HOW to STUDY for the AMC 8, AMC 10, and AMC 12: A method

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  • Опубликовано: 24 окт 2024

Комментарии • 59

  • @understand6764
    @understand6764 4 года назад +18

    Hey man I really love your content am recommending it to my school's math team. Please continue making stuff like this! Thanks!!

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +4

      That really means a lot man. Thank you for saying so. I hope the techniques and strategies discussed are useful to as many people as possible. If they happen to check it out, would love to hear their feedback or constructive criticisms. If I can inspire anyone to a deeper love or appreciation of Mathematics...then that's what I live for. ❤

  • @dakshin3934
    @dakshin3934 4 года назад +5

    I really appreciate your videos! I’ve just started studying for AMC 10 as a freshman so I know i’m late but your videos have really helped me with what I should do. I’ve ordered aops vol 1 and 2 so hopefully I can make AIME next year. Keep up the great work!

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      Thabks Dakshin, really good to hear. Something tells me we will all have a lot more time for studying at home in the coming months so yes, you should have a really good shot at it.

  • @mommycommonsensecooking2244
    @mommycommonsensecooking2244 4 года назад +2

    Thank you for all your math videos.

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      Glad I can help others to grow and appreciate the subject. You are very welcome. 🙂👍

  • @aashimasinghsisodia7567
    @aashimasinghsisodia7567 4 года назад +4

    What type of notes should you be taking if you’re learning out of an AOPS textbook? Like, for example, Intro to Geo?

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +3

      Honestly I would be extracting all useful concepts and formulas to the small notebook. As for diagramming problems, I suppose that is possible also, but I wouldn't be cutting up the book lol. Maybe you could make copies of pages you wished to cut the problem from. I would definitely be doing every problem cover to cover. Proofs if you cannot figure out an approach to, at least read the solution to gradually increase understanding and improve your approach to proofs.

  • @diegogonzalez23j
    @diegogonzalez23j 4 года назад +4

    Hey man, this is a really good video I like your content! I was wondering if you had an approach you liked to do for the last 2 or so problems (when the problems start to get really difficult) for amc 10 and 12. I know every problem is different but is there a way you like to start them off.

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +4

      Thanks. Sorry for late response, RUclips never sent me a notice that I had a comment this last week.
      Ummm off the top of my head I can only say, I like to save up time from going faster through earlier problems by recognizing available shortcuts, and then have more than 5 minutes per problem left for each of the last several. Once that has been achieved, I prefer "baby steps". Meaning go a little slower and start asking the questions "What do I know, and what can I do with what I know?" Meaning the given information has general meaning. What is that meaning? Is there a formula or underlying concept associated? You will hear me talk about this in several videos. Is it a sequence? Write down the first 5 to 10 terms or so and look for a pattern etc.
      Sometimes in the modern era(2015 and later) the last two require a fundamental concept that I personally have not taught myself yet, or if I did it was one time and I have forgotten it as it doesn't come up often in the contests so I never get to use it. Math being a use it or lose it subject.
      I hope this helps. Thank you for the kind words and stay safe.

  • @ishaanpanigrahi8258
    @ishaanpanigrahi8258 4 года назад +4

    Hi I frickin love this video! Thanks for the amazing in depth method. I am in 8th grade and I am preparing for AMC 10 and AIME, I know I am a little late. I had a question about the formulas. Do you add formulas which you learn from a problem or just ones u find? Thanks you again :)

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +1

      Don't worry about being a little late. This year I had a student who didn't begin studying til 8th grade and made AIME in 9th grade. It's never too late for those willing to put in the effort. 🙂
      As for formulas the answer is both. You can either write the formula that you learned from any given problem into the small notebook, or you can copy it from a list of formulas, or from a textbook that was teaching that formula at that time, etc. I think it's better to get the formula from someone's list than not get the formula at all, but it's far preferable if you encounter the formula in the effort to solve a problem. The reason is simple. In the second method you are learning the formula while simultaneously seeing an application of it in competition math. Like an example. That will make the memory of it stronger. If you just get it from a list, you might not understand how to apply it or might not think if it's potential application in crunch time.
      So maybe any formulas you get from a list, do some research on applications of that formula or concept to strengthen it's connection to your mind. Hope this helps and thank you for the comment. Feel free to add comments on other videos or even request certain tests or problems, I am unable to do every problem of course. I can do about 90% to 100% of most tests. Also feel free to share any videos you find particularly useful with any math circles/clubs/peer groups you participate in. 🙂

    • @ishaanpanigrahi8258
      @ishaanpanigrahi8258 4 года назад +1

      @@TheBeautyofMath Thank you for replying, you gave me a lot of insight. :). I wanted to ask if you knew the key concepts tested on the AMC 10 test for Geometry, Algebra, Number Theory and Counting. Sorry for the long question, I just want to use my time wisely across the summer, I was also going to buy the AoPS Volume 1 book, is it a good book? Thank you again.

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      @@ishaanpanigrahi8258 I am actually not 100% certain of a list of key concepts...I dream of making one myself some day. But I think there have been some lists created at some point by others. They are on like google docs or something. I recommemd making an Artofproblemsolving.com account and poat of their forums to inquire from others if any such document exists. Volume 1 is actually the best book for covering many topics, Volume 2 is a lot more challenging and tbh none of my students have ever fully completed it before they first qualified for AIME. It's a good book, but not as effective for AMC 10 as Vol 1.
      I think you might get a lot out of the following video. It's the most popular one on my channel. It gives an outline of a plan that can be followed to prepare, you will have to modify it to match your strengths and weaknesses but it still forms a solid backbone for how to strategically approach preparation for the test. It is found here:
      ruclips.net/video/OD3f_tqN-OE/видео.html

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      @@ishaanpanigrahi8258 actually if you go down this comment thread to Thomas Yemanes comment...he links to a formula sheet for common formulas.

  • @afafad3554
    @afafad3554 4 года назад +3

    THANKs it helped alot!

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      Great to hear. If you ever make AIME please stop by to share the accomplishment!

  • @viradeus4322
    @viradeus4322 4 года назад +2

    This seems awesome! Is this how you built up your mathematical intuition? I'm trying to do that now, but have no idea how to! Any tips?
    Edit: I have another question. What if you don't know how to solve a problem? What should I do then? What should I put in my problem book?

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +1

      I would absolutely use this method to build your intuition over time. This method should actually ONLY be used on problems you got wrong or skipped. So if you can't figure out how to solve it on your own, consult online solutions from Artofproblemsolving.com, or RUclips videos. After consulting ask yourself questions like "What is the first thing I should have observed in order to take the action the person who solved it took?" For example if they begim with Pythagorean theorem, ask yourself which of the words or statements given in the problem triggered the usage of Pythagorean? Then in the cut/paste study notebook highlight the portion of the sentence or phrase that indicated Pythagorean was available for use in yellow. And go from there? Respond similarly for other actions taken by the problem solver. Always ask what words in the problem or what results from previous work triggered the next step...then color code those words or information.
      Also don't forget to add any relevant shortcuts or formulas or important observational concepts to the small pocket notebook that you use as quick review before the test. Does this help?

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +1

      And yes, absolutely. When I was younger I used methods just like this to build up mathematical intuition when I was younger. In addition, I highly recommend you find someone/anyone to attempt to tutor for free (younger sibling, relative, neighbor kid, church friend, etc.) As teaching others FORCES the teacher to explain things in an organized fashion. Which organizes it within the mind of the teacher.

    • @viradeus4322
      @viradeus4322 4 года назад +2

      @@TheBeautyofMath interesting. Thanks for the quick reply and advice. So I shouldn't bother putting in the problems I know how to do?

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +1

      Correct. Why? Because it's a journal basically intended for you and perhaps a future student you teach. But it should be personalized to you. There are hundreds and hundreds of concepts. It would be too cumbersome to diagram every problem and you wouldn't learn fast enough. So only diagram problems you LEARNED something new on. You could diagram a problem where you learned a more efficient way though. Like a major shortcut or something.

    • @viradeus4322
      @viradeus4322 4 года назад

      @@TheBeautyofMath thanks for all the help! Like seriously, this channel is a godsend for all AMC test takers.
      Your reasoning makes sense. If I know how to do a problem, then I would just be wasting space in my notebook when I could be writing/studying and problem that I don't know.
      Now I have no geometry knowledge. I'm taking geo+alg 2 as a freshman. I'm thinking of buying aops intro to geometry and studying from that. After that I will probably start doing practice Problems.
      What do you think? Good idea?
      I also have AOPS vol 1.

  • @vik1250
    @vik1250 2 года назад

    Hi. I am a high school freshman. Well, sophomore next year. I will be taking the amc 10 in the fall. To prepare I have been watching your videos, keeping up a small formula notebook and reading AOPS Volume 1. I understand what the book’s saying. But when it comes to problems, I have a hard time thinking abt it to apply. I can completely understand the solution tho. If I see like a tiny idea from the solution. I can solve the problem. How could I go about this problem? Any suggestions would be appreciated. Thank you.

  • @mukeshd7417
    @mukeshd7417 2 года назад +2

    Hi I got 15 (16 if not for a stupid mistake) on my first year doing AMC8 or any math competition, I wanted to know is 15 a good score for someone’s first year?

    • @TheBeautyofMath
      @TheBeautyofMath  2 года назад +2

      Absolutely. Especially in the modern era. You can check out the statistics from the test by googling AMC 8 statistics and play around with the paramaters at their website. But that's a great score with very little prep...I think you would have an excellent shot if you study hard to make AIME(qualify through AMC 10) during high school.

  • @halcyondays4922
    @halcyondays4922 4 года назад +2

    Man I just need think like 5 times faster. I know all the questions on the practice AMC they sent me, but I didn't have enough time, so I ended up guessing a lot. I got a 7 out of 25. My mother told me that 13 is a good score. Am I just awful at this or something?

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      On which test? AMC 8 or 10? I have thoughts on both. Check back for replies though in case RUclips doesn't notify(they sometimes don't).

    • @halcyondays4922
      @halcyondays4922 4 года назад

      @@TheBeautyofMath AMC 8. I tried another AMC 8 test from a different year, and got a eight this time. I just don't have enough time to do everything, so I end up skimming the test for the easy ones and getting stressed out over the time left. Are 7 and 8 bad scores..?

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      Really sick right now. Will try and respond when well. Apologies.

    • @halcyondays4922
      @halcyondays4922 4 года назад +1

      @@TheBeautyofMath That’s okay. I’m happy you’re responding at all.

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +1

      It depends on several things.
      1. Which year was the test you got an 8?
      2. What grade are you in?
      3. What do you personally consider good.
      Let's take an example. The farthest back AMC 8 with statistics online found at: amc-reg.maa.org/reports/generalreports.aspx
      Shows a score of 8 overall would be better than 44% of all test takers. If you are in 4th grade...and have no experience with Competition Math...that would be excellent.
      If you are a 7th grader who has done AoPS Pre Algebra and all of Alcumus and been doing Competition Math for 3 years, that would be pathetic. If you are in 7th grade and have done none of those things above then it would be a good score for a person who has no experience.
      Fast forward to 2017 test. The same score of 8 is now in the top 50% of all test takers.
      You have to remember what these things mean. Who is taking a Competition Math test? Kids with C's in their math class? No. Only kids who are above average in math are interested in doing Competition Math. So that isn't top 50% of all school kids. It's top 50% of all ABOVE AVERAGE math students. Likely that would mean out of all kids in say 7th grade you would do better than likely 8 out of 10. I would say that's pretty good. So have perspective. The only way to get higher scores and faster is to massively increase your experience through hard work and dedication. If you want the reward of satisfaction...make the sacrifice to earn it. I hope this helps.

  • @AlexandrBorschchev
    @AlexandrBorschchev 4 года назад +2

    Thank you for the video. Btw do you have alternatives for Aops? Im thinking of something free or accessible online since I don’t have money 😅

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +2

      I don't exactly have alternatives, however a video I just recently made was exactly for people in your situation. Asking of an alternative to AoPS is akin to asking about an alternative player who can do what LeBron James in his prime could do. There is no alternative. But...this video might give you some ideas on work arounds:
      ruclips.net/video/e_dA6XH5lVM/видео.html

  • @poonamchauhan1318
    @poonamchauhan1318 4 года назад +2

    I am in 15, am I late for AMC 10?

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      It is never too late to improve yourself and your critical and creative thinking skills. You might even qualify for AIME by the time you graduate. All you can do is try. I hope this helps.

    • @poonamchauhan1318
      @poonamchauhan1318 4 года назад +1

      @@TheBeautyofMath thanks for replying to all questions...... So kind of you

  • @sahibakaur2930
    @sahibakaur2930 4 года назад +1

    Hello again!
    So for this whole extraction process, do you think it would be more beneficial to only do this for say, the last 10? Doing this for the whole test might take lots and lots of time, and generally, the first 15 are easier. What is your opinion on this?
    Also, you know how Richard Rusczyk started doing the last 5 problems from AMCs starting in 2012? Do you think you could do the last 5 for the tests before 2012? That would be awesome :D
    Have a great day!

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      Sorry I should have explained, generally the long extraction process should only be done on problems you LEARNED something NEW on. So if you already knew the underlying concept really really well, then I do not recommend doing it. Simply copy any formulas or underlying concepts into your small notebook so you can build up a personalized referenceable (new word) data set. Generally do the test first. Any that you got wrong or skipped or were not 100% confident in your answer are the types of problems you should diagram. For everything else you don't need highlighter color coating process. Let me know if this clears up your question.

  • @vadermadeaime7882
    @vadermadeaime7882 3 года назад

    Hi,
    I took AMC 10 this year, and probably got in the low 90's or high 80's. I feel that I need to work on Counting and Probability, and I was lucky that it wasn't stressed that much this year. I want to try to qualify for usa(j)mo. Do you have any ideas on what to do/how to prepare?
    Btw my parents have said that it's an ambitious goal. Is it feasible? I'm currently in 8th grade doing very well in school maths.

    • @TheBeautyofMath
      @TheBeautyofMath  3 года назад

      Hi Vader, sorry for late response. I highly recommend Intro to Counting amd Probability from Art of Problem Solving. I think the entire Intro Series is fantastic really, but I would start with the most popular video on my channel which is How to Prepare for the AMC 10: A plan.
      Keep in mind, it's a rough outline. You will need to modify it to fit your needs. Let me know if it helps.
      As for the ambitious goal. Your parents are correct. That doesn't mean you shouldn't try or that you can't do it. It means you need to be dedicated and push yourself harder then you have ever pushed yourself to achieve something. It's like the top 500 or so Competition Math students in the nation out of several million students. Kids who make it that far are as dedicated to their goal as any Athletic prodigy. Often with private coaches, tutors, camps, etc. They hone their craft several hours a day every day usually for a couple yeara before they can achieve it. But if you think you can...then get it done. I always did better when people doubted me any way. Meet any doubters? Use their doubt as fuel to push yourself. Best of luck!

    • @vadermadeaime7882
      @vadermadeaime7882 3 года назад +1

      @@TheBeautyofMath ​ Thank you! Other than Counting and Probability, what other books would you recommend? Note that I have finished the entire Intro series, except for C&P (currently working on as suggested) and Number Theory. What AoPS courses are good too for me?
      (deleted and reposted, as there was no response for 2-3 weeks)

    • @TheBeautyofMath
      @TheBeautyofMath  3 года назад

      @@vadermadeaime7882 sorry Vader, just lots of things going on, I am way behind on comment responses. As far as AoPS courses are concerned...I have currently limited knowledge and would not be the best person to recommend a course without doing more research. When I am able to get that research done, I will make a video on it. I would suggest going to Intermediate Algebra text next, and if possible perhaps try one of the Int Algebra courses from AoPS. I would assume they are likely perfect for your level and where you are at currently in development.

  • @pratikk7099
    @pratikk7099 3 года назад +1

    Can international students give amc?

    • @TheBeautyofMath
      @TheBeautyofMath  3 года назад

      Yes. Many international students take it every year. You can learn more about it on this page. International can take both the first round(AMC 10) and the second round (AIME). www.maa.org/math-competitions/international-registrations

  • @eunicepark2946
    @eunicepark2946 3 года назад

    Hi I'm in 7th grade right now. Would it be too late if I start preparing for AMC 8 now? Should I just prepare for a long time and try AMC 10 right away?

    • @TheBeautyofMath
      @TheBeautyofMath  3 года назад

      Never too late to improve your ability to think creatively and logically. Never too late to develop the ability to perform well under pressure. Start prep immediately with tenacity. Take the AMC 10 this year in 30 days time. Both the A and the B. Your purpose is not a high score. Your purpose is exposure to pressure.
      Knowing nothing about you I would predict offhand that you can maybe do 5 to 7 problems. Let's say you get 5 right 5 wrong, and skip 15. Your score? A paltry 52.5. But you just created your benchmark. Your starting point. Now the goal your 8th grade year is to beat your 2020 7th grade year score. This should be easily accomplished if you put forth the effort. Maybe score a 90 as an 8th grader. (Dedicate your summer to the goal) then you continue prep and qualify for AIME as a Freshman. Depending on your innate skill level and how quickly you learn, how well you take notes(Watch the How to Prepare video on my channel, find it in the Playlist this video is part of) and how well you perform under pressure this would be a reasonable trajectory. I had a girl not start prep until 8th grade. She qualified with 1 year prep time for AIME. It can be done. The question is...are you up for the challenge?

    • @eunicepark2946
      @eunicepark2946 3 года назад +1

      @@TheBeautyofMath Here some information about me, I'm currently getting A's for every single math test I take in school, and I'm quite a fast learner. So, you mean I should start preparing for AMC 10 right away? And also since I don't a lot of grade 9 and 10 math, (I do a know grade 8 math) should I start learning basic grade 9 and 10 math? And btw yes, I'm up for the challenge :)

    • @TheBeautyofMath
      @TheBeautyofMath  3 года назад

      This is the mindset you need. Yes. Take the AMC 10 right away this year. And then after start various forms of study that improve your knowledge base.
      Not to be dismissive, but for gifted or above average students which I suspect is a category you fall into getting an A is normal and expected. Most likely 95 to 100 percent of students who take the AMC 10 have never gotten a B in their School Math classes. It tends to be precisely that kind of student who is encouraged to take such Competitions as the AMC. Having a solid school math foundation is a good starting basis of course. But entering the world of competition math is on a whole nother level.
      While it's true you will likely be "competing" against all kids who have been getting A's in their math classes. They aren't really your competition. You are. Every day and every week you must defeat yourself. Your laziness. Your moments of lacking motivation. Your sometimes internal desire to lack intellectual curiosity. Some of course is allowed. In moderation. Breaks from study must be taken. But we are talking making consistent decisions to improve ones self and reasoning skills when other alternatives such as self entertainment are alluring. The trick then is to find joy in the problems. Then studying the beautiful and interesting mechanisms BECOMES self entertainment. You will be grinding. It's best to enjoy the grind or face burnout in one to two years time. When it ceases to be fun, step back for a week or two. Maybe even a month then return to it again with tenacity.
      If you never win any awards...then was the time wasted? No you trained your mind to be a better more adept, and more creative thinker. Such people make good citizens and contributors to society. Good luck on your upcoming journey of study. 🙂💯

  • @anvithkakkera7196
    @anvithkakkera7196 4 года назад +1

    Just wondering, do you still do the AMC 8/10/12 , AIME's , and USAJMO's and USAMO's contests that are released each year for fun? Would you recommend doing this method during AMC practice tests, or just do this method solely when doing practice problems that are not part of a timed test?

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад +1

      I still do up to AIME level problems for fun and to make sure I can answer the questions I am competent in answering when I am teaching. I have never really attempted things at the USAJMO or higher level due to lack of time in my current schedule and not having kids qualify every year. It is very rare. So I only get to try and teach it once every 3 or 4 years when one of my students reaches that level.
      Math is a use it or lose it subject, so as I don't get to use such problems in my daily work, it isn't really a good expenditure of my time currently to become competent at them to the level of being able to explain when I would only get one student for the content once every 4 years.
      I don't always do the problems under timed conditions, but sometimes I do. This year I plan to live solve the AMC 8 (do not discuss it) on November 17th. I am unsure of what time of day I will do it. but I believe it cannot be done until then as far as discussion goes. I will probably embarrass myself and get 2 wrong or something. Such is life.

    • @TheBeautyofMath
      @TheBeautyofMath  4 года назад

      As for the second question you should DEFINITELY use this method once the test is completed and add about 3-5 problems to the big notebook from each test where you are able to diagram the solution process with color coding. It is far more important on past AMC tests than it is for other material. For that is precisely the content that we are preparing for. Don't do it during the timed test taking though of course. But afterward for sure.

  • @rajvardhansinghsisodiya1095
    @rajvardhansinghsisodiya1095 3 года назад

    How to revise maths for OLMPYIAD

    • @TheBeautyofMath
      @TheBeautyofMath  3 года назад

      Interesting comment. Do you mean How should governments and schools redesign high school level curriculum in order yo develop more students capable of participating in OLYMPIAD level Mathematics?

    • @rajvardhansinghsisodiya1095
      @rajvardhansinghsisodiya1095 3 года назад

      @@TheBeautyofMath no I am asking before going for a math competition how one should revise what he has done. In school maths formula revision is only necessary but in competition maths one such many things other than formula and principles( strategies,insights etc.)