with individuals outside the testing center during that period; restroom use is permitted under the applicable rules. Students must follow the official instructions provided by the MAA and the testing center.

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These rules establish important boundaries. However, the existence of a written prohibition and the practical enforcement of that prohibition are distinct matters.

For example, effective implementation depends on students understanding the rules, testing personnel applying them consistently, and procedures being sufficiently clear to address ordinary situations. Students should know what they may carry, where they may go, whether they must remain in designated areas, and what actions are prohibited during the break. Ambiguity can create avoidable confusion even when the underlying objective is reasonable.

It is equally important not to assume, without evidence, that a ten-minute break creates a security problem or that the new procedures are ineffective. The appropriate question is whether the rules and their enforcement are proportionate to the risks they are intended to address.

The MAA could strengthen confidence in the new format by explaining the practical procedures that support the break restrictions and by providing clear, accessible guidance before students arrive at the testing center. Predictable procedures would benefit students and testing personnel alike.

5. Additional Administrative Burdens and Operational Complexity

The transition to professional testing centers changes the practical experience of taking the AIME.

For students, the new arrangement requires them to schedule and attend an examination at an authorized testing center, follow the center’s procedures, and complete an electronic examination under the prescribed conditions. For families, participation may involve additional travel, scheduling coordination, and planning around the testing appointment. The exact burden will vary depending on each student’s location and circumstances.

These considerations do not establish that the new system is unworkable. Professional testing centers may offer standardized procedures and specialized testing infrastructure that are difficult to reproduce consistently across a large network of schools and other venues. Centralized administration may also reduce certain risks associated with inconsistent local practices.

Nevertheless, the practical costs should be included in any evaluation of the policy. A testing system can improve one aspect of administration while introducing new difficulties in access, scheduling, or convenience. The relevant issue is not whether every student will experience the same burden, but whether the new arrangements create avoidable barriers for some students and whether reasonable measures can reduce them.

A useful evaluation would consider travel distances, appointment availability, accessibility needs, scheduling conflicts, and the procedures available to students who encounter unexpected difficulties. It would also examine whether students in rural areas or regions with fewer testing centers face disadvantages compared with students who live near multiple locations.

The aim should not be to reject centralized testing simply because it requires coordination. Rather, it should be to ensure that the operational benefits of centralization are assessed alongside its practical consequences for participation.

6. The Examinee’s Experience: Time Pressure, Concentration, and Psychological Burden

The AIME is already a demanding examination. Students must solve challenging problems under substantial time pressure, often while making difficult decisions about which approaches are most promising and how much time each problem deserves.

The two-part format adds a new feature to that experience: the end of Part 1 is an absolute cutoff. Students cannot return to the first eight questions once Part 2 begins. This can make time management in the first section especially consequential.

The effect will not be identical for every examinee. Some students may find the division helpful because it provides a clear structure. Others may find it difficult to leave an unfinished problem behind when they know they will not be able to revisit it. Students who work most effectively by alternating between problems may need to adjust their usual approach.

A ten-minute break may offer an opportunity to rest, but it also divides a single examination into two separate periods of concentration. The break’s effect on fatigue, focus, and performance is an empirical question rather than something that should be assumed in advance.

These considerations matter because the purpose of a mathematics competition is to assess mathematical ability, not to introduce incidental disadvantages that have little connection to the intended construct. Some time pressure is intrinsic to a timed contest, and no examination can eliminate every source of stress. The question is whether the new format introduces additional burdens that are necessary and proportionate to its benefits.

The MAA could help students adapt by providing clear descriptions of the format, sample practice sessions that reproduce the two-part timing, and guidance on the transition between sections. Such resources would not remove the challenge of the examination. They would help ensure that students understand the conditions under which they will be assessed.

7. A Related but Separate Question: What Does the AIME Score Measure?

The discussion of the new testing format also raises a broader question about the AIME’s role in recognizing mathematical achievement.

The AIME contains 15 questions, and each correct answer earns one point. The examination therefore reports a score from 0 to 15, with no additional points for a more difficult question.

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This scoring system is simple, transparent, and easy to administer. However, the difficulty of the questions may vary substantially. A student’s total score consequently records the number of questions answered correctly, rather than directly reflecting differences in the difficulty of the problems solved.

Whether this is the most appropriate way to measure achievement is a legitimate subject for discussion. It is also a distinct issue from the security and administration changes introduced for 2027.

A serious examination of alternative scoring systems would require careful analysis of historical question difficulty, score distributions, ranking stability, and the consequences for qualification decisions. A scoring system that appears more sensitive to difficulty in principle would not automatically be fairer in practice. Any proposed alternative would need to be tested against clear objectives and empirical evidence.

For that reason, the question of whether AIME questions should carry equal weight deserves a separate, focused discussion rather than being treated as a direct consequence of the new testing-center arrangements. The format of an examination, the security of its administration, and the meaning of its score are related but analytically different questions.

8. Other Competitions Show the Value of Examining Alternative Designs

The AIME does not exist in isolation. Mathematics competitions around the world use different approaches to question formats, scoring, and examination administration. These differences reflect the objectives of each competition and the populations it serves.

Comparisons must be made carefully. A contest that includes written proofs cannot be treated as directly equivalent to the AIME, which uses short numerical answers. Likewise, competitions with different curricula, participant populations, or selection purposes may offer useful ideas without providing a direct model for reform.

Nevertheless, the existence of alternative designs reinforces an important principle: established practices should be evaluated in light of their purposes rather than assumed to be the only reasonable options.

For the 2027 AIME, the most useful comparisons would focus on how comparable short-answer competitions balance examination security, accessibility, time limits, and the measurement of mathematical ability. Such comparisons could inform future discussion without presupposing that another competition’s approach should simply be adopted.

The objective should be to identify which design choices serve the AIME’s particular purposes most effectively, not to imitate another contest for its own sake.

9. Why These Questions Matter for the Olympiad Pathway

The implications of the 2027 changes extend beyond the AIME itself.

The MAA has announced that qualification for the 2027 USA Mathematical Olympiad (USAMO) and USA Junior Mathematical Olympiad (USAJMO) will be based primarily on AIME scores, with AMC scores no longer serving as a factor in qualification. This is a significant change in the relationship between the AMC and the national olympiad pathway.

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When an examination becomes more consequential for subsequent selection, the design of that examination deserves particular scrutiny. The reliability of the score, the consistency of administration, and the accessibility of the testing process all matter.

This does not mean that the AIME must be redesigned simply because its role in selection has changed. Nor does it mean that a two-part format necessarily produces less reliable results. It means that the consequences of the examination’s design should be considered in proportion to the decisions that depend on its results.

A well-designed selection examination should distinguish mathematical achievement as accurately as reasonably possible while maintaining appropriate security and consistent administration. Evaluating these objectives together would help the MAA assess whether the new arrangements support the broader goals of the competition pathway.

10. A Constructive Agenda for the MAA

The MAA has a legitimate responsibility to protect the integrity of its competitions. The transition to professional testing centers may be an appropriate way to pursue that responsibility. At the same time, major changes are most persuasive when their objectives, implementation, and outcomes can be examined clearly.

Several steps could make the 2027 AIME arrangements easier for students, families, educators, and the broader mathematical community to understand and evaluate.

First, explain the purpose of each major design choice separately. The benefits of using Pearson Professional Centers, dividing the examination into two timed parts, preventing students from returning to Part 1, and introducing a ten-minute break should be distinguished rather than treated as one indivisible policy. Each feature may serve a different purpose and may have different costs.

Second, provide clear and comprehensive examination-day guidance. Students should receive unambiguous instructions concerning the two parts, the transition between them, permitted and prohibited activities during the break, and the procedures they must follow at the testing center. Clear guidance can reduce uncertainty without compromising security.

Third, assess accessibility and operational burdens. The MAA should consider whether travel, appointment availability, disability-related needs, or other practical circumstances create avoidable barriers. Where possible, it should identify ways to address those barriers while preserving the integrity of the examination.

Fourth, evaluate the new format using evidence. After the new arrangements have been implemented, the MAA could examine relevant information about administration, student experience, security incidents, and examination performance. Any conclusions should distinguish observed results from assumptions and should account for the limitations of the available data.

Fifth, invite informed feedback. Students, parents, teachers, competition administrators, and testing personnel can offer different perspectives on how the new system works in practice. A structured feedback process would allow the MAA to identify unexpected difficulties and consider improvements without abandoning legitimate security objectives.

These recommendations do not require the MAA to disclose sensitive security procedures or compromise the examination. They call for transparency about policy objectives, clarity about student obligations, and a willingness to evaluate outcomes.

A secure examination and a well-designed examination are not competing ideals. The challenge is to achieve both.

11. Conclusion: A Better Examination Requires More Than a Secure Testing Environment

The 2027 AIME changes represent a substantial shift in how one of the most important examinations in the American mathematics competition pathway is administered. Moving to Pearson Professional Centers, delivering the examination electronically, dividing it into two separately timed parts, and imposing a firm boundary between those parts will change the conditions under which students demonstrate their mathematical abilities.

The MAA’s goal of protecting competition integrity is reasonable and important. But the legitimacy of that goal does not remove the need to evaluate the specific measures adopted to achieve it. The security benefits of professional testing centers, the additional effects of the two-part format, and the purpose of the ten-minute break are separate questions that deserve clear explanations and, where possible, evidence-based assessment.

The practical experience of examinees matters as well. Travel and scheduling requirements, time-management constraints, and the inability to revisit Part 1 may affect students in different ways. These consequences should neither be exaggerated nor dismissed without evidence.

Ultimately, the AIME should be administered in a way that protects the integrity of the competition while measuring mathematical achievement as effectively as possible. Security, accessibility, operational feasibility, and assessment quality should be treated as complementary responsibilities.

The most productive response to the 2027 changes is therefore neither automatic acceptance nor categorical opposition. It is a commitment to careful evaluation: identify the purpose of each policy, explain how it is expected to work, examine its consequences, and revise it when the evidence supports improvement.

A strong mathematics competition needs more than secure administration. It needs a testing system whose rules are clear, whose burdens are proportionate, and whose design is continually evaluated against the mathematical achievement it is intended to recognize.

Author’s Note

This article is an independent mathematics education commentary. It examines the publicly announced 2027 AIME administration changes and raises questions for discussion; it does not claim that the new format has been shown to reduce fairness, increase security risks, or impair student performance. Assessing those outcomes requires evidence from actual implementation.

The views expressed are those of the author and do not necessarily represent the views of the Mathematical Association of America or any other organization.

Official References

1. Mathematical Association of America. (2026, August 26). MAA Announces Official Testing Centers for the 2027 American Invitational Mathematics Examination. The MAA’s announcement of the move to Pearson testing centers and its stated objective of protecting competition integrity.

2. Mathematical Association of America. MAA Invitational Competitions. Official information about the AIME and the 2027 USAMO/USAJMO qualification changes.

3. Mathematical Association of America. Competitions Policies. The official location for MAA competition policies, including the AIME rules and policies applicable to the relevant competition cycle.

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

Session I: Fundamental Geometry
Five Sundays (EASTERN Time: 1:00 – 3:30 pm), Total: 12.5 Hours
Dates: 9/6, 9/13, 9/20, 9/27, 10/4
Session II: Advanced Geometry (Continuation of Session I)
Five Sundays (EASTERN Time: 1:00 – 3:30 pm), Total: 12.5 Hours
Dates: 10/11, 10/18, 10/25, 11/1, 11/8
View Course Outline

Format

Live online instruction, with class recordings included

Who Should Attend?

Students entering Grades 6–12 who want to strengthen their geometry skills for AMC 10/12 and AIME preparation.

Class Handout Sample

Online Registration is now open! Click HERE to register and pay.

Tuition (including all materials)
Session I (12.5 Hours)
New Student:	Via Zelle:  $690 (Phone: 240-300-4380) Please include your child’s name and “AIME Fall I” in the “Memo” box.
	Via PayPal:  $718
Returning Student:	Via Zelle:  $680 (Phone: 240-300-4380) Please include your child’s name “AIME Fall I” in the “Memo” box.
	Via PayPal:  $707
Session II (12.5 Hours)
New Student:	Via Zelle:  $690 (Phone: 240-300-4380) Please include your child’s name “AIME Fall II” in the “Memo” box.
	Via PayPal:  $718
Returning Student:	Via Zelle:  $680 (Phone: 240-300-4380) Please include your child’s name “AIME Fall II” in the “Memo” box.
	Via PayPal:  $707
Sessions I & II (25 Hours)
New Student:	Via Zelle:  $1,370 (Phone: 240-300-4380) Please include your child’s name and “AIME Fall I and II” in the “Memo” box.
	Via PayPal:  $1,426
Returning Student:	Via Zelle:  $1,350 (Phone: 240-300-4380) Please include your child’s name and “AIME Fall I and II” in the “Memo” box.
	Via PayPal: $1,404
Click HERE to see payment and refund policy.

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.