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How to Study for the Math Olympiad: AMC 10/AMC 12

Other High School

Have you ever wondered what it would take to represent America at the International Math Olympiad? Or maybe you're a strong math student who is wondering what opportunities are available to you outside the classroom?

In this article, we'll answer all your Math Olympiad questions! We'll explain what it takes to qualify for the International Math Olympiad and how to ace the qualifying tests—the AMC 10 and AMC 12.

How Do You Qualify for Math Olympiad?

In this section we discuss the three key steps to qualifying for Math Olympiad.

Step 1: Take the AMC 10 or AMC 12

The AMC 10 and AMC 12 are nationwide tests administered by the Mathematical Association of America that qualify you for the American Invitational Mathematics Exam (AIME). Only those with top scores will be invited to take the AIME. The MAA recommends 9th and 10th graders take the AMC 10, and 11th and 12th graders take the AMC 12. You can take the AMC 10 and/or 12 multiple times.

The AMC 10 and AMC 12 each have 25 questions. You have 75 minutes for the entire exam. Each correct answer is worth 6 points (for a maximum score of 150) and each unanswered question is worth 1.5 points. There is no deduction for wrong answers.

Note that you don't need to get all of the questions right to get a qualifying score. You just have to do better than most of the other students taking the exam! Keep that in mind as you come up with a strategy for the test.

You need to be in the top 5% of scorers on the AMC 12 or the top 2.5% of scorers on the AMC 10 to qualify, so the vast majority of people who take the AMC exams don't qualify. But, if you do qualify, you can take the American Invitation Mathematics Examination, or AIME.

Step 2: Take the AIME

The AIME is a 15-question, three-hour exam, and each answer is an integer between 0 and 999, inclusive. Regardless of whether you took the AMC 10 or AMC 12, everyone takes the same AIME. It's offered once a year (with an alternate test date available for those who can't make the official exam date) in the spring.

Unlike the AMC 10 and the AMC 12, you can only take the AIME once per qualification. So while you can take the AMC 10 or AMC 12 multiple times to qualify, once you qualify, you've only got one shot at the AIME. That means you want to make sure you do your best on it.

After you take the AIME, your AIME score is multiplied by ten and added to your AMC score to determine if you qualify for Math Olympiad. The cutoff score for qualifying changes yearly, but it's set so about 260-270 students qualify for Math Olympiad each year.

Step 3: Qualify for and Compete in Math Olympiad

If you do well on the AIME, you can qualify for the US Mathematical Olympiad. The top scorers from that competition then have the opportunity to train to be on the US team that competes at the International Math Olympiad. (You can find more info on this process over at the Mathematical Association of American website .)

If you took the AMC 10, you'll compete in the USA Junior Mathematical Olympiad (USAJMO). Students who took the AMC 12 will compete in the USA Mathematical Olympiad (USAMO).

It's a long process to get to the IMO, and very few students make it that far. But even just taking the AIME can set you apart in the college admissions process, especially if you are interested in engineering programs. Along with a high GPA and strong SAT/ACT scores, taking the AIME is a way to signal to colleges you have superior math and problem-solving skills.

How Can You Learn Math Olympiad Content?

Math through pre-calculus covers most topics tested on the AMC 10 and 12 and the AIME, but math competition problems will be trickier than what you see on your usual math homework assignments.

If you're not up to pre-calculus in school yet, your first task will be learning the content before focusing on how to solve problems that the AMC 10 and 12 tend to ask.

See if there is a teacher or peer who is willing to tutor you if you haven't taken pre-calculus. You could also see if it's possible to take the course over the summer to get caught up quickly. There may also be private tutoring available in your area that can help get your precalculus skills up to speed!

In the meantime, you can explore parts of your own math textbook you haven't gotten to yet, or ask to borrow textbooks from teachers at your school if you want to brush up on a topic not covered in the math class you're taking this year.

Also check out these online content resources from the MAA to help you study (you'll need to create an online account).

How Can You Learn Problem-Solving Skills?

The key to doing well on AMC is not just knowing math and being able to do rote problems, but to know concepts inside and out and be able to use them to solve tricky problems.

Think outside the textbook.

The website Art of Problem Solving is a hub for math competition resources and problems, and has been mentioned by many former AMC-takers as a top resource. They have pages on learning to solve certain types of problems, advice on the best prep books, and forums where you can talk to other AIME hopefuls about studying and strategy.

This page provides links to practice problems and prep books and is a great place to get started.

Our advice to study for the AMC is to do lots of practice problems, and then correct them. Carefully analyze your weaknesses. Don't just notice what you did wrong, get inside your head and figure out why you got a problem wrong and how you will work to get it correct the next time.

To improve your problem-solving ability, you can also consider borrowing or purchasing books specifically about solving math problems. Try How To Solve It by George Polya, Problem-Solving Strategies by Arthur Engel, or Challenging Problems in Algebra by Alfred Posamentier and Charles Salkind. These books will give you skills not typically taught in your math classes.

How to Prepare for Math Olympiad

Studying is more than just putting the time in. You want to make sure you are using the best practice problems and really analyzing your weak points to get your math skills to where they need to be.

Read on to learn the six tips you need to follow to study like a pro.

#1: Use Quality Practice Problems

Use practice problems from past AMCs when possible. You want to prepare for the format and type of questions on the AMC. Any problem-solving practice you get will be helpful, but if you're set on qualifying the AIME, you should spend the majority of your time prepping for AMC-type questions.

If you're unclear on how to solve a problem, ask your math teacher, a math team friend, or an online forum like the one at Art of Problem Solving . The better you understand each AMC problem you encounter, the more likely you are to be prepared for the real thing.

#2: Don't Lounge Around

Quality practice time is key! Make sure to time yourself and simulate real test-taking conditions when doing practice problems— find a quiet room, don't use outside resources while you test, and sit at a proper table or desk (don't lounge in bed!). As you review problems, bring in your outside resources, from websites to problem-solving books, but remember to stay alert and focused.

Don't let study time turn into naptime!

#3: Focus on Your Weak Areas

When studying, spend the most time focusing on your weak areas. As you work through practice problems, keep track of problems you didn't know how to solve or concepts you're shaky on. You can log your mistakes into a journal or notebook to help focus your studying.

And don't just log your mistakes and move on, figure out why you made those mistakes —what didn't you know, what you assumed—and make a plan to get similar problems right in the future.

#4: Beware of Tiny Mistakes

Be very, very careful about small mistakes—like forgetting a negative sign, accidentally moving a decimal point, or making a basic arithmetic error. You could get the meat of a problem correct but still answer a problem wrong if you make a tiny mistake . Get in the habit of being hyper-vigilant and careful when you practice, so you don't make these mistakes when you take the exam for real. Never assume you're too smart for a silly mistake!

#5: Schedule Regular Study Time

Finally, set aside dedicated time each week for studying. By practicing at least once a week, you will retain all of the skills you learn and continue to build on your knowledge. Build studying into your schedule like it's another class or extracurricular . If you don't, your studying could fall by the wayside and you'll lose out on getting the amount of practice you need.

#6: Attend Other Math Competitions

If there is a math team or club at your school, join for the practice! Doing smaller competitions can help you learn to deal with nerves and will give you more opportunities to practice. It will also help you find a community of students with similar interests who you can study with.

Also, the earlier you can start, the better. Some middle schools and even elementary schools have math clubs that expose you to tricky problem-solving questions in a way your standard math classes will not.

What Should You Do the Night Before a Competition?

After all your preparation, you don't want to trip at the finish line and ruin all your hard work right before the competition. Don't do tons of studying the night before you take the AMC. By that point, you will have done all of the work you can. Focus on relaxing and getting in the right mindset for the exam.

Also, make sure you get enough sleep the night before, and follow our other tips for the night before a test . Don't waste all of your hard work studying by staying up late the night before!

Finally, make sure you are set to go in the morning with transportation and directions to where you are taking the test. You don't want to deal with a morning-of crisis! Plan to get to the exam center early in case you hit traffic or any other last-minute snags.

What's Next?

Curious about the math scores it takes to get into top tech schools like MIT and CalTech? Read more about admission to engineering schools .

Going for a perfect math SAT or ACT score? Get tips from our full-scorer on how to get to a perfect 800 on SAT math or a perfect 36 on ACT math .

Wondering about paying for college? Check out automatic scholarships available for high ACT and SAT scores.

These recommendations are based solely on our knowledge and experience. If you purchase an item through one of our links, PrepScholar may receive a commission.

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Halle Edwards graduated from Stanford University with honors. In high school, she earned 99th percentile ACT scores as well as 99th percentile scores on SAT subject tests. She also took nine AP classes, earning a perfect score of 5 on seven AP tests. As a graduate of a large public high school who tackled the college admission process largely on her own, she is passionate about helping high school students from different backgrounds get the knowledge they need to be successful in the college admissions process.

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Evan Chen《陳誼廷》

  •   CV

Teaching (otis),   •   otis excerpts,   •   mock aime,   •   for beginners,   •   for coaches,   •   problems,   •   mop,   •   elmo,   •   usemo, personal/hobbies,   •   puzzle hunts,   •   games,   •   photos, youtube/twitch,   •   discord, plz learn code,   •   filesys concepts,   •   learning path,   •   latex style,   •   asy guide, publications,   •   egmo book,   •   napkin (v1.6),   •   course notes,   •   18.02 recitation, recommendations,   •   mentors,   •   quotes,   •   faqs,   •   rec letters.

MOPper World 2.0

About MOP #

This section of the website is dedicated to public-facing material from various years of MOP. It’s similar in spirit to the MOPper world that ran between 1997 and 2004. This page isn’t a puzzle.

Between 2015 and 2024, MOP was held at Carnegie Mellon under Po-Shen Loh , besides 2020 and 2021 when the camp was run on Discord due to COVID-19. Prior to 2015, the camp was held in Nebraska .

See FAQ CR-7 for invitation rules.

I am currently the assistant academic director of MOP. (There is no academic director or assistant director.) Staff includes instructors, RA ’s, and teaching assistants (aka graders).

For many years, the official name for MOP was “MOSP”, but the letter S was universally ignored by staff and students, and its omission became an ongoing gag. The S was finally officially deleted in 2017.

T-shirt designs #

Traditionally, MOP T-shirts are printed in black on grey. Except for 2020 and 2021, there is usually only a front design, and the back contains everyone’s signature.

• The ELMO is written by returning MOPpers for new MOPpers, featuring “teams” and coordination. See ELMO page .
• The Mock IMO is run by staff using ISL ; it also features a mock coordination . It’s one of several practice tests run by the staff at MOP each year. You can download the problems here:
• The staff also provide MOP homework to work on before camp starts, mostly for fun and so people have something to talk about at airports. Here are recent homework problems:

Schedules #

Here are calendars for recent years of MOP:

For more concrete times, here was the 2022 weekday timetable as an example (which should be read alongside the 2022 calendar ):

• 07:00-09:00 Breakfast
• 09:00-10:30 Morning class 1
• 10:40-12:10 Morning class 2
• 12:10-13:20 Lunch
• 13:20-14:50 Afternoon class,
• 13:20-17:50 Mock olympiad / Team Selection Test, OR
• 13:20-14:00 Assembly meeting (for announcements, etc.)
• 17:00-20:00 Dinner hours
• 19:15-20:00 Test review (presenting solutions to test problems) OR seminar on higher math (both optional)
• 22:30-23:00 Evening check-in

There is a lot of free time built into the schedule, and this is intentional. Some examples of recent activities include singing troupe (see below), the double-elimination fish tournament, the plank countdown, trips to Waffallonia, dance tutorials, live-action Mafia and StarCraft (both no longer banned), and too many water balloons.

Singing troupe #

The MOP Singing Troupe is a tradition dating back to around 2010, started by Evan o’Dorney; it starts and ends the closing ceremony. Here are recent songs we performed:

• Another Day of Sun
• How Far I’ll Go
• Defying Gravity
• Blank Space
• A Million Dreams
• Unravel (English version)
• Rewrite the Stars
• Into the Unknown
• Music of the Night
• Good For You
• My Heart Will Go On
• Do You Hear the People Sing
• One Short Day
• Shall We Dance
• The Music of the Night
• The Phantom of the Opera
• The Point of No Return
• The Wizard and I
• Defying Gravity, and parody Coordinate Bashing
• Do You Hear The People Sing, and parody Do You Hear the Teapot Sing
• Finite Simple Group of Order Two
• Shall We Dance?
• Think of Me
• Wishing You Were Somehow Here Again

I would say this was not my idea, but that would be a lie.

• Me Gustas Tu (GFriend)
• As If It’s Your Last (Blackpink)
• Lady (EXID)
• Bboom Bboom (MOMOLAND)
• Super Shy (NewJeans)
• After Like (IVE)
• Blue Flame (Le Sserafim)
• Ddu Du Ddu Du (Blackpink)
• Snapping (Chungha)
• Time for the Moon Night (GFriend)
• Dalla Dalla (ITZY)
• Don’t Know What To Do (Blackpink)
• Dolphin (Oh My Girl)
• What is Love? (TWICE)
• Navillera (GFriend)

MOP Puzzle Hunt #

mosp.evanchen.cc hosts:

• A miniature one-round hunt written by Evan Chen, Isabella Quan, Sanjana Das, and Serena An for MOP 2021.
• A 2022 puzzle hunt led by Luke Robitaille.
• Alex: “That isn’t a hypercube, that’s two Pringles and two lines.”
• Alexander: “I hate transition metals”. Andrew: “I ate transition metals.”
• Aprameya: “I want to thank my mom for giving me this hair and my dad for being bald.”
• Andrew, to Two Sigma speaker: “Is the company mail service called sigma mail?”
• Benny: “I looked left, I looked right, then I realized I didn’t remember the cubic discriminant”.
• Carl, to Luke about his LaTeX usage: “There are no excuses to a crime of this magnitude for a man of your stature.”
• Daniel: “We should have told them we’re shuffling Red 1 and Red 2, and then just swap Red 1 and Red 2”.
• David, while eating cereal for dinner: “Cereal is objectively a lunch food but the waffle machine is broken.”
• Evan: “okay by popular request we’re shuffling Red 1 and Red 2 🎲 i’m sorry for the last minute notice since i’m sure you’re all asleep by now 🌙 but good morning 🌞 If you’re a student in red, to determine your new group: • Convert each letter in your first and last name via A1Z26 and take the sum • You’re in Red 1️⃣ if this sum is a quadratic residue modulo 239, and Red 2️⃣ otherwise. If you need help computing the Legendre symbol, either use Python builtin pow , or quadratic reciprocity if you want to do it by hand. (We don’t recommend ChatGPT. We tried it and it had 50% success.)”
• Gloria: “Everything is a fork if you stab hard enough.”
• Gloria: “I bought 24 copies of Anki, so I can have different decks open and stuff.” (It cost \$480.)
• Henry: “Is Evan Chen bad for your lungs?”
• Henry: “Sorry, but I can’t read your name tag because I’m black-white colorblind.”
• Henry, to Hannah: “Your hair is a defense mechanism!”
• Jordan: “Are we sides of the quadrilateral formed by the other 4 intersections of a conic with 2 circles that intersect at 2 points on the conic? Because we never meet.”
• Jordan: “Why does GeoGebra name my point B'''_3 ??”
• Julia: “I saw a woman with orange hair and thought she was a live size red panda.”
• Krishna: “No, it’s actually kind of hard. But yeah, it’s trivial.”
• Exhibit A: 0.4 style score
• Exhibit B: 3 staples
• Exhibit C: 1 more staple
• Exhibit D: the other staple (front)
• Exhibit E: request for style points (denied)
• Exhibit F: Table of contents
• Mingyue: “Your hyperbola got you seven points. I don’t get it, I thought you could only pass it through five.”
• Mingyue’s rap during talent show
• Owen: “Life is not a mountain of pain but a valley of fun.”
• Raz: “The Schiffler point is the leader of the Libertarian party.”
• Richard: “I really don’t like eigenvalues.”
• Ritwin: “When do you think the last time I did integral was?” Henry: “Wasn’t integration completed in 1964?” Jonathan: “Before 1964 did they use Riemann sums?” Henry: “Yeah they split into parts.”
• Wendy: “All food is edible, you just die because your body’s a skill issue.”
• Wendy: “I’m not getting to let the word xooks outlive me.”
• Wendy: “I trust your oddness more than I trust my oddness”
• Zack: “Here’s some fact about circle points.” Alexander: “You can Cayley-Bacharach with them.” Zack: “That is not a fun fact about circle points.”
• Aaryan: “Showering is a 35 MOHS task.”
• Alec: “What are some characteristics of a buffalo?” Andrew: “It touches grass.”
• Allen: “If I slept for the entire day I would have swept the test in 2 hours.” Elliott: “If you sleep for 24 hours, you’re dead.”
• Allen: “I visualized the 770070 on the scoreboard, but if you visualize something for too long it becomes a reality. So I stopped visualizing and solved the problem.”
• Aprameya: “We’re not nice people, we’re geometry mains.”
• Derek: “When I see a geo problem with circumcircle gamma, I lose the gamma.”
• Derek: “Why are we complex bashing combo problems?”
• Enrico: “Sometimes I think I’m too stupid to be this smart, and sometimes I think I’m too smart to be this stupid.”
• Evan: “What year?” Milan: “Twenty-something.” Evan: “Gee, thanks!”
• Henry: “Hey Razzi, I saw your handwriting. Are you going to med school?” Razzi: “No, I don’t think so.” Aaron: “What a waste of talent.”
• Henry: “This orzing was sponsored by Raid Shadow Legends.”
• Krishna P.: “Moving points moves your points from 7 to 0.”
• Luke: “It should be obvious that a job is work, but it never really hit me.”
• Po-Shen Loh: “It’s a lot easier to get good grades when you have two classes.”
• Po-Shen Loh: “How many MOPpers does it take to do trigonometry?”
• Neal, on Krishna’s messy geometry diagrams: “But he uses nuclear weapons, so it doesn’t really matter.”
• Tristan (44 minutes before class ends): “For sake of time I will go over the solution.”
• Vivian: “Evan Chen is the new 🐭.”
• Yotam: “Bashing turns geo into points.”
• “If we are clowns, then dotted is a walking circus.”
• “To solve problem 2, it is not enough to not be a potato. You have to be a napa cabbage.”
• Franklyn Wang: “Evan has contributed to a decrease in Resnik’s reputation.” Brandon Wang: “Evan is not solely responsible, right? Others are also responsible.” Franklyn Wang: “Yeah, like Resnik.”
• Luke Robitaille: “I did not make ARML tiebreakers as a 12-year-old this year.”
• Staff: “Let O be a point inside cyclic quadrilateral ABCD. Diagonals AC and BD intersect at P. Let X be the isogonal conjugate of B with respect to ODP. Show that one of the two points X and B lies on BX.”
• Also staff: “Alice says, ‘you are a doofus’. Bob says, ‘no you’. Compute the total number of words exchanged.”
• Milan Haiman: “This is a 2-page solution right?” Po-Shen Loh: “No, it’s 15.”
• Sign on the way to breakfast: “Statue removed for restoration.” Espen Slettnes: “What statue? I don’t see it.”
• Andrew Lin: “There’s nothing wrong with light mode.”
• Luke Robitaille: “Some people should sing louder. This is Singing Troupe, not Singing Luke.”
• Found on a fortune cookie: “Hard work pays off in the future. Laziness pays off now.”
• Kevin Wu: “Their corn tastes more like their garlic bread than their garlic bread does.”
• Franklyn Wang: “As Winston Churchill said during World War Two, ‘If you’re going through hell, keep going.’ That’s what you do for this problem.”
• Evan Chen, while teaching class: “I can’t wait for class to end.”
• Rachel Zhang: “Evan’s like, tiny, right?”
• Henry Jiang: “I lose everything. One time I lost something, and then someone picked it up, and then he lost it, so I found it again.”
• Jeff Lin: “Teaching your four-year-old to drink is like teaching your eight grader bary.”
• Po-Shen Loh: “And I think this is a lesson we can all learn from, especially for the IMO team: when you do something, do it with full commitment.” Luke Robitaille: “So basically, you’re saying that a full commitment is what you’re thinking of?”
• Franklyn Wang: “Do piranha plants exist? Or are they just a Mario thing?”
• Holden Mui: “How’s the corn?” Po-Shen Loh: “It’s very dehydrated. It’s like they forgot to add water.” Sophie Liu: “I described it as pieces of matter that just so happen to be yellow.”
• Derek Liu: “If four of you took 7 days to solve ELMO 6, by pigeonhole one of you took only one day to solve it.”
• Cordelia Hu: “Any solution is a one-liner if the line is sufficiently long.” Evan Chen: “Aren’t lines supposed to be infinite in length or something?”
• “One day [Resnik] had corn, then the next day they had corn with green beans, and you could clearly tell it was yesterday’s corn. Then the next day they had fried rice with corn and green beans.”
• Feodor Yevtushenko: “This rice tastes like rice except one in every like 20 grains is uncooked.” (Derek Liu: “Did you mean one in every 20 grains is cooked?”)
• Many people: “Mr. Turtle, Mr. Turtle, come out of your shell @Holden”
• Brandon Wang: “A bunch of geo people are good at bashing; then they are the committee and write problems that can’t be bashed; then the students can’t bash; and the circle continues.”
• Henry Jiang: “If you play a wrong note really loudly, that’s just called jazz.”
• Jeff Chen: “It’s not wrong, it’s just misguided.”
• Jeff Chen: “Walking is nontrivially hard. It’s $O(n)$ effort, whereas sitting here is $O(1)$ effort”
• Jeff Chen: “I’m too high; I’m going to go run around.”
• Victoria Hu: “Oh yeah didn’t u donate Raina to me at the airport?”
• Debbie Lee: “I don’t think Jane Street would appreciate all their thousands of dollars going to fruit snacks.”
• Derek Liu: “Dude, I haven’t made a single haiku in all of MOP. What the heck.”
• Alex Zhao: “Combo is only enjoyable when you can solve it.”
• Ethan Liu: “I kinda don’t want to do any more math, I just want to do algebra”
• Evan Chen: “I get crabby when people don’t do what I tell them to. It’s why I can never have a boss.”
• Evan Chen: “I hate trying to be nice.”
• Evan Chen: “I’m Evan. I guess I’m a PhD student at MIT?”
• Evan Chen: “Most problems require you to be awake.”
• Evan Chen: “Where’s Po? I think I actually need him for once.”
• Holden Mui: “almost to 3 hours” (during office hours)
• Jeffrey Chen: “Base times height is not area. This is probably a useful fact to know.”
• (right after) “Just to check, $\frac{K}{2a}$ is the height of a triangle, right?”
• Jeffrey Chen: “Is fermented spit not fine?”
• Noah Walsh: “The lesson I am learning from this is: when you see hard combo, take a nap”
• Raymond Feng: “OP STICK”
• Serena Xu: “Panel topic: why don’t you want to be a panelist?”
• David Yang: “You look at the problem and ask ‘what’s the solution?’ and then you write down the solution.”
• Derek Liu: “jstris anyone?”
• Derek Liu: “Please misquote me.”
• Evan Chen: “I trust the Russians.”
• Holden Mui: “How many points do we get for misreading the problem?”
• Jaedon Whyte: “Wait so Max is alive now? Sad.”
• Po-Shen Loh: “RA’s means remote assistants this year.”
• Solutions packet for Test 7: “By trying to make all three of $(x+1)(x+2)$, $(x+1)(x+3)$, $(x+2)(x+3)$ squares, we may try the substitution $x + 2 = \frac{(t^2+1)^2}{4t(t^2-1)}$.”
• Tristan Shin: “Proof: coordinates!”
• William Yue: “That’s just true by combo.”

Nebraska trip #

In 2018, I flew back to the University of Nebraska-Lincoln the weekend before MOP to visit the venue again, since that was where MOP was held when I was a student. You can see photos of the Nebraska venue if you want to see why I keep saying things were better in the good old days.

The dorm we stayed in was called Neihardt Hall, and it had four sub-halls inside it named Heppner, Love, Piper, and Raymond. We had a lot of different lounge spaces, which also had names:

• The Blue Room was the primary lounge on the ground floor, which was where orientation was held and a lot of activities.
• There were side lounges on the ground floor called the Grey Parlor , the Gold Parlor , and the Sun Room , among others. We held singing troupe here since there was a piano.
• There was an old-fashioned elevator with a curtain-like door that you pulled by hand. That elevator was labeled “OTIS”, and my training program is secretly named after this elevator.
• The ground floor had a bunch of small classroom areas where test review used to be held. In addition to the red paintings, they had these little coasters, and people would throw them around a lot.
• There was a meeting room with a green chalkboard where we held all the ELMO meetings.
• The basement had a stage with some tables and chairs nearby where we held the ELMO and the talent show, as well as another giant lounge area nearby complete with several sofas, another TV, and a pool table.
• Neihardt Hall itself enclosed a little garden area, that you could go outside and walk around in.

Also, the Selleck dining is amazing . Just saying.

High School Competition Math

If you are interested in math contests like  AMC 10, AMC 12, AIME, ARML, CHIMMC, HMMT, BMT, SMT, CHMMC, ARML, USA(J)MO, IMO, etc. here is a  comprehensive list of the best books and resources to help you prepare.

Also, here is a list of Math Contests that you can participate in.

Free Online Resources

Mastering AMC 10/12 Book and Video Series

This free book covers the most important concepts on the AMC 10/12 and includes video lectures for every chapter, formulas for every topic, and hundreds of examples and practice problems with detailed video solutions.   

Omega Learn Free AMC 10/12 Classes

These classes cover the most important concepts required for the AMC 10/12 tests. These are specially great for beginners who are starting to prepare for the AMC 10/12 exams.

AoPS Math Jams

Math Jams are free online discussions hosted by Art of Problem Solving for a variety of purposes, including:

Informational sessions about Art of Problem Solving classes

Review of the AMC and AIME competitions

Introductions to new topics in math and other areas of study

Evan Chen's Site

An amazing collection of handouts and other resources for anyone preparing for math olympiads.

AHSME Tests

AHSME (American High School Mathematics Exam) is basically an old version AMC 10/12 from 1950 to 1999.

AMC 10 Tests

Art of Problem Solving has all of the past AMC 10's. Check out   Math Contests  for information about the AMC 10.

AMC 12 Tests

This page has all of the past AMC 12 tests. Check out Math Contests for information about the AMC 12.

This page has all of the past AIME tests. Check out Math Contests for information about the AIME.

Brilliant helps to build quantitative skills in math, science, and computer science with fun and challenging interactive explorations. All of their courses are crafted by award-winning teachers, researchers, and

professionals from MIT, Caltech, Duke, Microsoft, Google, and more, with these principles of learning in mind.

Beauty of Math YouTube Channel

This is a channel focusing on all Competition Math such as American Mathematics Competitions, AIME, Math Counts, Math Kangaroo, content from Art of Problem Solving and various other Mathematical Topics.

AoPS Wiki Problem Generator

This problem generator generates random problems from the aops wiki 1 at a time or in groups. 

AMC Trivial

Trivial is a site for unlimited problem practice and other learning features, based on the vast database of the  Art of Problem Solving Wiki.

Best Books for Competition Math

Art of problem solving books are some of the best books to prepare for math competitions. make sure to get the solution manual for each book, as many of the problems are quite challenging and the solutions manual includes detailed solutions., books for amc 10/12 ​ preparation.

Free Resources for AIME

David Altizio's Web Page

David (popularly known as djmathman on AoPS Forums) is an MAA problem writer, and has an amazing page with a lot of useful resources for AMC 10/12 and AIME preparation. Some notable resources:

Collection of AIME like Problems

Collection of AIME Solutions

Free Classes (AMC 10/12 Advanced/AIME level)

Youth Conway Math Association (YCMA)

Youth Conway provides high quality, free, virtual instruction as well as engaging mathematical immersion activities in a time when many similar events have been canceled due to this global crisis.

Math Divulged Classes

Math Divulged is a COMPLETELY FREE online series of classes! They offer a diverse set of topics and levels and participants have complete control over the classes they choose to attend, allowing them to craft their dream schedule. Math Divulged is composed of dedicated competitive math veterans, including MathCounts National Champion, MOPpers, IMO Gold Medal winner, etc

Everaise Academy

Everaise provides 5 week STEM outreach program for middle and high school students that seeks to challenge participants through engaging courses in mathematics, physics, astronomy, linguistics, and biology. ​

Euclid's Orchard

Euclid's Orchard serves to provide high quality handouts to teach those who are interested in a variety of subjects.

Trinity School NYC Math Team Classes

TrinMAC offered free, virtual math camp ​ during the summer of 2020.

Mallstars Classes

MoTown All Stars Mathematics Team is a team of motivated students dedicated to improving the mathematics community. They offer a number of classes from middle school to Olympiad level.

The Mathematical Advancement by Self Training program (MAST) is targeted towards AIME qualifiers who want to do better on the AIME.

Paid Classes ​

If you are looking for paid Math classes, here is a list of the most popular paid classes.

AlphaStar Academy​

AlphaStar Academy offers extensive training programs for gifted students towards national and international Math and Science competitions such as MathCounts, American Mathematics Competitions, USA Math Olympiads, USA Computing Olympiads, F=ma, and USA Physics Olympiads.

Art of Problem Solving

Since 2003, the AoPS online school has provided a unique learning experience carefully designed for outstanding students studying online. We offer a full math curriculum for middle and high school, introductory programming courses, and specialty courses to prepare students for particular math and science competitions. Most of our courses meet weekly for live sessions, and have a variety of types of weekly homework.

Momentum Learning

Momentum Learning provides tutoring services to elementary and high school students in the Sugar Land, Texas area. Their comprehensive services cover the critical subject areas for educational success in these grades. They provide weekly classes covering a variety of subjects including school math, contest math, coding, science, English, and public speaking.

OTIS is an olympiad training program for students aiming to do well on USA(J)MO or similar level contests. It is designed for contestants who are comfortable reading and writing proofs and can usually qualify for national olympiad, (for example, consistently 10+ on AIME for American contestants is fine). Students at other levels should feel welcome to contact me for referrals to other mentors.

Awesome Math

AwesomeMath is devoted to providing enriching experiences in mathematics for intellectually curious learners. Through summer camps, publications, curriculum, and competitions AwesomeMath fosters a community that values critical thinking, creativity, passionate problem solving, and lifetime mathematical learning.

IDEA MATH’s comprehensive teaching materials are modeled after those of one of the nation’s strongest math teams, the Phillips Exeter Academy math team.  IDEA MATH’s materials cover everything from introductory algebra, counting, and geometry, to complex materials at the Olympiad level and beyond. The program also puts emphasis on student leadership, critical study skills, and positive attitudes that are conducive to learning.

Achievable (save 25%)

Achievable provides AMC 8 and AMC 10/12 courses through their memory-reinforcing platform which automatically prioritizes the material students need and then trains them to remember it more effectively on test day.

Books for AIME ​ preparation

Resources for USA(J)MO, IMO, and other olympiads

Online Resources​

Olympiad Combinatorics by Pranav A. Sriram

Olympiad Number Theory Through Challenging Problems

A Beautiful Journey Through Olympiad Geometry

The OTIS Excerpts by Evan Chen

Evan Chen's Olympiad Page

AoPS Forum with a list of Olympiad Handouts

Big List of Olympiad Handouts

AoPS Contest Collections

AoPS Olympiads Archive

Osman Nal's YouTube Channel

Osman goes over solutions to various problems from AIME,  USA(J)MO, IMO, etc.

Olympiad Problems and Solutions from US, UK, Canada

A good collection of Olympiad problems with solutions

Olympiad Problems with Solutions from regional, national and international contests

Popular Books for Olympiads ​

AwesomeMath Books Many more AwesomeMath books on Amazon The full list of Awesom eMath books can also be found at the  Awesome Math bookstore . ​

MyMathCounts Books

* these books often have typos and errors.

Math competition season is approaching fast!  Have you  enrolled in a contest preparation class ?

How Classes Work

Course catalog, class schedule, recommendations, prospective students & parents handbook, current students & parents handbook, general information, the homework, more information, information for parents.

Need help finding the right class? Have a question about how classes work?

Homework Overview

For more information about the Homework tab on your course homepage, please see this page .

If you're having trouble with the homework, we're here to help! Check out the When You Get Stuck guide for suggestions and to learn more all the resources available to you.

On this page

What is the homework, description of homework types, the aops honor code, homework faqs.

Find the name of your class below for more information about the types of homework and other practice. You can find brief descriptions of each type below .

Textbook Readings

The textbook readings provide a brief introduction to the week's class topics. The assigned chapters or sections are listed on both the Overview and Homework tabs of your Course Homepage . Readings should be completed before that week's live class session, to help you get the most out of the class.

Handouts provide a brief introduction to the week's class topics. Handouts can be found on the Handouts tab of your Course Homepage and should be read before that week's live class session, to help you get the most out of the class.

Alcumus is our online learning system, and it is the main source of practice you'll have in this course. Alcumus monitors your progress and carefully selects problems, just for you, based on your performance on earlier problems. The course homepage will tell you what subjects are assigned each week. Alcumus feeds you problems, checks your answers, provides solutions, and then picks more problems.

If your course has Alcumus assignments, these are the problems we recommend starting with, before the Challenge or Writing Problems.

For more about Alcumus assignments, please see this page .

Short-Answer Challenge Problems

Short-answer problems are those for which you'll enter a "short" answer of some sort, such as a number, letter, or expression. These problems are graded instantly by the computer; you'll immediately know if your answer was correct. As their name suggests, these problems are meant to be challenging !

For more details on Short-Answer Challenge Problems, please see this page .

Writing Problems

Writing Problems will ask you to write complete solutions to the problems, not just a sentence or final answer. You will get feedback on both the style and content of your solutions to these writing problems. Writing problems are those that give you true practice as a mathematician, communicating all of your ideas.

For more about Writing Problems, please see this page .

For more information on what to do if you need a little more time for a writing problem, please see our Extensions page .

Python Writing Problems: What good is a programming course without some actual programming practice? For more information on the unique homework in our Python courses, please see this page .

Practice Tests

Contest-preparation courses for the AMC 10, AMC 12, and AIME each provide one practice test in the style of that exam. We strongly encourage students to take the exam under test conditions. If the test is available, students will find a link to the test problems as well as a space to enter their answers. If the test is not yet available, its release date will be indicated. Once answers are submitted, the students will immediately be shown their score. Answers to these practice tests may not be re-submitted.

There is a due date for the test answers to be entered on this page—students are asked not to discuss the content of the test until after that date, but answers can be submitted after that date.

Discussion Problems

Discussion Problems invite you to engage directly with your peers. Collaborating and communicating are vital skills for any mathematician. Discussion Problems are a place to bounce ideas off of other students and explore new mathematical concepts together. You may be asked to dive deeper into class concepts, experiment with mathematical constructions, trade proofs of a theorem, or challenge your peers by writing your own math problems.

A student must agree to the AoPS Honor Code before accessing the course homepage. This honor code outlines our major expectations of students throughout the course.

The Art of Problem Solving Honor Code is as follows:

• I will be respectful of all other AoPS users while in this class and on this site as stated in the AoPS Terms of Service .
• I will not misrepresent another person's words or ideas as my own.

More details about the Honor Code can be found here .

When and in what order should I work?

In general, our most successful students start by reading the textbook or handouts (when available) before class, then attending class or reviewing the transcript, and then finally attempting the homework. Within the homework, we recommend Alcumus first, then the Challenge Problems on the Homework tab, then the Writing Problems. You can find more details on the Working Through Class Material page.

Many classes also have a My Goals tab on the course homepage to help you keep track of and pace yourself with the the weekly assignments.

When is the homework due?

Homework is typically due 8 days after the class. The due date for a week's assignment will be displayed in the top-left gray box on the Homework tab of the course homepage . Writing Problems due dates are most strictly tied to those deadlines. You'll need to request an extension if you need more time to work on those problems. Short-Answer Challenge Problems can be solved at any point after they are available, and Alcumus assignments may be completed after the due date. However, we encourage you to keep up with the due dates as much as possible so that you do not fall behind the class!

How can I get help?

We're glad you've asked! The course message board is the best place to get help with any class material, whether you need some clarification about a topic, you have a question about a homework problem, or you'd like some help understanding a particular solution. Course staff, other AoPS administrators, and even your classmates are able to help answer you questions, make suggestions, or provide any other assistance you might need!

Check out our guide for When You Get Stuck , which outlines the other resources available as part of the course and recommendations for how to use them!

How do I keep track of my homework?

The information displayed at the top of Homework tab will help you keep track of all the assignments due each week and their due dates. We've also created a few other ways to help you keep track of how it's going, including the Report tab, the My Goals tab , and weekly class reminder emails with a summary of your progress. Check out the Tracking Your Progress page for more information.

We also offer Parent Tools for parents to help their students keep track of their progress.

What is my grade?

The data we put on the class homepage is there to communicate with you about what work is assigned and to help you complete that work. This page provides more information about the different ways you can track your progress in the class. At the end of any subject or computer science course, we should be able to provide a letter grade upon request. Visit our Grades and Documentation page for instructions on how to submit a request, as well as more details on our grading philosophy.

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Mathematical Association of America

American mathematics competitions.

• AMC Regisration Info
• AMC Policies
• AMC Registration Portal

Founded in 1950, the AMC is the preeminent math competition for students K-12. Today, over 300,000 students in 50 states and over 30 countries take the AMC to bolster their confidence and passion for math.

Empowering the next generation of problem solvers.

The AMC program is more than just a competition; it’s a national effort to strengthen the mathematical capabilities of our next generation of innovators. By challenging students with engaging problems, the AMC sets the stage for lifelong mathematical exploration, discovery, and achievement.

Registration is Open

MAA AMC 2024-25 Registration is open! Find step-by-step instructions on how to use our new registration platform in the guide .

For more information on our new registration process and pricing structure, please refer to our  FAQ .

Who can participate in the AMC?

The AMC proudly engages with a dedicated group of participants, each crucial to the success of our mathematical community:

• Students: Young mathematicians from middle and high schools are at the heart of the AMC. Their curiosity, passion, and problem-solving skills shape the future of mathematics.
• Competition Managers: Educators and math circle teachers play a pivotal role in developing students’ mathematical abilities and ensuring the smooth operation of the AMC.
• Parents: Their support and encouragement are essential as their children navigate their journey of mathematical discovery and growth.

Dive into mathematics with the AMC 8, a 25-question, 40-minute competition designed to promote developing and enhancing problem-solving skills. Start your mathematical journey today and register for the AMC 8 , where curiosity meets challenge!

For : Middle school students, typically in grades 6-8, though younger students may also participate.

What : A 25-question, 40-minute multiple-choice examination designed to promote the development of problem-solving skills.

When : Held annually in January.

Early Bird Registration Deadline: Oct 28, 2024

AMC 10 and AMC 12

Elevate your mathematical skills with the AMC 10 and AMC 12, challenging competitions that are the gateway to further opportunities, including the AIME and USAMO. Take the next step in your mathematical odyssey and sign up for the AMC 10 and AMC 12 , paving your way to mathematical excellence!

For : High school students in grades 10 and below, with a maximum age of under 17.5 years on the day of the competition.

What : A 25-question, 75-minute multiple-choice examination focused on high school mathematics up to the 10th-grade level.

When : Held annually in November.

For : High school students in grades 12 and below, with a maximum age of under 19.5 years on the day of the competition.

What : A 25-question, 75-minute multiple-choice examination that covers high school mathematics up to the 12th-grade level.

When : Also held annually in November.

Early Bird Registration Deadline: Sept 30, 2024

The AMC aims to create a more inclusive and empowered math community. Through examinations and curriculum materials, we support educators in fostering the analytical skills to drive future innovations.

What the community can expect this cycle 

Increased Security for Competition Distribution: We are upgrading competition distribution procedures to enhance digital security, including adding features to prevent unauthorized access and shortening release windows to minimize leaks.

Restructured Program Management: We have brought in seasoned leaders to support the operations staff and continue to collaborate with technology partners and our network of dedicated teachers to improve security.

Additional Reviewing and Vetting of Test Sites and Managers: We will review and vet every competition site beginning in the 2024-2025 competition cycle and ensure that all new competition sites undergo rigorous checks.

More Community Engagement: We encourage the community to report any threats to exam integrity through a dedicated email address, with staff assigned to follow up on these concerns.

Get Involved

Eager to dive into the AMC? Here's how you can become a part of this transformative experience:

Students : Discover how to register for the AMC, access preparation materials, and begin tackling challenges. Competition Managers : Find out how to organize an AMC competition at your school or institution, providing a platform for students to shine. Parents : Explore registration details for your child and learn how you can support their mathematical journey.

Together, we're not just solving mathematical problems - we're preparing for a brighter future. Join the AMC community in advancing the understanding and appreciation of mathematics. Let’s embark on this exciting journey together.

For more information on registration, preparation resources, and upcoming competition dates, explore our site further.

Mathematical Olympiad Program (MOP)

The Mathematical Association of America (MAA) is seeking proposals from qualified colleges, universities, or other venues to host our summer Mathematics Olympiad training program. The program provides intensive training to talented mathematics students June 3 through June 26, 2025 in a residential setting. This RFP  outlines our requirements and expectations for hosting this event.

The Mathematical Association of America (MAA) is seeking proposals from qualified colleges, universities, or other venues to host our summer Mathematics Olympiad training program. The program provides intensive training to talented mathematics students in a residential setting from June 3 through June 26, 2025. This RFP  outlines our requirements and expectations for hosting this event.

Your Mathematical Journey: AMC to IMO

AMC 8, AMC 10, and AMC 12 : Begin your adventure with the AMC 8 for an introductory challenge or the AMC 10/AMC 12 for a chance to advance further in competitive mathematics. Register for the AMC and take the first step.

American Invitational Mathematics Examination (AIME) : Excel in the AMC 10 or AMC 12 to qualify for the AIME, a more challenging examination that tests your problem-solving prowess and mathematical ingenuity.

USA Mathematical Olympiad and USA Junior Mathematical Olympiad (USAMO/USAJMO) : Achieve high scores in the AIME and AMC 10/AMC 12 to earn an invitation to the USAMO or USAJMO, where the nation's top mathematical talents compete in proof-based problems.

Mathematical Olympiad Program (MOP) : Outstanding performance in the USAMO or USAJMO could lead to participation in the MOP, an intensive training camp designed to prepare the best young mathematicians for international competition.

International Mathematical Olympiad (IMO) : Excel at the MOP to join the elite team representing the United States at the IMO, the pinnacle of pre-college mathematics competition, where you'll challenge yourself against the world's best.

What is the history of the AMC?

In 1950, the first Mathematical Contest, sponsored by the New York Metropolitan Section of the Mathematical Association of America (MAA), took place. It was given in approximately 200 schools to around 6,000 students in the New York area only. Today, the competition has grown to over 300,000 students participating annually, in over 4,000 schools.

Where can I take the MAA AMC?

This search page can assist in finding a school where you could take one of the AMC contests, displaying those who registered for the past or upcoming contest. You are responsible for contacting the school to see if they are willing to accept you to take the contest at their location.

All contest results and qualifying awards will be sent to the hosting school.

Search here

When is the MAA AMC happening this year?

The 2024-25 MAA AMC dates are:

AMC 10 A and AMC 12 A  – Wednesday, November 6, 2024

AMC 10 B and AMC 12 B – Tuesday, November 12, 2024

AMC 8  – January 22-28, 2025

AIME I -February 6, 2025 (Invite Only)

AIME II – February 12, 2025 (Invite Only)

USAMO/USAJMO – March 19-20, 2025 (Invite Only)

Where do I get more info about registration?

Registration information for AMC 8, AMC 10, and AMC 12 is here .

Who do I contact for questions about MAA AMC?

Call the MAA AMC Help Desk at 1-800-527-3690 Monday through Friday between 8:30 am and 5:00 pm ET or email [email protected]

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SOF International Mathematics Olympiad Sample Papers

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The SOF has made available the sample papers for the IMO 2024-25 exam. The SOF IMO International Mathematics Olympiad Sample Question Paper can be accessed in PDF format to aid students in their exam readiness. Through practicing this sample question paper, students can gain familiarity with the exam structure, and latest IMO syllabus to evaluate their current preparedness level. This resource serves as a valuable tool for revision, offering students the opportunity to practice solving questions typically found in the Olympiad exam. For the complete PDF version of the sample papers, students are encouraged to refer to the IMO Sample Papers. This initiative by SOF aims to support students in their exam preparation and enhance their confidence by providing them with a means to practice and refine their skills in mathematics.

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Math Olympiads for Elementary and Middle Schools

The MOEMS ® Contests

• Division E (grades 4-6)
• Division M (grades 6-8)
• If a team has any 7th or 8th graders, it must be in the DIVISION M.
• If a team has NO 7th or 8th graders, we strongly recommend that it be in the DIVISION E.
• NO team may have any student who has completed grade 8.
• Teams may not be split between two divisions.

There are five contests, November through March, each with five questions. PICOs have access to the contests one week before scheduled Olympiad date. Contests may be administered at the time and date chosen by the PICO* within a four-week window. * P erson I n C harge O f O lympiads

• Schools, homeschools, and institutes may participate. 
• Teams with members from more than one school are called “District Teams” or “Institute        Teams” and are not eligible for team awards.

Administration

MOEMS ® On Paper (traditional administration) and MOEMS ® Online administration include the same contest problems.

• Contests consist of five non routine problems that must be completed in 30 minutes.
• Students work alone, scoring 1 point for each correct answer.
• Calculators, rulers, graph paper, and other aids or resources are not permitted. 
• Problems introducing more advanced concepts include all necessary definitions.
• PICO scores each contest and submits scores to MOEMS ® using answer key provided.
• Answer key provides detailed solution and follow-up questions that could be used for future team practices.
• Our records will determine which awards are to be shipped after the last contest. STUDENT SCORE (0 – 25) is the number of problems answered correctly.
• TEAM SCORE (0-250) is the sum of the ten highest student scores, taken after the fifth contest.

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Math Olympiad Contest Problems, Volume 2 (REVISED) Solutions Manual

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It's easier to figure out tough problems faster using Chegg Study. Unlike static PDF Math Olympiad Contest Problems, Volume 2 (REVISED) solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn. You can check your reasoning as you tackle a problem using our interactive solutions viewer. Plus, we regularly update and improve textbook solutions based on student ratings and feedback, so you can be sure you're getting the latest information available.

Our interactive player makes it easy to find solutions to Math Olympiad Contest Problems, Volume 2 (REVISED) problems you're working on - just go to the chapter for your book. Hit a particularly tricky question? Bookmark it to easily review again before an exam. The best part? As a Chegg Study subscriber, you can view available interactive solutions manuals for each of your classes for one low monthly price. Why buy extra books when you can get all the homework help you need in one place?

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CREST Mathematics Olympiad Class 8 Sample Paper

>> Join CREST Olympiads WhatsApp Channel for latest updates. Sample PDF of CREST Mathematics Olympiad for Class 8:

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Section 1: Rational Numbers, Squares and Square Roots, Cubes and Cube Roots, Exponents and Powers, Comparing Quantities, Algebraic Expressions and Identities, Linear Equations in One Variable, Understanding Quadrilaterals, Constructions, Mensuration, Visualizing Solid Shapes, Data Handling, Direct and Inverse Variations, Factorization, Introduction to Graphs, Playing with Numbers.

Achievers Section: Higher Order Thinking Questions - Syllabus as per Section 1

Your Score: 0 /10

Answers to Sample Questions from CREST Olympiads:

Are you a student and planning to register for the biggest CREST Mathematics Olympiad? Then you must be worried about how to give your preparation a final touch. Here’s the best tip to bind up your preparation! Maths Olympiad sample papers are a unique way of summing up your months of preparation for the Olympiad exams. With the help of Maths Olympiad previous years’ question papers for class 8 students can test all they have prepared and studied for the examination. It works as a mirror to show candidates their weak areas and strengths. This allows students to then work particularly on the topics that they are lacking in. CREST Olympiads offers sample papers for class 8 online for free download and practice. Get your hands on these sample papers and give your preparation the perfect ending.

Solving Maths Olympiad questions has enormous benefits like developing problem-solving skills, improving time management skills and so on. It also gives an idea about the questions asked in the actual examination. So always remember to add practicing sample papers in your preparation guide for the Olympiad exams.

Q.1 : d | Q.2 : d | Q.3 : c | Q.4 : a | Q.5 : b | Q.6 : a | Q.7 : d | Q.8 : d | Q.9 : c | Q.10 : c

Other Classes Sample Papers

• CREST Mathematics Olympiad Paper for Class KG
• CREST Mathematics Olympiad Paper for Class 1
• CREST Mathematics Olympiad Paper for Class 2
• CREST Mathematics Olympiad Paper for Class 3
• CREST Mathematics Olympiad Paper for Class 4
• CREST Mathematics Olympiad Paper for Class 5
• CREST Mathematics Olympiad Paper for Class 6
• CREST Mathematics Olympiad Paper for Class 7
• CREST Mathematics Olympiad Paper for Class 9
• CREST Mathematics Olympiad Paper for Class 10

Other Subjects Sample Papers

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The Legend of Question Six: One of The Hardest Maths Problems Ever

It's a secret to no one that maths is hard , so when you start talking about the hardest maths problems ever, things start to get a little crazy. Take the innocuously named Question 6, which is so complex, it can bring mathematicians to tears.

As mathematician Simon Pampena explains the Numberphile video above , the Legend of Question 6 spawned from a maths competition for high-schoolers held in Australia in 1988. (Yep, they make 'em tough down here.)

The competition was the International Mathematical Olympiad, which is held every year in a different country, and only six kids from every country are selected to compete. Points are scored on how each 'mathlete' performs on six different questions.

In 1988, the Australian Olympiad officials decided to throw a massive curveball to the kids on the final day of competition, and it's gone down in history as one of the toughest problems out there.

Just to give you an idea of how tough it was, Australian-American mathematician Terence Tao - recipient of the 2006 Fields Medal (the mathematician's 'Nobel Prize') - scored a 1 out of 7 when he attempted it. But, you know, he was 13 at the time, so let's cut the man some slack.

What made Question 6 so hard is that it actually tried to pay mind games with you as you solved it. 

"In a way, they're actually designed to kind of throw you off if you know high school maths too well," says Pampena . "So say if you really know how to solve quadratic equations, and you see something that looks like a quadratic equation, it almost throws you down the wrong path."

Question 6 was actually submitted to the Australian Olympiad officials by a mathematician from West Germany, and the officials gave themselves SIX HOURS to solve it to see if it should be included in the event.

Not one official could solve Question 6 within the time limit. Some of the best mathematicians in the world at the time.

But they put it on a test for kids anyway, and only gave them about 90 minutes to solve it, because mathematicians are ridiculous.

So you just want to know wtf this problem is, right? Okay, here it is:

Let a and b be positive integers such that ab + 1 divides a 2  + b 2 . Show that  a 2  + b 2 / ab + 1 is the square of an integer.

What's the solution? Well, we're going to let the Numberphile video above explain that one to you… nope sorry, there's no way they're fitting all that into a single video.

The video above will tell you what the question actually means, and then the video below will give you the answer:

Just please don't pop a vein in your head or something if you attempt it yourself. And if you somehow crush it, here's six more to try .