AoPS Community

Middle School Math Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

VNew Topic kLocked

Middle School Math Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

VNew Topic kLocked

51,285 topics

2 users

TOPICS

Topic

First Poster

Last Poster

k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
Sunday, Apr 13 - Aug 10
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29

Prealgebra 2 Self-Paced

Prealgebra 2
Sunday, Apr 13 - Aug 10
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
Sunday, Jun 29 - Oct 26
Friday, Jul 25 - Nov 21

Introduction to Algebra A Self-Paced

Introduction to Algebra A
Monday, Apr 7 - Jul 28
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28

Introduction to Counting & Probability Self-Paced

Introduction to Counting & Probability
Wednesday, Apr 16 - Jul 2
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19

Introduction to Number Theory
Thursday, Apr 17 - Jul 3
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30

Introduction to Algebra B Self-Paced

Introduction to Algebra B
Wednesday, Apr 16 - Jul 30
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Wednesday, Apr 23 - Oct 1
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19

Intermediate: Grades 8-12

Intermediate Algebra
Monday, Apr 21 - Oct 13
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22

Intermediate Counting & Probability
Wednesday, May 21 - Sep 17
Sunday, Jun 22 - Nov 2

Intermediate Number Theory
Friday, Apr 11 - Jun 27
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
Wednesday, Apr 9 - Sep 3
Friday, May 16 - Oct 24
Sunday, Jun 1 - Nov 9
Monday, Jun 30 - Dec 8

Advanced: Grades 9-12

Olympiad Geometry
Tuesday, Jun 10 - Aug 26

Calculus
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17

Group Theory
Thursday, Jun 12 - Sep 11

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Wednesday, Apr 16 - Jul 2
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

MATHCOUNTS/AMC 8 Advanced
Friday, Apr 11 - Jun 27
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21

AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22

AMC 12 Final Fives
Sunday, May 18 - Jun 15

F=ma Problem Series
Wednesday, Jun 11 - Aug 27

WOOT Programs
Visit the pages linked for full schedule details for each of these programs!

MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT

Programming

Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22

Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
Monday, Jun 30 - Sep 22

USACO Bronze Problem Series
Tuesday, May 13 - Jul 29
Sunday, Jun 22 - Sep 1

Physics

Introduction to Physics
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15

Physics 1: Mechanics
Thursday, May 22 - Oct 30
Monday, Jun 23 - Dec 15

Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)

0 replies

jlacosta

Apr 2, 2025

0 replies

9 Was the 2025 AMC 8 harder or easier than last year?

Sunshine_Paradise 180

Also what will be the DHR?

180 replies

Sunshine_Paradise

Jan 30, 2025

aichinara

4 minutes ago

Doubt on a math problem

AVY2024 9

Solve for x and y given that xy=923, x+y=84

9 replies

AVY2024

Apr 8, 2025

evt917

23 minutes ago

cutoffs for RSM IMC

bubby617 9

what are the percentile cutoffs for the RSM IMC? i got in with an 82nd percentile so im curious on the requirements for advancement in R1/prizes in R2

9 replies

bubby617

Yesterday at 10:18 PM

jb2015007

41 minutes ago

State target p8 sol

EaZ_Shadow 81

This solution was so educational! It helped me understand how to solve this problem in many ways I couldn't, and I feel so enlightened!

81 replies

1 viewing

EaZ_Shadow

Apr 6, 2025

RandomMathGuy500

2 hours ago

High School Math Grades 9-12, Ages 13-18

Grades 9-12, Ages 13-18

VNew Topic kLocked

High School Math Grades 9-12, Ages 13-18

Grades 9-12, Ages 13-18

VNew Topic kLocked

120,329 topics

5 users

TOPICS

Topic

First Poster

Last Poster

k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Apr 2, 2025

0 replies

NC State Math Contest Wake Tech Regional Problems and Solutions

mathnerd_101 9

Problem 1: Determine the area enclosed by the graphs of $y=|x-2|+|x-4|-2, y=-|x-3|+4.$ Hint
Solution to P1

Problem 2: Calculate the sum of the real solutions to the equation $x^\frac{3}{2} -9x-16x^\frac{1}{2} +144=0.$
Hint
Solution to P2

Problem 3: List the two transformations needed to convert the graph $\frac{x-1}{x+2}$ to $\frac{3x-6}{x-1}.$
Hint
Solution to P3

Problem 4: Let $a,b$ be positive integers such that $a^2-b^2=20,$ and $a^3-b^3=120.$ Determine the value of $a+\frac{b^2}{a+b}.$
Hint
Solution for P4

Problem 5: Eve and Oscar are playing a game where they roll a fair, six-sided die. If an even number occurs on two consecutive rolls, then Eve wins. If an odd number is immediately followed by an even number, Oscar wins. The die is rolled until one person wins. What is the probability that Oscar wins?
Hint
Solution to P5

Problem 6: In triangle $ABC,$ $M$ is on point $\overline{AB}$ such that $AM = x+32$ and $MB=x+12$ and $N$ is a point on $\overline{AC}$ such that $MN=2x+1$ and $BC=x+22.$ Given that $\overline{MN} || \overline{BC},$ calculate $MN.$
Hint
Solution to P6

Problem 7: Determine the sum of the zeroes of the quadratic of polynomial $Q(x),$ given that $Q(0)=72, Q(1) = 75, Q(3) = 63.$
Hint

Solution to Problem 7

Problem 8:
Hint
Solution to P8

Problem 9:
Find the sum of all real solutions to $(x-4)^{log_8(4x-16)} = 2.$ Hint
Solution to P9

Problem 10:
Define the function
$f(x) = \begin{cases} x - 9, & \text{if } x > 100 \\ f(f(x + 10)), & \text{if } x \leq 100 \end{cases}$
Calculate $f(25)$ .

Hint

Solution to P10

Problem 11:
Let $a,b,x$ be real numbers such that $log_{a-b} (a+b) = 3^{a+b}, log_{a+b} (a-b) = 125 \cdot 15^{b-a}, a^2-b^2=3^x.$ Find $x.$
Hint

Solution to P11

Problem 12: Points $A,B,C$ are on circle $Q$ such that $AC=2,$ $\angle AQC = 180^{\circ},$ and $\angle QAB = 30^{\circ}.$ Determine the path length from $A$ to $C$ formed by segment $AB$ and arc $BC.$

Hint
Solution to P12

Problem 13: Determine the number of integers $x$ such that the expression $\frac{\sqrt{522-x}}{\sqrt{x-80}}$ is also an integer.
Hint

Solution to Problem 13

Problem 14: Determine the smallest positive integer $n$ such that $n!$ is a multiple of $2^15.$

Hint
Solution to Problem 14

Problem 15: Suppose $x$ and $y$ are real numbers such that $x^3+y^3=7,$ and $xy(x+y)=-2.$ Calculate $x-y.$
Funnily enough, I guessed this question right in contest.

Hint
Solution to Problem 15

Problem 16: A sequence of points $p_i = (x_i, y_i)$ will follow the rules such that
$p_1 = (0,0), \quad p_{i+1} = (x_i + 1, y_i) \text{ or } (x_i, y_i + 1), \quad p_{10} = (4,5).$ How many sequences $\{p_i\}_{i=1}^{10}$ are possible such that $p_1$ is the only point with equal coordinates?

Hint
Solution to P16

Problem 18: (Also stolen from akliu's blog post)
Calculate

$\sum_{k=0}^{11} (\sqrt{2} \sin(\frac{\pi}{4}(1+2k)))^k$
Hint
Solution to Problem 18

Problem 19: Determine the constant term in the expansion of $(x^3+\frac{1}{x^2})^{10}.$

Hint
Solution to P19

Problem 20:

In a magical pond there are two species of talking fish: trout, whose statements are always true, and \emph{flounder}, whose statements are always false. Six fish -- Alpha, Beta, Gamma, Delta, Epsilon, and Zeta -- live together in the pond. They make the following statements:
Alpha says, "Delta is the same kind of fish as I am.''
Beta says, "Epsilon and Zeta are different from each other.''
Gamma says, "Alpha is a flounder or Beta is a trout.''
Delta says, "The negation of Gamma's statement is true.''
Epsilon says, "I am a trout.''
Zeta says, "Beta is a flounder.''

How many of these fish are trout?

Hint
Solution to P20
SHORT ANSWER QUESTIONS:
1. Five people randomly choose a positive integer less than or equal to $10.$ The probability that at least two people choose the same number can be written as $\frac{m}{n}.$ Find $m+n.$

Hint
Solution to S1

2. Define a function $F(n)$ on the positive integers using the rule that for $n=1,$ $F(n)=0.$ For all prime $n$ , $F(n) = 1,$ and for all other $n,$ $F(xy)=xF(y) + yF(x).$ Find the smallest possible value of $n$ such that $F(n) = 2n.$

Hint
Solution to S2

3. How many integers $n \le 2025$ can be written as the sum of two distinct, non-negative integer powers of $3?$
Huge shoutout to OTIS for teaching me how to solve problems like this.

Hint

Solution to S3

4. Let $S$ be the set of positive integers of $x$ such that $x^2-5y^2=1$ for some other positive integer $y.$ Find the only three-digit value of $x$ in $S.$
Hint
Solution to S4

5. Let $N$ be a positive integer and let $M$ be the integer that is formed by removing the first three digits from $N.$ Find the value of $N$ with least value such that $N = 2025M.$
Hint

Solution to S5

9 replies

mathnerd_101

Friday at 11:40 AM

BackToSchool

29 minutes ago

geometry parabola problem

smalkaram_3549 9

How would you solve this without using calculus?

9 replies

smalkaram_3549

Friday at 9:52 PM

smbellanki

an hour ago

Alternate WOOT PAIME 2 #15 (2018 Winter Break AIME P14)

AOPS12142015 10

Let $x,y,z$ be real numbers satisfying the equations $y=x^2-2x$ $z=y^2-2y$ $x=z^2-2z.$ Find the sum of all distinct values of $x^2$ .

Proposed by mathfun5

10 replies

AOPS12142015

Mar 19, 2018

Giant_PT

an hour ago

Help me pls

trito11 6

Let 2017 positive integers $a_1,a_2,...a_{2017}$ and an integer $a>1$ which $a_1*a_2*...*a_{2017}|a$ .Prove that $a^{2018}+a-1$ isn't divisible by $(a+a_1-1)(a+a_2-1)(a+a_3-1)...(a+a_{2017}-1)$

6 replies

trito11

Dec 23, 2018

HuongToiVMO

an hour ago

Contests & Programs AMC and other contests, summer programs, etc.

AMC and other contests, summer programs, etc.

VNew Topic kLocked

Contests & Programs AMC and other contests, summer programs, etc.

AMC and other contests, summer programs, etc.

VNew Topic kLocked

34,613 topics

3 users

TOPICS

Topic

First Poster

Last Poster

k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Apr 2, 2025

0 replies

PROM^2 for Girls 2025

mathisfun17 24

Hi everyone!

The Princeton International School of Math and Science (PRISMS) Math Team is delighted that $PROM^2$ for Girls, PRISMS Online Math Meet for Girls, is happening this spring! https://www.prismsus.org/events/prom/home/index

We warmly invite all middle school girls to join us! This is a fantastic opportunity for young girls to connect with others interested in math as well as prepare for future math contests.

This contest will take place online from 12:00 pm to 3:00 pm EST on Saturday, April 26th, 2025.

The competition will include a team and individual round as well as activities like origami. You can see a detailed schedule here. https://prismsus.org/events/prom/experience/schedule.

Registration is FREE, there are cash prizes for participants who place in the top 10 and cool gifts for all participants.

1st place individual: $500 cash
2nd place individual: $300 cash
3rd place individual: $100 cash
4th-10th place individual: $50 cash each

Some FAQs:
Q: How difficult are the questions?
A: The problem difficulty is around AMC 8 or Mathcounts level.

Q: Are there any example problems?
A: You can find some archived here: https://www.prismsus.org/events/prom/achieve/achieve

Registration is open now. https://www.prismsus.org/events/prom/register/register. Email us at prom2@prismsus.org with any questions.

The PRISMS Peregrines Math Team welcomes you!

24 replies

mathisfun17

Feb 22, 2025

Lhaj3

36 minutes ago

smt format pmo...?

alcumusftwgrind 6

they cant be serious on the 4th one...

UGHHHHHHHHHHHHHHHHHHHHH this better not happen on general or I'm literally gonna quit the test and go play ultimate ??????

6 replies

alcumusftwgrind

5 hours ago

youlost_thegame_1434

40 minutes ago

9 best high school math competitions hosted by a college/university

ethan2011 13

I only included college-hosted comps since MAA comps are very differently formatted, and IMO would easily beat the rest on quality since mathematicians around the world give questions, and so many problems are shortlisted, so IMO does release the IMO shortlist for people to practice. I also did not include the not as prestigious ones(like BRUMO, CUBRMC, and others), since most comps with very high quality questions are more prestigious(I did include other if you really think those questions are really good).

13 replies

ethan2011

Yesterday at 2:15 AM

Danielzh

2 hours ago

How Should I Get Started/Train

ThrowAway23871241 3

Hi guys so this might not be the place to post this but I was wondering what I should do to start training for Math Olympiads, i.e. what resources to use. I'm in 11th grade right now and don't have any competitive math experience whatsoever, but I'm interested in starting. Any recommendations or tips would be helpful. Thanks!

3 replies

ThrowAway23871241

Yesterday at 5:57 PM

NamelyOrange

2 hours ago

High School Olympiads Regional, national, and international math olympiads

Regional, national, and international math olympiads

VNew Topic kLocked

High School Olympiads Regional, national, and international math olympiads

Regional, national, and international math olympiads

VNew Topic kLocked

311,803 topics

18 users

TOPICS

Topic

First Poster

Last Poster

k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Apr 2, 2025

0 replies

Problem 3 IMO 2005 (Day 1)

Valentin Vornicu 120

Let $x,y,z$ be three positive reals such that $xyz\geq 1$ . Prove that
$\frac { x^5-x^2 }{x^5+y^2+z^2} + \frac {y^5-y^2}{x^2+y^5+z^2} + \frac {z^5-z^2}{x^2+y^2+z^5} \geq 0 .$
Hojoo Lee, Korea

120 replies

Valentin Vornicu

Jul 13, 2005

Nguyenhuyen_AG

4 minutes ago

Transform the sequence

steven_zhang123 0

Given a sequence of $n$ real numbers $a_1, a_2, \ldots, a_n$ , we can select a real number $\alpha$ and transform the sequence into $|a_1 - \alpha|, |a_2 - \alpha|, \ldots, |a_n - \alpha|$ . This transformation can be performed multiple times, with each chosen real number $\alpha$ potentially being different
(i) Prove that it is possible to transform the sequence into all zeros after a finite number of such transformations.
(ii) To ensure that the above result can be achieved for any given initial sequence, what is the minimum number of transformations required?

0 replies

steven_zhang123

33 minutes ago

0 replies

prove that any quadrilateral satisfying this inequality is a trapezoid

mqoi_KOLA 3

Prove that any Trapezoid/trapzium satisfies the given inequality $|r - p| < q + s < r + p$ where $p,r$ are lengths of parallel sides and $q,s$ are other two sides.

3 replies

mqoi_KOLA

Yesterday at 3:48 AM

mqoi_KOLA

33 minutes ago

Number Theory Chain!

JetFire008 41

I will post a question and someone has to answer it. Then they have to post a question and someone else will answer it and so on. We can only post questions related to Number Theory and each problem should be more difficult than the previous. Let's start!

Question 1

41 replies

+2 w

JetFire008

Apr 7, 2025

pooh123

37 minutes ago

College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

VNew Topic kLocked

College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

VNew Topic kLocked

114,104 topics

4 users

TOPICS

Topic

First Poster

Last Poster

k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Apr 2, 2025

0 replies

high school math

aothatday 5

Let $x_n$ be a positive root of the equation $x_n^n=x^2+x+1$ . Prove that the following sequence converges: $n^2(x_n-x_{ n+1})$

5 replies

aothatday

Apr 10, 2025

aothatday

an hour ago

two solutions

τρικλινο 3

in a book:CORE MATHS for A-LEVEL ON PAGE 41 i found the following

1st solution

$x^2-5x=0$

$x(x-5)=0$

hence x=0 or x=5

2nd solution

$x^2-5x=0$

$x-5=0$ dividing by x

hence the solution x=0 has been lost

is the above correct?

3 replies

τρικλινο

Yesterday at 6:20 PM

maxamc

an hour ago

Putnam 2003 B1

btilm305 13

Do there exist polynomials $a(x)$ , $b(x)$ , $c(y)$ , $d(y)$ such that $1 + xy + x^2y^2= a(x)c(y) + b(x)d(y)$ holds identically?

13 replies

btilm305

Jun 23, 2011

clarkculus

4 hours ago

High School Integration Extravaganza Problem Set

Riemann123 12

Source: River Hill High School Spring Integration Bee

Hello AoPS!

Along with user geodash2, I have organized another high-school integration bee (River Hill High School Spring Integration Bee) and wanted to share the problems!

We had enough folks for two concurrent rooms, hence the two sets. (ARML kids from across the county came.)

Keep in mind that these integrals were written for a high-school contest-math audience. I hope you find them enjoyable and insightful; enjoy!

[center]Warm Up Problems[/center]
$\int_{1}^{2} \frac{x^{3}+x^2}{x^5}dx$ $\int_{2025}^{2025^{2025}}\frac{1}{\ln\left(2025\right)\cdot x}dx$ $\int(\sin^2(x)+\cos^2(x)+\sec^2(x)+\csc^2(x))dx$ $\int_{-2025.2025}^{2025.2025}\sin^{2025}(2025x)\cos^{2025}(2025x)dx$ $\int_{\frac \pi 6}^{\frac \pi 3} \tan(\theta)^2d\theta$ $\int \frac{1+\sqrt{t}}{1+t}dt$ -----
[center]Easier Division Set 1[/center]
$\int \frac{x^{2}+2x+1}{x^{3}+3x^{2}+3x+3}dx$ $\int_{0}^{\frac{3\pi}{2}}\left(\frac{\pi}{2}-x\right)\sin\left(x\right)dx$ $\int_{-\pi/2}^{\pi/2}x^3e^{-x^2}\cos(x^2)\sin^2(x)dx$ $\int\frac{1}{\sqrt{12-t^{2}+4t}}dt$ $\int \frac{\sqrt{e^{8x}}}{e^{8x}-1}dx$ -----
[center]Easier Division Set 2[/center]
$\int \frac{e^x}{e^{2x}+1} dx$ $\int_{-5}^5\sqrt{25-u^2}du$ $\int_{-\frac12}^\frac121+x+x^2+x^3\ldots dx$ $\int \cos(\cos(\cos(\ln \theta)))\sin(\cos(\ln \theta))\sin(\ln \theta)\frac{1}{\theta}d\theta$ $\int_{0}^{\frac{1}{6}}\frac{8^{2x}}{64^{2x}-8^{\left(2x+\frac{1}{3}\right)}+2}dx$ -----
[center]Harder Division Set 1[/center]
$\int_{0}^{\frac{\pi}{2}}\frac{\sin\left(x\right)}{\sin\left(x\right)+\cos\left(x\right)}+\frac{\sin\left(\frac{\pi}{2}-x\right)}{\sin\left(\frac{\pi}{2}-x\right)+\cos\left(\frac{\pi}{2}-x\right)}dx$ $\int_0^{\infty}e^{-x}\Bigl(\cos(20x)+\sin(20x)\Bigr) dx$ $\lim_{n\to \infty}\frac{1}{n}\int_{1}^{n}\sin(nt)^2dt$ $\int_{x=0}^{x=1}\left( \int_{y=-x}^{y=x} \frac{y^2}{x^2+y^2}dy\right)dx$ $\int_{0}^{13}\left\lceil\log_{10}\left(2^{\lceil x\rceil }x\right)\right\rceil dx$ -----
[center]Harder Division Set 2[/center]
$\int \frac{6x^2}{x^6+2x^3+2}dx$ $\int -\sin(2\theta)\cos(\theta)d\theta$ $\int_{0}^{5}\sin(\frac{\pi}2 \lfloor{x}\rfloor x) dx$ $\int_{0}^{1} \frac{\sin^{-1}(\sqrt{x})^2}{\sqrt{x-x^2}}dx$ $\int\left(\cot(\theta)+\tan(\theta)\right)^2\cot(2\theta)^{100}d\theta$ -----
[center]Bonanza Round (ie Fun/Hard/Weird Problems) (In No Particular Order)[/center]
$\int \ln\left\{\sqrt[7]{x}^\frac1{\ln\left\{\sqrt[5]{x}^\frac1{\ln\left\{\sqrt[3]{x}^\frac1{\ln\left\{\sqrt{x}\right\}}\right\}}\right\}}\right\}dx$ $\int_{1}^{{e}^{\pi}} \cos(\ln(\sqrt{u}))du$ $\int_e^{\infty}\frac {1-x\ln{x}}{xe^x}dx$ $\int_{0}^{1}\frac{e^{x}}{\left(x^{2}+3x+2\right)^{\frac{1}{2^{1}}}}\times\frac{e^{-\frac{x^{2}}{2}}}{\left(x^{2}+3x+2\right)^{\frac{1}{2^{2}}}}\times\frac{e^{\frac{x^{3}}{3}}}{\left(x^{2}+3x+2\right)^{\frac{1}{2^{3}}}}\times\frac{e^{-\frac{x^{4}}{4}}}{\left(x^{2}+3x+2\right)^{\frac{1}{2^{4}}}} \ldots \,dx$
For $x$ on the domain $-0.2025\leq x\leq 0.2025$ it is known that $\displaystyle f(x)=\sin\left(\int_{0}^x \sqrt[3]{\cos\left(\frac{\pi}{2} t\right)^3+26}\ dt\right)$ is invertible. What is $\displaystyle (f^{-1})'(0)$ ?

12 replies

Riemann123

Friday at 2:11 PM

jkim0656

Yesterday at 5:20 PM

Site Support Tech support and questions about AoPS classes and materials

Tech support and questions about AoPS classes and materials

VNew Topic kLocked

Site Support Tech support and questions about AoPS classes and materials

Tech support and questions about AoPS classes and materials

VNew Topic kLocked

18,610 topics

1 user

TOPICS

Topic

First Poster

Last Poster

k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Apr 2, 2025

0 replies

bot posts

Speedysolver1 21

see the link

21 replies

Speedysolver1

Yesterday at 4:05 PM

Sotowa

4 hours ago

how do u know how much friends u have?

jkim0656 15

how do u know how much friends u have?
I've seen ppl talk about having like random number/1000 friends but idk how to find the number :sob:
[RESOLVED]
[realized that i need more friends]

15 replies

jkim0656

Yesterday at 4:45 PM

Sotowa

4 hours ago

Who can add and remove admins?

LawofCosine 2

I have a question:

Who can add and remove admins to a forum?

Thanks!

2 replies

LawofCosine

5 hours ago

LawofCosine

5 hours ago

Introducing myself at AoPS, and what's your magic wand?

asuth_asuth 787

Hi!

I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.

Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops

I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.

787 replies