How do I prepare for AIME?

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5818 posts

#1 h Mar 9, 2015, 7:49 PM • 172 Y

Y by mathsolver101, 15Pandabears, TheMaskedMagician, spartan168, jh235, amburger66, bharatputra, cobbler, Not_a_Username, ingenio, NormanWho, brandbest1, ProblemSolver1026, hesa57, MSTang, hamup1, Royalreter1, knittingfrenzy18, m-c-geometry, noobynoob, mathisfun7, DigitalKing257, droid347, TheCrafter, wu2481632, kenneth102099, spin8, yojan_sushi, Eugenis, afroromanian, ThisIsASentence, budu, Stens, republicofalvinia, champion999, AstrapiGnosis, mrowhed, poonicle, TheOneYouWant, atmchallenge, hy2015, rafa2be, PiDude314, JayJuly, sturdyoak2012, adihaya, yan_justin98, DanielL2000, CornSaltButter, ythomashu, mingxu, math101010, Dukejukem, Awesomekid05, dhwang314, brianapa, m1234567, rlybd5, Mathlete55, elitechicken, coolrg, RegularHexagon, lucasxia01, starburst, janabel, popsiclebirdiepotato, dantx5, CML, noodlemaster, crosby87, ssk9208, checkmatetang, Carrots101, muti66, bestwillcui1, create, joey8189681, Adi123, BobThePotato, ishankhare, skys, AstroCarp, Wave-Particle, sophie8, IdentityChaos2020, Samchooo, CurryinaHurry, JasperL, Dhman2727, mathcrazymj, Mudkipswims42, snow_monkey, 3_14152, Mathcat1234, psa, alifenix-, franchester, kj2002, Aldwyn22, low, GeneralCobra19, bigmath, ccx09, BCZ01, potato36, Debussy, AlphaSiege, tapir1729, Math-Ninja, wwilliamtang, thecoolchicken, mgrimalo, Pimaster314, mathlogician, nikhil.mudumbi, shootingstar8, Mathisfun04, FleetyFlight, k2005, TopNotchMath, tiger528, User360702, mathleticguyyy, AntaraDey, middletonkids, Williamgolly, Jay17, Toinfinity, Zorger74, SuperJJ, Qwerty2005, Sedro, ChikaFujiwara, OliverA, jacoporizzo, centslordm, fuzimiao2013, csong, OlympusHero, j4ck, RubixMaster21, Taco12, spiritshine1234, Bradygho, hh99754539, Flying-Man, pog, megarnie, nikitadas, NoSignOfTheta, mahaler, FIREDRAGONMATH16, Mathbee2020, ThisUsernameIsTaken, CadenR26, doulai1, rayfish, Lamboreghini, EpicBird08, de-Kirschbaum, peelybonehead, smartguy888, roribaki, Adventure10, parmenides51, mathmax12, evanhliu2009, mathking999, bowenying24, MathRook7817, clarkculus, aidan0626

The AIME is right around the corner, which means a lot of last-minute preparation will be occurring over the next few days. In the interest of guiding such preparation, I've compiled what I view as the most important concepts and techniques that appear on the AIME. Please feel free to offer comments or suggestions for improvement!

The document can be found here, at this direct link (https://www.dropbox.com/s/icds9u5yo0xypyf/AIMElist.pdf?dl=0), or in the attachment below. I suggest using the Dropbox link, as any changes to this article will be automatically updated there.

Changelog:

$1^3+2^3+\hdots+n^3=(1+2+3+\hdots+n)^2$ rather than $(1+2+3+\hdots+n)^3$ . [3/9 17:30]

Attachments:

AIMElist.pdf (301kb)

This post has been edited 1 time. Last edited by BOGTRO, Mar 9, 2015, 9:30 PM
Reason: Added changelog

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TheMaskedMagician

2955 posts

TheMaskedMagician

#2 h Mar 9, 2015, 7:54 PM • 2 Y

Y by Adventure10, Mango247

Great article!

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spartan168

1472 posts

spartan168

#3 h Mar 9, 2015, 8:07 PM • 2 Y

Y by Adventure10, Mango247

Thanks Bogtro!
Looks really good.

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Benq

3396 posts

Benq

#4 h Mar 9, 2015, 8:08 PM • 3 Y

Y by yajmr, Adventure10, Mango247

Darn I never organize my work when I practice (partly because I'm doing it in school

)

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jh235

910 posts

jh235

#5 h Mar 9, 2015, 8:25 PM • 2 Y

Y by Adventure10, Mango247

Thanks so much BOGTRO! The combo section is helpful, especially the part about "states". That first problem was on the AMC 12 this year, and though I got it right, I used the infinite series method.

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kkpanu9

335 posts

kkpanu9

#6 h Mar 9, 2015, 8:56 PM • 3 Y

Y by BOGTRO, Adventure10, Mango247

There is a typo in the sum of consecutive cubes

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brandbest1

259 posts

brandbest1

#7 h Mar 10, 2015, 12:04 AM • 1 Y

Y by Adventure10

I'm not understanding the solution on Page 8 about Alice and Bob, about where $\frac{1+p}{2}$ comes from.

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Eugenis

2404 posts

Eugenis

#8 h Mar 10, 2015, 1:52 AM • 2 Y

Y by Adventure10, Mango247

Sorry to comment BOGTRO, but on line 9 you say "thi slisting". A small typo.

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IMOJonathan

907 posts

IMOJonathan

#10 h Nov 28, 2015, 6:10 AM • 2 Y

Y by Adventure10, Mango247

There is a small typo in the document. 1^3+2^3+...+n^3 should equal (1+2+...+n)^2 not (1+2+...+n)^3.

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budu

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budu

#11 h Nov 28, 2015, 6:39 AM • 3 Y

Y by bududu, Adventure10, Mango247

IMOJonathan wrote:

There is a small typo in the document. 1^3+2^3+...+n^3 should equal (1+2+...+n)^2 not (1+2+...+n)^3.

...where does it say that $1^3+2^3+...+n^3 = (1+2+...+n)^3$ ?

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spartan168

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spartan168

#12 h Nov 28, 2015, 7:32 AM • 1 Y

Y by Adventure10

IMOJonathan wrote:

There is a small typo in the document. 1^3+2^3+...+n^3 should equal (1+2+...+n)^2 not (1+2+...+n)^3.

Look at the OP for the Changelog

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daniellionyang

1840 posts

daniellionyang

#13 h Dec 1, 2015, 7:54 AM • 2 Y

Y by budu, Adventure10

There is an error on page $3$ where $1+3+5...2(n-1)$ is supposed to be $1+3+5+...+2n-1$ .

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budu

1515 posts

budu

#14 h Dec 1, 2015, 8:05 AM • 2 Y

Y by Adventure10, Mango247

daniellionyang wrote:

There is an error on page $3$ where $1+3+5...2(n-1)$ is supposed to be $1+3+5+...+2n-1$ .

Oh yeah, I think you're right...btw it's actually at the top of page 4

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DeathLlama9

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DeathLlama9

#15 h Mar 2, 2016, 3:36 PM • 2 Y

Y by Adventure10, Mango247

I think there's a typo on the roots of unity section as it refers to the $n$ th roots of unity as $cis (\frac{2 \pi n}{k})$ instead of $cis (\frac{2 \pi k}{n})$ . Thanks for the great resource, though!

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2_confirm_

13 posts

2_confirm_

#16 h Mar 2, 2016, 6:31 PM • 2 Y

Y by Adventure10, Mango247

Just to clarify, If I qualify through the 10 A and the 12B, can I take the AIME I and II? I really don't want to start another AIME rule thread, so I'm just asking here.

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Raihan2123

4 posts

Raihan2123

#38 h Mar 16, 2019, 6:35 PM • 3 Y

Y by samrocksnature, Adventure10, Mango247

Dang it, should've read this before I took the AIME

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TRex_1

2715 posts

TRex_1

#39 h Mar 16, 2019, 6:42 PM • 2 Y

Y by samrocksnature, Adventure10

@above, I'm taking the AIME II.

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ChikaFujiwara

157 posts

ChikaFujiwara

#41 h Mar 9, 2021, 4:10 PM • 2 Y

Y by samrocksnature, Mango247

BAHHHHAHAHAHAHAHAHAHAHAHAHAHAH TYPOOOO

Attachments:

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pog

4917 posts

pog

#42 h Mar 9, 2021, 4:11 PM • 1 Y

Y by samrocksnature

What typo?

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vvluo

1574 posts

vvluo

#43 h Mar 9, 2021, 4:13 PM • 1 Y

Y by samrocksnature

pog wrote:

What typo?

AIME #1: Find $42 \cdot 6$ .

to be honest: I'm bad enough that someone could convince me $42 \cdot 6 =264$ for 10 seconds.

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ChikaFujiwara

157 posts

ChikaFujiwara

#44 h Mar 9, 2021, 4:15 PM • 1 Y

Y by samrocksnature

pog wrote:

What typo?

._.

What is $42 \cdot 16$ ?

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Lingjun

89 posts

Lingjun

#45 h Mar 9, 2021, 4:15 PM • 1 Y

Y by samrocksnature

ChikaFujiwara wrote:

BAHHHHAHAHAHAHAHAHAHAHAHAHAHAH TYPOOOO

lol that was probably the point... 42*16=684 is a mistake that they're showing how you're more likely to miss it if you don't write out intermediate steps.

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ChikaFujiwara

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ChikaFujiwara

#46 h Mar 9, 2021, 4:17 PM • 1 Y

Y by samrocksnature

They were trying to show how writing out these steps increased accuracy...

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