High School Basics Difficulty - Read BEFORE Posting Problems

MCrawford

Throughout the history of this site it has been difficult to keep the Getting Started Forum at the appropriate difficulty level. For this reason I have decided to create a guide to help users understand what material is appropriate for this forum.

First, an explanation of suitable problems:

$\bullet$ Most AoPS Volume 1 material. Volume 2 nearly always belongs in the Intermediate Topics forum and sometimes the Pre-Olympiad forum (non-trivial proofs).
$\bullet$ Topics from Algebra 1 which you generally do not see in Pre-Algebra
$\bullet$ Topics from Algebra 2 - through *very* basic trig
$\bullet$ Topics from High School Geoemtry
$\bullet$ Most AMC 10 problems (between the first 5 and the last 3-5)
$\bullet$ Harder MATHCOUNTS problems
$\bullet$ Harder AMC 8 problems
$\bullet$ The very simplest AIME problems are also reasonable
$\bullet$ Most problems from most local competitions
$\bullet$ The easier problems from current ARML (or about half of those from 10 to 25 year old ARML/NYSML contests)
$\bullet$ Most math league problems, though harder problems such as the last 3 or so individual problems on a Mandelbrot competition should go in Intermediate.

Note: If a problem involves a non-trivial step using more than one area of mathematics (algebra with number theory, geometry with serious algebra, etc.) then it does not belong in the Getting Started forum. Remember that the average score on a typical AIME is 2-3 problems. That's given the fact that AIME participants already score well on a qualifying exam. At most 1 in 20 AIME problems belong in this forum.

It is always better to err on the side of putting a problem in a more advanced forum than in a too easy forum.

Please do not post that a message belongs in a different topic. Moderators will move posts as appropriate.

To help clarify, here is a sample list of appropriate problems, though be aware that some of these are on the harder side of problems that should be posted in this forum. If a problem is harder than these, or requires more steps, it probably belongs in the Intermediate forum. Please do not work any of these problems in this thread so that we can keep it clean for discussion of appropriate difficulty. I will create a separate thread for each problem.

Algebra

$\bullet$ Factoring (other than monomial factoring), including roots and zeros

$\bullet$ Domain and range problems

$\bullet$ Graphing non-linear equations

$\bullet$ If $f(x) = \frac {x^{4} + x^{2}}{x + 1}$ , find $f(i)$ , where $i = \sqrt { - 1}$ .

$\bullet$ If $a = \log_{8}{225}$ and $b = \log_{2}{15}$ , then
$\text{(A)}\ a = b/2\ \ \ \ \text{(B)}\ a = 2b/3\ \ \ \ \text{(C)}\ a = b\ \ \ \ \text{(D)}\ b = a/2\ \ \ \ \text{(E)}\ a = 3b...$
$\bullet$ The sum of an infinite geometric series with common ratio $r$ such that $|r| < 1$ is 15, and the sum of the squares of the terms of this series is 45. The first term of the series is
$\text{(A)}\ 12\qquad\text{(B)}\ 10\qquad\text{(C)}\ 3\qquad\text{(D)}\ 3\qquad\text{(E)}\ 2$
Geometry

$\bullet$ A sphere is inside a circumscribing cube. What fraction of the volume of the cube is inside the sphere?
$\text{(A)}\ \frac {1}{2}\qquad\text{(B)}\ \frac {\pi}{3}\qquad\text{(C)}\ \frac {3}{4}\qquad\text{(D)}\ \frac {\pi}{4}\qquad\...$
$\bullet$ The point (1, 1, 1) is rotated $180^{\circ}$ about the $y$ -axis, then reflected through the $y$ - $z$ plane, reflected through the $x$ - $z$ plane, rotated $180^{\circ}$ abou the $y$ -axis, and reflected through the $x$ - $z$ plane. Find the coordinates of the point now.

$\bullet$ Let $ABC$ be an equilateral triangle of side $s$ . Construct a circular triangle as follows. Consider the circular arc from $A$ to $B$ with center of the arc at $C$ . Another arc is from $B$ to $C$ with center at $A$ . A third arc is from $C$ to $A$ with center at $B$ . Find the formula for the area of the circular triangle, i.e., the area enclosed by the three circular arcs.
$\text{(A)}\ \sqrt {3}s^{2}\qquad\text{(B)}\ \frac {\pi}{3}s^{2}\qquad\text{(C)}\ \left(\frac {\pi}{2} + \frac {\sqrt {3}}{2}\...$

$\text{(D)}\ \left(\frac {\pi}{2} - \frac {\sqrt {3}}{2}\right)s^{2}\qquad\text{(E) None of these answers}$
Counting

$\bullet$ How many positive integers less than 101 are multiples of either 5 or 7, but not both at once?

$\bullet$ How many positive integers less than 1991 are of the form $x^{n}$ , where $x\ge 1$ and $n\ge 2$ are integers?

$\bullet$ In how many ways can 3 identical algebra books and 3 identical geometry books be arranged on a shelf?

Probability

$\bullet$ Find the probability of flipping at least 4 heads in 6 tosses of a fair coin.

$\bullet$ A positive integer $n$ not exceeding 100 is chosen in such a way that if $n\le 50$ , then the probability of choosing $n$ is $p$ , and if $n > 50$ , then the probability of choosing $n$ is $3p$ . The probability that a perfect square is chosen is
$\text{(A)}\ .05\qquad\text{(B)}\ .065\qquad\text{(C)}\ .08\qquad\text{(D)}\ .09\qquad\text{(E)}\ .1$
$\bullet$ Rocky and Bullwinkle are playing Risk. Rocky rolls one six-sided die, while Bullwinkle rolls two of them. What is the probability that Rocky's roll is as high as Bullwinkle's largest number?

Number Theory

$\bullet$ The number $10!$ , when written in the base 12 system, ends with exactly how many zeroes?
$\text{(A)}\ 1\qquad\text{(B)}\ 2\qquad\text{(C)}\ 3\qquad\text{(D)}\ 4\qquad\text{(E)}\ 5$
$\bullet$ Find the greatest integer that will divide 13511, 13903, and 14589 and leave the same remainder.

$\bullet$ The product of any two of the positive integers 30, 72, and $N$ is divisible by the third. What is the smallest possible value of $N$ ?

**Posted:** Fri Apr 08, 2005 10:50 am

MCrawford

Recently I have moved a few proof-related posts from this forum. Unless the proofs are extremely elementary, they do not belong here.

I have begun banning users from specific forums in which they post off-difficulty problems. I will generally give warnings, but if a student is posting Olympiad level problems in general, I don't mind simply banning them and waiting for a request to return to this forum because they should be focusing on other forums to begin with.

**Posted:** Wed Aug 10, 2005 12:54 pm

beans

Would it be possible to give any non-Americans an indication on the level of the education system in America? I am ignorant, for example of how old people in high school tend to be. Ninja

**Posted:** Sun Dec 30, 2007 7:31 pm

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10000th User

The first post is a good indication of the level and topics presented normally in a typical high school in America, and this same post is a good example what type of problems and their difficulty that fits in this subforum's category. The age can vary slightly but we all know the ages aren't much different from country to country, usually 13-18, excluding exceptional cases.

**Posted:** Mon Dec 31, 2007 9:00 am

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Disclaimer: I'll revive old threads if: 1) something ambiguous in the solution or wrong argument, 2) no solution, 3) I got new insight to input.

levans

Please take the time to review to level of difficulty for the forum. We have had to move far too many posts to different forums lately.

**Posted:** Tue Apr 29, 2008 8:15 am

moogra

Actually the majority of problems posted here are above the level. The level for some meet intermediate topics level, but are not moved there since a higher level of expectation is in intermediate level now. I think we should just change the rules a bit and allow more difficult material.

**Posted:** Tue Apr 29, 2008 8:16 pm

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10000th User

**Posted:** Wed Apr 30, 2008 11:24 am

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$\mathrm{Hom}(\mathbb{Z},\mathbb{Z})\cong\mathbb{Z}$
Disclaimer: I'll revive old threads if: 1) something ambiguous in the solution or wrong argument, 2) no solution, 3) I got new insight to input.

levans

Bump because we are getting way too many intermediate level problems in the forum.

**Posted:** Fri Jul 04, 2008 10:19 pm

Valentin Vornicu

We do need a couple of extra moderators for this forum to help us keep the problem level where it should be, as described in the first couple of posts. If you would like to volunteer, please send me a PM.

**Posted:** Mon Jul 13, 2009 12:34 pm

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We all use math everyday: to forecast weather, to tell time, to handle money; we also use math to analyze crime, reveal patterns, predict behavior. Using numbers we can solve the biggest mysteries we know.

myyellowducky82

Valentin: Should there be specific qualifications we should have before PM-ing you? I don't want to PM you (or anyone else to) who are a spammer and do not deserve to be a moderator.
Also, do you already have to be a moderator to sign up? Or can anyone PM you for this?

Thanks! Smile

**Posted:** Tue Jul 14, 2009 2:34 pm

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Valentin Vornicu

It's done for now, we don't need any more Moderators. When the time comes again that we would need any, I will make a post here, as before. So no more PMs please.

**Posted:** Tue Jul 14, 2009 3:02 pm

_________________
We all use math everyday: to forecast weather, to tell time, to handle money; we also use math to analyze crime, reveal patterns, predict behavior. Using numbers we can solve the biggest mysteries we know.