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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
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.

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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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9 What is the most important topic in maths competition?
AVIKRIS   52
N 3 minutes ago by Nab-Mathgic
I think arithmetic is the most the most important topic in math competitions.
52 replies
AVIKRIS
Apr 19, 2025
Nab-Mathgic
3 minutes ago
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Kindle Scribe on Purple Comet?
RabtejKalra   4
N 37 minutes ago by GallopingUnicorn45
Can I bring a Kindle Scribe to the Purple Comet examination, because I've downloaded lot of formulas into it, but don't want to waste the paper to print all of it. PLEASE ANSWER SOON, THE COMPETITION IS IN 4 HOURS!
4 replies
RabtejKalra
an hour ago
GallopingUnicorn45
37 minutes ago
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1234th Post!
PikaPika999   235
N an hour ago by aok
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
235 replies
PikaPika999
Apr 21, 2025
aok
an hour ago
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Two similar geometry question
ERMSCoach   1
N an hour ago by Math-lover1
I have two questions for you to solve.
However, the particular question I am asking here is
Given the 1st question has answer x, find an easy solution to 2nd question in terms of x.
Essentially are these the same question, or is it a coincidence that the answers are similar?

First question, Equilateral triangle ABC has circle O tangent to BC and passing through A. Circle O intersects AB and AC at D and E, with AD=10 and AE=11. What is the length of BC?

Second question, Quadrilateral ABCD has AB=3, AD=4, B and D are right angles, C is 60 degrees.
What is the length of AC?
1 reply
ERMSCoach
Apr 25, 2025
Math-lover1
an hour ago
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Double Sum
P162008   2
N an hour ago by soryn
Compute the value of $\Omega = \sum_{m=0}^{\infty} \sum_{n=0}^{\infty} \frac{\left(\frac{1}{4}\right)^{m+n}}{(2m + 1)(m + n + 1)}.$
2 replies
P162008
Yesterday at 9:31 AM
soryn
an hour ago
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Combination
aria123   1
N 2 hours ago by aria123
Prove that three squares of side length $4$ cannot completely cover a square of side length $5$, if the three smaller squares do not overlap in their interiors (i.e., they may touch at edges or corners, but no part of one lies over another).
1 reply
aria123
Apr 15, 2025
aria123
2 hours ago
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Inequalities
sqing   0
3 hours ago
Let \( x, y \geq \frac{3}{2} \). Prove that
$$ \frac{2}{1+xy} + x + y \geq \frac{x}{y} + \frac{y}{x}+ \frac{21}{13}$$Let \( x, y \geq 2 \). Prove that
$$ \frac{2}{1+xy} + x + y \geq \frac{x}{y} + \frac{y}{x}+ \frac{12}{5}$$Let \(0< x, y \leq \frac{3}{2} \). Prove that
$$ \frac{2}{1+xy} + x + y \leq \frac{x}{y} + \frac{y}{x}+\frac{21}{13}$$Let \(0< x, y \leq 2 \). Prove that
$$ \frac{2}{1+xy} + x + y \leq \frac{x}{y} + \frac{y}{x}+\frac{12}{5}$$
0 replies
sqing
3 hours ago
0 replies
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Number theory
MathsII-enjoy   2
N 3 hours ago by MathsII-enjoy
$Find$ $all$ $integers$ $n$ $such$ $that$ $n-1$ $and$ $\frac{n(n+1)}{2}$ $is$ $a$ $perfect$ $number$.
2 replies
MathsII-enjoy
Today at 5:21 AM
MathsII-enjoy
3 hours ago
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Sequence
lgx57   5
N 3 hours ago by lgx57
$a_1=1,a_{n+1}=a_n+\frac{1}{a_n}$. Find the general term of $\{a_n\}$.
5 replies
lgx57
5 hours ago
lgx57
3 hours ago
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set of sum of three or fewer powers of 2, 2024 TMC AIME Mock #13
parmenides51   5
N 3 hours ago by vincentwant
Let $S$ denote the set of all positive integers that can be expressed as a sum of three or fewer powers of $2$. Let $N$ be the smallest positive integer that cannot be expressed in the form $a-b$, where $a, b \in S$. Find the remainder when $N$ is divided by $1000$.
5 replies
parmenides51
Yesterday at 8:16 PM
vincentwant
3 hours ago
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trigonogeometry 2024 TMC AIME Mock #15
parmenides51   3
N 3 hours ago by franklin2013
Let $\vartriangle ABC$ have angles $ \alpha, \beta$ and $\gamma$ such that $\cos (\alpha) = \frac1 3$ and $\cos (\beta) = \frac{1}{17}$ . Moreover, suppose that the product of the side lengths of the triangle is equal to its area. Let $(ABC)$ denote the circumcircle of $ABC$. Let $AO$ intersect $(BOC)$ at $D$, $BO$ intersect $(COA)$ at $ E$, and $CO$ intersect $(AOB)$ at $F$. If the area of $DEF$ can be written as $\frac{p\sqrt{r}}{q}$ for relatively prime integers $p$ and $q$ and squarefree $r$, find the sum of all prime factors of $q$, counting multiplicities (so the sum of prime factors of $48$ is $2 + 2 + 2 + 2 + 3 = 11$), given that $q$ has $30$ divisors.
3 replies
parmenides51
Yesterday at 8:22 PM
franklin2013
3 hours ago
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Max and min of a/5+b/4+c/3+d/2 under a/4+b/3+c/2+d=1/2 and a^2/7+b^2/5+c^2/3+...
tom-nowy   1
N 4 hours ago by steve4916
Let $a, b, c, d$ be real numbers satisfying the following two conditions:
\begin{align*} &\frac{a}{4}+\frac{b}{3}+\frac{c}{2}+d=\frac{1}{2}, \\ &\frac{a^2}{7}+\frac{b^2}{5}+\frac{c^2}{3}+d^2 + \frac{ab}{3}+\frac{2ac}{5}+\frac{ad}{2} +\frac{bc}{2}+\frac{2bd}{3}+\frac{cd}{2}=\frac{1}{3} . \end{align*}Find the possible maximum and minimum values of
$$\frac{a}{5}+\frac{b}{4}+\frac{c}{3}+\frac{d}{2}.$$
1 reply
tom-nowy
Today at 11:48 AM
steve4916
4 hours ago
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20 fair coins are flipped, N of them land heads 2024 TMC AIME Mock #6
parmenides51   3
N 5 hours ago by ostriches88
$20$ fair coins are flipped. If $N$ of them land heads, find the expected value of $N^2$.
3 replies
parmenides51
Yesterday at 8:05 PM
ostriches88
5 hours ago
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Inequalities
sqing   10
N 5 hours ago by sqing
Let $ a,b \in [0 ,1] . $ Prove that
$$\frac{a}{ 1-ab+b }+\frac{b }{ 1-ab+a } \leq 2$$$$ \frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 }+\frac{ab }{2+ab } \leq 1$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+ab }\leq \frac{5}{2}$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+2ab }\leq \frac{7}{3}$$$$\frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 } +\frac{ab }{1+ab }\leq \frac{7}{6 }$$
10 replies
sqing
Apr 25, 2025
sqing
5 hours ago
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Math Competitions
anishka14   8
N Apr 1, 2025 by nmlikesmath
Hi everyone!

So I am currently in grade 6, and if anyone could give any tips for getting high scores in math competition, that would be great!

I haven't been doing so well in AMC 8, and other competitions like Math Kangaroo, etc....

I feel like i'm stuck, so if anyone could give any resources that helped you learn and score better, could you share that with me?

Thank you so much!

( also how much time should i spend on math every day? )
8 replies
anishka14
Mar 29, 2025
nmlikesmath
Apr 1, 2025
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Math Competitions
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Reveal topic tags
AMC 8
Math Kangaroo
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anishka14
19 posts
anishka14
#1 h  Mar 29, 2025, 7:55 PM
Y by
Hi everyone!

So I am currently in grade 6, and if anyone could give any tips for getting high scores in math competition, that would be great!

I haven't been doing so well in AMC 8, and other competitions like Math Kangaroo, etc....

I feel like i'm stuck, so if anyone could give any resources that helped you learn and score better, could you share that with me?

Thank you so much!

( also how much time should i spend on math every day? )
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Dream9
82 posts
Dream9
#2 h  Mar 29, 2025, 8:06 PM
Y by
Just practice problems. A lot of problems. If your stuck then the worst thing to do is not do anything because you don't know what to do(if that makes sense). Just find problems and do them.
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anishka14
19 posts
anishka14
#3 h  Mar 29, 2025, 8:27 PM
Y by
Where could I find practice questions?
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eddie.li
32 posts
eddie.li
#4 h  Mar 29, 2025, 8:40 PM
Y by
You can find extra problems on Alcumus
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Dream9
82 posts
Dream9
#5 h  Mar 29, 2025, 10:00 PM
Y by
anishka14 wrote:
Where could I find practice questions?

Take past years amc 8s or math kangaroos. That's what I did. Or if you're finished with those, try to do some AOPS community-made mock tests for amc 8.
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iwillregretthisnamelater
18 posts
iwillregretthisnamelater
#6 h  Mar 30, 2025, 4:33 AM
Y by
Do you live in the US? Because then you’d be able to go to mathcounts
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anishka14
19 posts
anishka14
#7 h  Mar 30, 2025, 10:19 PM
Y by
No, i'm from Canada
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WiseHawkCuteFriendly
581 posts
WiseHawkCuteFriendly
#8 h  Mar 31, 2025, 1:43 AM
Y by
which pronvince?
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nmlikesmath
503 posts
nmlikesmath
#9 h  Apr 1, 2025, 6:25 AM
Y by
anishka14 wrote:
No, i'm from Canada

then i don't think u can do mathcounts sry
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