{"id":61303,"date":"2026-04-21T21:49:25","date_gmt":"2026-04-21T13:49:25","guid":{"rendered":"https:\/\/blog-admin.thethinkacademy.com\/?p=61303"},"modified":"2026-04-21T22:05:47","modified_gmt":"2026-04-21T14:05:47","slug":"amc-ten-past-contests-solutions-canada","status":"publish","type":"post","link":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/04\/21\/amc-ten-past-contests-solutions-canada\/","title":{"rendered":"AMC 10 Past Contests and Solutions: Full Archive by Year"},"content":{"rendered":"\n

Past AMC 10 papers are the single most valuable preparation resource available to Canadian students aiming for competition math success. Every contest from AMC 10A and AMC 10B going back to 2000 is available through the Mathematical Association of America and the Art of Problem Solving community, giving students hundreds of problems at every difficulty level to work through. This guide explains where to find AMC 10 past papers, how to use them effectively rather than just completing them, what the 2024 and 2025 papers tell us about current difficulty trends, and includes worked examples from recent contests with full explanations so you can see exactly what AMC 10 problems require.<\/p>\n\n\n\n

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Where to find AMC 10 past contests<\/strong><\/h2>\n\n\n\n

AMC 10 past papers are freely available from two main sources.<\/p>\n\n\n\n

The first is the Mathematical Association of America website at maa.org<\/a>, which publishes official past papers and answer keys. This is the authoritative source for every AMC 10 contest going back to its introduction in 2000.<\/p>\n\n\n\n

The second is the Art of Problem Solving community at artofproblemsolving.com<\/a>, which hosts not just the papers and answer keys but detailed solution discussions for every single problem. The AoPS wiki pages for AMC 10 past contests include multiple solution approaches for each problem, discussion of common errors, and connections between problems across different years. For students who want to understand why a solution works rather than just what the answer is, AoPS is the more useful resource.<\/p>\n\n\n\n

Both sources are free. There is no reason to pay for past paper access \u2014 everything you need is publicly available.<\/p>\n\n\n\n

AMC 10A and AMC 10B \u2014 what is the difference?<\/strong><\/h3>\n\n\n\n

Each year the AMC 10 is offered in two versions: AMC 10A and AMC 10B, administered approximately one week apart. The two versions contain entirely different problems but are designed to be equivalent in difficulty. Students may sit one or both.<\/p>\n\n\n\n

When working through past papers, treat AMC 10A and AMC 10B as separate papers. A student preparing for the current year has access to both versions of every past year, effectively doubling the number of practice papers available. Work through them in order from most recent backward \u2014 AMC 10 2025, AMC 10 2024, AMC 10 2023 \u2014 so your preparation reflects the current style and difficulty of the competition.<\/p>\n\n\n\n

For more information on the AMC 10, check out AMC 10 Math Competition: The Complete Guide for Canadian Students and Parents<\/a>.<\/p>\n\n\n\n

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How to use AMC 10 past contests effectively<\/strong><\/h2>\n\n\n\n

Most students use past papers the wrong way. They complete a paper, check their score, feel good or bad about it, and move on. This approach produces much slower improvement than deliberate review.<\/p>\n\n\n\n

The most effective use of AMC 10 past papers involves four stages.<\/p>\n\n\n\n

Stage one: complete under real conditions.<\/strong> Sit the paper for exactly 75 minutes with no notes, no calculator, and no interruptions. Do not look anything up mid-paper. Answer every question you can and leave blank any question where you have no reasonable basis for attempting it \u2014 remember that a blank answer scores 1.5 points and a wrong answer scores 0.<\/p>\n\n\n\n

Stage two: score and categorise.<\/strong> After the paper, score it using the answer key. Then go through every question \u2014 including those you answered correctly \u2014 and categorise each one by topic area: algebra, geometry, number theory, combinatorics, or probability. Note which topic areas produced the most errors.<\/p>\n\n\n\n

Stage three: review every wrong answer.<\/strong> For each incorrect answer, find the solution on AoPS and read it carefully. Do not just check whether your method was right or wrong \u2014 understand why the correct method works and whether there is a more efficient approach. Many AMC 10 problems have elegant short solutions that are not obvious at first but become recognisable with practice.<\/p>\n\n\n\n

Stage four: build weak areas before the next paper.<\/strong> If your topic categorisation shows consistent errors in number theory, spend two or three study sessions working specifically on number theory problems before attempting the next past paper. Completing paper after paper without addressing specific weaknesses produces diminishing returns.<\/p>\n\n\n

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\"AMC<\/figure>\n<\/div>\n\n\n
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AMC 10 difficulty trends: what recent papers tell us<\/strong><\/h2>\n\n\n\n

AMC 10 2025<\/strong><\/h3>\n\n\n\n

The AMC 10 2025 papers continued the trend from recent years of placing greater emphasis on multi-concept problems \u2014 questions that require students to combine algebra with geometry, or number theory with combinatorics, within a single solution. Students who prepared by drilling individual topic areas found the later questions more challenging than expected for this reason.<\/p>\n\n\n\n

The 2025 papers also featured a higher proportion of questions requiring careful case analysis \u2014 a skill that is specifically developed through competition math practice and does not appear frequently in school curriculum. Students preparing for AMC 10 2026 should make sure their preparation includes deliberate work on case analysis problems.<\/p>\n\n\n\n

AMC 10 2024<\/strong><\/h3>\n\n\n\n

The AMC 10 2024 papers were notable for the difficulty of questions 15 to 20, which were harder than comparable questions in several previous years. The cutoff score for AIME qualification from the 2024 AMC 10A was higher than the year before, reflecting an overall stronger performance from the cohort rather than an easier paper.<\/p>\n\n\n\n

AoPS AMC 10 2024 solution discussions are particularly useful for understanding the standard approaches to the harder questions \u2014 the community solutions on AoPS often show significantly more efficient methods than the approaches most students attempt under competition conditions.<\/p>\n\n\n\n

What this means for preparation<\/strong><\/h3>\n\n\n\n

Looking across AMC 10 past contests from 2020 to 2025, three patterns are consistent:<\/p>\n\n\n\n

Geometry and algebra together account for roughly 40% of questions across every paper. Students who are weak in either of these areas will consistently lose marks regardless of how strong they are in other topics.<\/p>\n\n\n\n

Questions 21 to 30 increasingly require proof-style thinking \u2014 the ability to construct a logical argument rather than just calculate an answer. This skill is specifically developed through practice with full-solution problems, not just multiple choice work.<\/p>\n\n\n\n

Time management separates students at the boundary of AIME qualification. Many students who know how to solve most of the questions on a paper fail to qualify because they spend too long on hard early questions and run out of time before reaching questions where they could have scored points.<\/p>\n\n\n\n

One practical note for Canadian students: the AMC 10 takes place in November each year in two sittings. Registration goes through a registered test centre – either your school or an independent centre. If your school does not offer the AMC 10, registration deadlines are strict and spaces at independent centres fill up. It is worth sorting registration well before you begin your final preparation push so a missed deadline does not end the year before the exam. See our full guide on AMC Registration in Canada: How to Sign Up<\/a> for step-by-step registration instructions.<\/p>\n\n\n\n

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Worked examples from AMC 10 past contests<\/strong><\/h2>\n\n\n\n

The following examples are drawn from recent AMC 10 past papers. Each includes the problem, a full worked solution, and an explanation of the key insight required \u2014 because understanding why a solution works is more valuable for preparation than just knowing the answer.<\/p>\n\n\n\n

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Example 1 \u2014 Number theory (difficulty: questions 1 to 10 level)<\/strong><\/h3>\n\n\n\n

This type of problem tests divisibility and basic number theory, which appear in almost every AMC 10 past paper.<\/p>\n\n\n\n

Problem type:<\/strong> A positive integer n has the property that n, n+1, and n+2 are each divisible by a different prime. What is the smallest possible value of n?<\/em><\/p>\n\n\n\n

Key insight:<\/strong> Work through small values of n systematically. For n=2: 2 is divisible by 2, 3 by 3, 4 by 2 \u2014 but 4 shares its prime (2) with n. For n=3: 3 is divisible by 3, 4 by 2, 5 by 5 \u2014 three different primes. The answer is n=3.<\/p>\n\n\n\n

What this tests:<\/strong> The ability to work systematically through cases rather than trying to find an algebraic shortcut. Students who try to set up equations for this type of problem often make it harder than it needs to be. Recognising that small case checking is the most efficient approach is the key skill.<\/p>\n\n\n\n

Preparation note:<\/strong> Problems like this appear in the first ten questions of most AMC 10 past contests. They are designed to be solvable with careful thinking rather than advanced knowledge. Students who practice working systematically and checking small cases develop the habit of identifying the most efficient approach quickly.<\/p>\n\n\n\n

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Example 2 \u2014 Geometry and algebra combined (difficulty: questions 11 to 20 level)<\/strong><\/h3>\n\n\n\n

This type of problem requires combining geometric reasoning with algebraic calculation \u2014 a combination that appears frequently in the middle section of AMC 10 past papers.<\/p>\n\n\n\n

Problem type:<\/strong> A rectangle has perimeter 40 and its diagonal has length 15. What is the area of the rectangle?<\/em><\/p>\n\n\n\n

Key insight:<\/strong> Let the sides be a and b. From the perimeter: 2(a+b) = 40, so a+b = 20. From the diagonal using the Pythagorean theorem: a\u00b2 + b\u00b2 = 225. Use the identity (a+b)\u00b2 = a\u00b2 + 2ab + b\u00b2 to find 2ab: 400 = 225 + 2ab, so 2ab = 175 and ab = 87.5. The area is ab = 87.5.<\/p>\n\n\n\n

What this tests:<\/strong> The ability to connect multiple pieces of information \u2014 perimeter, diagonal, Pythagorean theorem \u2014 and use an algebraic identity to find the answer efficiently. Students who try to solve for a and b individually using the quadratic formula will get the right answer but take significantly longer, risking running out of time.<\/p>\n\n\n\n

Preparation note:<\/strong> The identity (a+b)\u00b2 = a\u00b2 + 2ab + b\u00b2 appears in AMC 10 past contests across many different years in many different contexts. Recognising when to use it is a specific competition math skill that school curriculum does not develop explicitly. Students who have seen this identity applied in multiple contexts through past paper review will spot the opportunity quickly under competition conditions.<\/p>\n\n\n\n

\"Think<\/a>
Find the right course level for your child.<\/figcaption><\/figure>\n\n\n\n
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Example 3 \u2014 Combinatorics (difficulty: questions 15 to 25 level)<\/strong><\/h3>\n\n\n\n

Combinatorics problems in the harder section of AMC 10 past papers typically require careful case analysis or a counting technique that is not taught in standard school curriculum.<\/p>\n\n\n\n

Problem type:<\/strong> How many ways can you arrange the letters A, B, C, D, E in a row such that A appears before B and C appears before D?<\/em><\/p>\n\n\n\n

Key insight:<\/strong> Total arrangements of 5 letters = 5! = 120. By symmetry, in exactly half of all arrangements A appears before B (regardless of where C, D, E are). So 60 arrangements have A before B. Of those 60, exactly half will have C before D by the same symmetry argument. So 30 arrangements satisfy both conditions.<\/p>\n\n\n\n

What this tests:<\/strong> The symmetry argument is the key insight. Students who try to count directly by listing cases will either make errors or run out of time. Recognising that symmetry makes the counting trivial is a specific problem-solving approach that appears repeatedly across AMC 10 past contests in different forms.<\/p>\n\n\n\n

Preparation note:<\/strong> The symmetry argument \u2014 recognising that for any two elements in a random arrangement, each is equally likely to come first \u2014 is one of the most useful tools in AMC 10 combinatorics. Students who have seen it applied in several different contexts through past paper review will recognise it immediately in new problems. Students who have not will attempt direct counting, which is far more error-prone and time-consuming.<\/p>\n\n\n\n

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Example 4 \u2014 Probability (difficulty: questions 20 to 30 level)<\/strong><\/h3>\n\n\n\n

The hardest probability problems in AMC 10 past contests typically involve multiple events, conditional probability, or geometric probability.<\/p>\n\n\n\n

Problem type:<\/strong> Two fair dice are rolled. Given that the sum is at least 9, what is the probability that both dice show the same number?<\/em><\/p>\n\n\n\n

Key insight:<\/strong> Use conditional probability. First count the outcomes where the sum is at least 9: (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6) \u2014 that is 10 outcomes. Of these, the outcomes where both dice show the same number are (5,5) and (6,6) \u2014 2 outcomes. The conditional probability is 2\/10 = 1\/5.<\/p>\n\n\n\n

What this tests:<\/strong> The ability to correctly apply conditional probability by restricting the sample space to only the outcomes where the given condition holds. Students who calculate the probability without restricting the sample space get the wrong answer. This is one of the most common error types on probability questions in AMC 10 past papers.<\/p>\n\n\n\n

Preparation note:<\/strong> Conditional probability problems appear in almost every AMC 10 past paper. The most common error is forgetting to restrict the sample space. Students who explicitly write out the restricted sample space before calculating \u2014 even if it takes a few extra seconds \u2014 make significantly fewer errors on this problem type than students who try to calculate directly.<\/p>\n\n\n\n

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\"AMC<\/figure>\n<\/div>\n\n\n

Building a past paper study plan<\/strong><\/h2>\n\n\n\n

Working through AMC 10 past contests without a plan produces slower improvement than structured preparation. Here is a practical study plan for students at different stages.<\/p>\n\n\n\n

For students starting<\/em> AMC 10 preparation (12 to 18 months before competition)<\/strong><\/p>\n\n\n\n

Students who have not yet sat the AMC 8 should consider whether to start there first. A student who is new to competition math and jumping straight to AMC 10 past papers often finds the difficulty gap discouraging. Working through AMC 8 preparation first builds the foundational problem-solving habits that make AMC 10 work significantly more productive. See AMC 8 Math Competition: The Complete Guide for Canadian Students and Parents<\/a> for guidance on whether AMC 8 preparation is the right starting point.<\/p>\n\n\n\n

In the first three months, do not complete full past papers under timed conditions. Instead, work through questions 1 to 15 from three or four past papers without a time limit, focusing entirely on understanding the solution to every question. Read the AoPS solution discussions<\/a> for every problem you could not solve. After three months you will have built familiarity with the main problem types before the pressure of timed conditions.<\/p>\n\n\n\n

From month four onward, begin completing full papers under timed conditions once a month, then spending two review sessions on each paper before attempting the next.<\/p>\n\n\n\n

For students in the final six months<\/em> before competition<\/strong><\/p>\n\n\n\n

Complete one full past paper under timed conditions every two weeks. Alternate between AMC 10A and AMC 10B papers from recent years, working backward from AMC 10 2025 and AMC 10 2024. After each paper spend two study sessions reviewing every question, focusing more time on questions 21 to 30 even if you answered them correctly \u2014 understanding the elegant solutions to hard problems is what builds performance at the top end of the score range.<\/p>\n\n\n\n

In the final month before competition, complete the two most recent past papers \u2014 AMC 10 2025 and AMC 10 2024 \u2014 under strict timed conditions and review them carefully. These are the best indication of what the current paper will look like.<\/p>\n\n\n\n

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What AIME qualification requires from AMC 10 past paper performance<\/strong><\/h2>\n\n\n\n

AIME qualification goes to approximately the top 2.5% of AMC 10 scorers. The exact cutoff varies each year \u2014 for AMC 10 2024 it was in the range of 100 to 115 out of 150 depending on the version. The official cutoff is published by the MAA after each sitting.<\/p>\n\n\n\n

To understand what this means in practice: a student who scores 100 out of 150 on the AMC 10 has answered approximately 15 questions correctly, left around 8 questions blank, and answered the remaining 7 incorrectly. This requires strong performance on questions 1 to 20 and at least partial success on some questions in the 20 to 30 range.<\/p>\n\n\n\n

Students using AMC 10 past papers to track their AIME qualification trajectory should monitor not just their total score but their performance by question range. Consistent accuracy on questions 1 to 15, improving accuracy on questions 16 to 20, and deliberate work on questions 21 to 30 is the progression that leads to AIME qualifying scores.<\/p>\n\n\n\n

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Frequently Asked Questions<\/strong><\/h2>\n\n\n\n
Where can I find AMC 10 past contests?<\/strong> <\/summary>\n

AMC 10 past papers are available free through the Mathematical Association of America website at maa.org<\/a> and through the Art of Problem Solving community at artofproblemsolving.com<\/a>. AoPS also hosts detailed solution discussions for every past problem going back to 2000. Both sources are free.<\/p>\n<\/details>\n\n\n\n

How many AMC 10 past papers are available?<\/strong> <\/summary>\n

The AMC 10 has been offered since 2000 in two versions each year \u2014 AMC 10A and AMC 10B. This means there are over 40 past papers available, each containing 30 questions. Combined with AMC 10 2024 and AMC 10 2025, students have access to hundreds of past contest problems at every difficulty level.<\/p>\n<\/details>\n\n\n\n

What is the difference between AMC 10 past contests and AMC 10 previous tests?<\/strong> <\/summary>\n

These terms refer to the same thing \u2014 the archive of past AMC 10 papers from previous years. AMC 10 past contests, AMC 10 previous tests, and AMC 10 past papers all describe the same resource: the official papers and solutions from every AMC 10 sitting since 2000.<\/p>\n<\/details>\n\n\n\n

How should I use AMC 10 past papers to prepare?<\/strong> <\/summary>\n

Complete papers under timed conditions, then review every question carefully including those answered correctly. Categorise errors by topic area and work specifically on weak areas before attempting the next paper. Reading AoPS solution discussions for every problem \u2014 not just the ones you got wrong \u2014 develops familiarity with efficient problem-solving approaches that are hard to discover independently.<\/p>\n<\/details>\n\n\n\n

What do AMC 10 2024 and 2025 papers tell us about the current competition?<\/strong> <\/summary>\n

Recent papers show a continued emphasis on multi-concept problems that combine algebra with geometry or number theory with combinatorics. The difficulty of questions 15 to 20 has been high in recent years. Students preparing for AMC 10 2026 should ensure their preparation covers all topic combinations and includes deliberate practice on case analysis problems.<\/p>\n<\/details>\n\n\n\n

What score do I need on AMC 10 past papers to be ready for AIME qualification?<\/strong> <\/summary>\n

Consistently scoring above 100 out of 150 on timed past papers \u2014 equivalent to approximately 15 correct answers with good blank-answer discipline \u2014 indicates readiness for AIME qualification attempts. Students who are scoring in the 80 to 100 range consistently are close and should focus their remaining preparation on questions 16 to 25.<\/p>\n<\/details>\n\n\n\n

Is AMC 10B harder than AMC 10A?<\/strong> <\/summary>\n

The two versions are designed to be equivalent in difficulty and the AIME cutoffs for each are set independently based on that year’s performance. In practice, minor differences in difficulty exist from year to year but neither version is consistently harder than the other. Students sitting both have a second opportunity to achieve a qualifying score.<\/p>\n<\/details>\n\n\n\n

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\"Think<\/a>
Expert teachers. Live classes. Proven results. Think Academy is an official AMC test centre \u2014 register and prepare in one place.<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"

Past AMC 10 papers are the single most valuable preparation resource available to Canadian students aiming … AMC 10 Past Contests and Solutions: Full Archive by Year<\/span>Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":61308,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17153,1752,12665],"tags":[12572,17151,17150,17152,254],"class_list":["post-61303","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-amc-category","category-competitions","category-math-contest-past-papers","tag-amc-10","tag-amc-10-past-contests-and-solutions","tag-amc-10-past-papers","tag-amc-10a-10b","tag-thinkacademy"],"yoast_head":"\nAMC 10 Past Contests and Solutions: Full Archive by Year<\/title>\n<meta name=\"description\" content=\"A complete guide to AMC 10 past contests for Canadian students: how to use past papers, examples with solutions, and recent 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