Competition Math Formula Sheet

by eashang1, Jul 12, 2017, 2:52 AM

I have compiled a list of useful formulas for math competitions. Keep in mind that preparation does not equate to memorizing formulas. Training your ability to think and visualize math problems (intuition) is far more important and can only come from practice. That being said, knowing your formulas is a quick way to improve and make many common types of questions trivial. Hope this helps!

EDIT: So this somehow became the first Google result for "competition math formulas", which I wasn't at all expecting. In order to improve the quality, please leave any typos/errors you find in the comments. I will delete them as I fix stuff so the comments section can be a running list of errata. Thanks!

I've posted a few practice tests and a more advanced handout called "Introduction to Olympiad Inequalities" on my blog. Be sure to check them out:)

Updated version is attached

Attachments:

CompetitionMathFormulaSheet.pdf (364kb)

This post has been edited 7 times. Last edited by eashang1, Jan 30, 2020, 7:54 PM

formulas

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16 Comments

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That’s really nice. Thanks!

by Shubhashubha, Jan 25, 2019, 7:07 PM

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Hello!

Firstly, this is amazing. I have several suggestions. Consider adding a separate inequality section (why is the trivial inequality in NT while RMS-AM-GM-HM is in Algebra??). Also, the hockey stick identity is extremely useful; you should include it. Next, add the circumradius formula 4AR = abc. Finally, and this is minor, but it is interesting and helpful to note that 1.18 reduces to 1.17 when d=0.

Could I please have a copy of the original latex? PM me.

~Rowechen :alien:

Sure, I'll make the edits and PM you the source. I actually made a much more comprehensive inequalities handout a couple of months ago. You should check it out

This post has been edited 1 time. Last edited by eashang1, Jan 30, 2020, 7:19 PM

by rowechen, Jan 30, 2020, 2:01 AM

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Hello, in the Shoelace Theorem(1.30), shouldn't the area end in a.n and b.n+1 instead of a.n and b.1

by rajukaju, Jun 12, 2020, 1:03 PM

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Hello!

I think there's a small mistake with 3.5 regarding the root-mean-square. For the nth term, the n in the superscript should be a 2. Thank you very much for making this document. It's been very helpful!

by Haylaylo, Feb 4, 2021, 2:57 AM

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For 1.19, shouldn't the $AB^2=BC*CD$

by ConcaveTriangle, Mar 10, 2021, 3:38 AM

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For 1.19, shouldn't the $AB^2=BC*CD$ be $AB^2=BC*BD$ ?

by ConcaveTriangle, Mar 10, 2021, 3:39 AM

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Great work making this! Thanks! :-D

by aops-g5-gethsemanea2, Mar 16, 2021, 10:18 PM

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1.21 Menelaus Theorem has a mistake.

In Menelaus Theorem (like Ceva Theorem), the segments on each side of the product are not touching. Each product is formed by going around the triangle skipping every second segment.

by oinava, Mar 28, 2021, 1:01 PM

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Very cool formula list. I will keep coming back to it to remember better. Thank you so much for it!

by auwebber23, Jul 19, 2021, 3:23 PM

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I also want to add that it is not so important to know the formulas, but the main thing is to be able to use them. I solve many examples, but sometimes I come across examples that I get stuck in solving. I turn to https://plainmath.net/post-secondary/algebra/linear-algebra/ for explanations, because there are many experts who know mathematics well. This service has helped me better prepare for exams and tests in college, so I recommend it to you.

by RobertPoster, Jul 19, 2021, 3:31 PM

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The labels in the diagram of 1.21 Menelaus’ Theorem are not visible properly.

by Aditya_Mittal, May 24, 2022, 6:55 AM

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Maybe add newton sums?

by ConcaveTriangle, Jan 20, 2023, 10:29 PM

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Hi, I really appreciate this formula sheets.
But I do recommend adding a few more trig formulas like the R-formula and the value for cos a + cos b and the sine version

But still thanks for the formula sheet, I couldn't find any other one as comprehensive as yours

by Mather314159, Jun 18, 2023, 10:09 AM

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Thank you so much!!!!!

by rayford, Aug 18, 2023, 8:52 PM

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I really appreciate it eashang1!!!

by rayford, Aug 18, 2023, 8:53 PM

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As someone who likes having the latest and greatest when it comes to reference materials, you should consider putting that information in the title of the document. Adding that info to the document name will let users know which version they are using. This is my suggestion:
CompetitionMathFormulas R3 Oct23
This lets the user know they are using revision 3 made in October, 2023.

by proudsailor, Oct 31, 2023, 2:56 PM

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Nice math formula sheet
by Tem8, Nov 8, 2024, 3:34 AM
Hey, what's up? It's been a minute since I've been on here. I feel so old now haha
by eashang1, May 31, 2024, 3:23 PM
Hi eashang! long time no see, but i'm happy hear about your quant offer
by AntonioMacaronio, Apr 24, 2024, 11:16 AM
thank you!!
by ritzceoAOPS, Nov 6, 2021, 10:07 PM
Wow this is a great blog!!
by ajax31, Oct 14, 2021, 10:11 PM
how are you so good? HOW ARE YOU SO GOOD.
by centslordm, Aug 2, 2021, 12:58 AM
thank u xd
by eashang1, Jun 12, 2021, 8:09 PM
cool blog (several months shout)
by pith0n, May 25, 2021, 11:59 PM
thank you:)
by eashang1, Mar 10, 2021, 5:24 PM
nice blog!
by judgefan99, Mar 9, 2021, 1:58 PM
lol it's kinda dead, but i appreciate it
by eashang1, Jan 12, 2021, 2:38 AM
This is the best blog in the world lel
by aryanpadarthi, Jan 2, 2021, 10:55 PM
Thanks! I've been doin fine ig... making the best of quarantine. wbu?
by eashang1, Oct 25, 2020, 10:27 PM
hey eashang, how are you doing? hopefully college is doing you well I like your posts
by AntonioMacaronio, Oct 23, 2020, 12:23 PM
:O \8char
by eashang1, Apr 29, 2020, 5:58 PM
Yeah lol. There are actually many GA AoPSers, but most aren't (unfortunately) active right now :/
by eashang1, Oct 1, 2017, 2:14 AM
wow, another GA AoPSer! yay!
by HydroMarioUSA, Oct 1, 2017, 1:18 AM
The guy who originally made the CSS
by eashang1, Aug 22, 2017, 2:19 AM
Who is NMK?
by mathwiz0803, Aug 20, 2017, 9:45 PM
This is NMK's (most others are variations of his)

It's a cool CSS though
by eashang1, Aug 20, 2017, 9:09 PM
Lol, I also used Ashford's CSS
by mathwiz0803, Aug 20, 2017, 9:02 PM
Thanks
by eashang1, Jul 23, 2017, 7:04 PM
Very nice problems!
by icosahedron1729, Jul 23, 2017, 4:25 PM
okay, thanks!
by Iamawesome1, Jul 16, 2017, 9:07 PM
Yeah sure go ahead I copied it from someone else and made a few minor edits... Most of the credit should go to NMK who designed the CSS in the first place
by eashang1, Jul 16, 2017, 3:48 AM
Can I copy your CSS? It looks awesome.
by Iamawesome1, Jul 15, 2017, 6:14 PM
i no like geo
by NotKipper, Jul 12, 2017, 6:38 PM
vee_inhaince
by themoocow, Jul 11, 2017, 3:56 AM
first shout >
by doitsudoitsu, Jul 9, 2017, 3:13 AM

74 shouts

Math ∩ Life

Competition Math Formula Sheet

by eashang1, Jul 12, 2017, 2:52 AM

16 Comments