https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Xpmath&feedformat=atomAoPS Wiki - User contributions [en]2021-06-22T17:01:47ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=32961User:Xpmath2009-11-21T00:11:11Z<p>Xpmath: Undo revision 32960 by Thunder365 (Talk)</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
<br />
Moems: - 5 - - -<br />
<br />
USAMTS: 17 - 17 10 <br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, <br />
<br />
1st state written, 1st state bracket countdown, 9th state team.<br />
<br />
27th nats written, 17th place team<br />
<br />
144 AMC 10A<br />
<br />
109.5 AMC 12B<br />
<br />
6 AIME II<br />
<br />
<br />
<br />
==Goals for 9th grade==<br />
MOPPPPP<br />
<br />
== Stuff to do during summer==<br />
Sleep.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=32345User:Xpmath2009-07-16T16:15:33Z<p>Xpmath: /* Goals for 9th grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
<br />
Moems: - 5 - - -<br />
<br />
USAMTS: 17 - 17 10 <br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, <br />
<br />
1st state written, 1st state bracket countdown, 9th state team.<br />
<br />
27th nats written, 17th place team<br />
<br />
144 AMC 10A<br />
<br />
109.5 AMC 12B<br />
<br />
6 AIME II<br />
<br />
<br />
<br />
==Goals for 9th grade==<br />
MOPPPPP<br />
<br />
== Stuff to do during summer==<br />
Sleep.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1965_IMO_Problems/Problem_6&diff=323421965 IMO Problems/Problem 62009-07-16T15:45:31Z<p>Xpmath: Created page with '== Problem == In a plane a set of <math>n</math> points (<math>n\geq 3</math>) is given. Each pair of points is connected by a segment. Let <math>d</math> be the length of the lo…'</p>
<hr />
<div>== Problem ==<br />
In a plane a set of <math>n</math> points (<math>n\geq 3</math>) is given. Each pair of points is connected by a segment. Let <math>d</math> be the length of the longest of these segments. We define a diameter of the set to be any connecting segment of length <math>d</math>. Prove that the number of diameters of the given set is at most <math>n</math>.<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1965_IMO_Problems/Problem_5&diff=323411965 IMO Problems/Problem 52009-07-16T15:44:58Z<p>Xpmath: Created page with '== Problem == Consider <math>\triangle OAB</math> with acute angle <math>AOB</math>. Through a point <math>M \neq O</math> perpendiculars are drawn to <math>OA</math> and <math>O…'</p>
<hr />
<div>== Problem ==<br />
Consider <math>\triangle OAB</math> with acute angle <math>AOB</math>. Through a point <math>M \neq O</math> perpendiculars are drawn to <math>OA</math> and <math>OB</math>, the feet of which are <math>P</math> and <math>Q</math> respectively. The point of intersection of the altitudes of <math>\triangle OPQ</math> is <math>H</math>. What is the locus of <math>H</math> if <math>M</math> is permitted to range over (a) the side <math>AB</math>, (b) the interior of <math>\triangle OAB</math>?<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1965_IMO_Problems/Problem_4&diff=323401965 IMO Problems/Problem 42009-07-16T15:44:26Z<p>Xpmath: Created page with '== Problem == Find all sets of four real numbers <math>x_1</math>, <math>x_2</math>, <math>x_3</math>, <math>x_4</math> such that the sum of any one and the product of the other …'</p>
<hr />
<div>== Problem ==<br />
Find all sets of four real numbers <math>x_1</math>, <math>x_2</math>, <math>x_3</math>, <math>x_4</math> such that the sum of any one and the product of the other three is equal to <math>2</math>.<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1965_IMO_Problems/Problem_3&diff=323391965 IMO Problems/Problem 32009-07-16T15:43:53Z<p>Xpmath: Created page with '== Problem == Given the tetrahedron <math>ABCD</math> whose edges <math>AB</math> and <math>CD</math> have lengths <math>a</math> and <math>b</math> respectively. The distance be…'</p>
<hr />
<div>== Problem ==<br />
Given the tetrahedron <math>ABCD</math> whose edges <math>AB</math> and <math>CD</math> have lengths <math>a</math> and <math>b</math> respectively. The distance between the skew lines <math>AB</math> and <math>CD</math> is <math>d</math>, and the angle between them is <math>\omega </math>. Tetrahedron <math>ABCD</math> is divided into two solids by plane <math>\varepsilon </math>, parallel to lines <math>AB</math> and <math>CD</math>. The ratio of the distances of <math>\varepsilon </math> from <math>AB</math> and <math>CD</math> is equal to <math>k</math>. Compute the ratio of the volumes of the two solids obtained.<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1965_IMO_Problems/Problem_2&diff=323381965 IMO Problems/Problem 22009-07-16T15:43:14Z<p>Xpmath: Created page with '== Problem == Consider the system of equations <cmath>a_{11}x_1 + a_{12}x_2 + a_{13}x_3 = 0</cmath> <cmath>a_{21}x_1 + a_{22}x_2 + a_{23}x_3 = 0</cmath> <cmath>a_{31}x_1 + a_{32}…'</p>
<hr />
<div>== Problem ==<br />
Consider the system of equations<br />
<cmath>a_{11}x_1 + a_{12}x_2 + a_{13}x_3 = 0</cmath><br />
<cmath>a_{21}x_1 + a_{22}x_2 + a_{23}x_3 = 0</cmath><br />
<cmath>a_{31}x_1 + a_{32}x_2 + a_{33}x_3 = 0</cmath><br />
with unknowns <math>x_1</math>, <math>x_2</math>, <math>x_3</math>. The coefficients satisfy the conditions:<br />
<br />
(a) <math>a_{11}</math>, <math>a_{22}</math>, <math>a_{33}</math> are positive numbers;<br />
<br />
(b) the remaining coefficients are negative numbers;<br />
<br />
(c) in each equation, the sum of the coefficients is positive.<br />
<br />
Prove that the given system has only the solution <math>x_1 = x_2 = x_3 = 0</math>.<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1965_IMO_Problems/Problem_1&diff=323371965 IMO Problems/Problem 12009-07-16T15:42:21Z<p>Xpmath: </p>
<hr />
<div>== Problem ==<br />
Determine all values <math>x</math> in the interval <math>0\leq x\leq 2\pi </math> which satisfy the inequality<br />
<cmath>2\cos x \leq \left| \sqrt{1+\sin 2x} - \sqrt{1-\sin 2x } \right| \leq \sqrt{2}.</cmath><br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1965_IMO_Problems/Problem_1&diff=323361965 IMO Problems/Problem 12009-07-16T15:41:35Z<p>Xpmath: Created page with '== Problem == Determine all values <math>x</math> in the interval <math>0\leq x\leq 2\pi </math> which satisfy the inequality <cmath>2\cos x \leq \left| \sqrt{1+\sin 2x} - \sqrt{…'</p>
<hr />
<div>== Problem ==<br />
Determine all values <math>x</math> in the interval <math>0\leq x\leq 2\pi </math> which satisfy the inequality<br />
<cmath>2\cos x \leq \left| \sqrt{1+\sin 2x} - \sqrt{1-\sin 2x } \right| \leq \sqrt{2}.</cmath><br />
<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_6&diff=323351964 IMO Problems/Problem 62009-07-16T15:40:00Z<p>Xpmath: /* Problem */</p>
<hr />
<div>== Problem ==<br />
In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0</math> are drawn through <math>A,B</math> and <math>C</math>. These lines intersect the planes <math>BCD, CAD</math> and <math>ABD</math> in points <math>A_1, B_1,</math> and <math>C_1</math>, respectively. Prove that the volume of <math>ABCD</math> is one third the volume of <math>A_1B_1C_1D_0</math>. Is the result true if point <math>D_o</math> is selected anywhere within <math>\triangle ABC</math>?<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_6&diff=323341964 IMO Problems/Problem 62009-07-16T15:39:48Z<p>Xpmath: /* Solution */</p>
<hr />
<div>== Problem ==<br />
In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0</math> are drawn through <math>A,B</math> and <math>C</math>. These lines intersect the planes <math>BCD, CAD</math> and <math>ABD</math> in points <math>A_1, B_1,</math> and <math>C_1</math>, respectively. Prove that the volume of <math>ABCD</math> is one third the volume of <math>A_1B_1C_1D_0</math>. Is the result true if point <math>D_o</math> is selected anywhere within <math>\triangle ABC</math><br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_5&diff=323331964 IMO Problems/Problem 52009-07-16T15:39:12Z<p>Xpmath: /* Solution */</p>
<hr />
<div>== Problem ==<br />
Suppose five points in a plane are situated so that no two of the straight lines<br />
joining them are parallel, perpendicular, or coincident. From each point perpendiculars<br />
are drawn to all the lines joining the other four points. Determine<br />
the maximum number of intersections that these perpendiculars can have.<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_4&diff=323321964 IMO Problems/Problem 42009-07-16T15:38:48Z<p>Xpmath: /* Solution */</p>
<hr />
<div>== Problem ==<br />
Seventeen people correspond by mail with one another - each one with all<br />
the rest. In their letters only three different topics are discussed. Each pair<br />
of correspondents deals with only one of these topics. Prove that there are<br />
at least three people who write to each other about the same topic.<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_3&diff=323311964 IMO Problems/Problem 32009-07-16T15:38:23Z<p>Xpmath: /* Solution */</p>
<hr />
<div>== Problem ==<br />
A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Each of these tangents cuts off a triangle from <math>\triangle ABC</math>. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).<br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_2&diff=323301964 IMO Problems/Problem 22009-07-16T15:37:38Z<p>Xpmath: /* Solution */</p>
<hr />
<div>== Problem ==<br />
Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <br />
<br />
<cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath><br />
<br />
== Solution ==<br />
{{solution}}</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_6&diff=323281964 IMO Problems/Problem 62009-07-15T23:36:00Z<p>Xpmath: Created page with '== Problem == In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0<…'</p>
<hr />
<div>== Problem ==<br />
In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0</math> are drawn through <math>A,B</math> and <math>C</math>. These lines intersect the planes <math>BCD, CAD</math> and <math>ABD</math> in points <math>A_1, B_1,</math> and <math>C_1</math>, respectively. Prove that the volume of <math>ABCD</math> is one third the volume of <math>A_1B_1C_1D_0</math>. Is the result true if point <math>D_o</math> is selected anywhere within <math>\triangle ABC</math><br />
<br />
== Solution ==</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_5&diff=323271964 IMO Problems/Problem 52009-07-15T23:35:29Z<p>Xpmath: Created page with '== Problem == Suppose five points in a plane are situated so that no two of the straight lines joining them are parallel, perpendicular, or coincident. From each point perpendicu…'</p>
<hr />
<div>== Problem ==<br />
Suppose five points in a plane are situated so that no two of the straight lines<br />
joining them are parallel, perpendicular, or coincident. From each point perpendiculars<br />
are drawn to all the lines joining the other four points. Determine<br />
the maximum number of intersections that these perpendiculars can have.<br />
<br />
== Solution ==</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_4&diff=323261964 IMO Problems/Problem 42009-07-15T23:34:45Z<p>Xpmath: Created page with '== Problem == Seventeen people correspond by mail with one another - each one with all the rest. In their letters only three different topics are discussed. Each pair of correspo…'</p>
<hr />
<div>== Problem ==<br />
Seventeen people correspond by mail with one another - each one with all<br />
the rest. In their letters only three different topics are discussed. Each pair<br />
of correspondents deals with only one of these topics. Prove that there are<br />
at least three people who write to each other about the same topic.<br />
<br />
== Solution ==</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_3&diff=323251964 IMO Problems/Problem 32009-07-15T23:34:03Z<p>Xpmath: Created page with '== Problem == A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Eac…'</p>
<hr />
<div>== Problem ==<br />
A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Each of these tangents cuts off a triangle from <math>\triangle ABC</math>. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).<br />
<br />
== Solution ==</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_2&diff=323241964 IMO Problems/Problem 22009-07-15T23:33:05Z<p>Xpmath: Created page with '== Problem == Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath> == Solution =='</p>
<hr />
<div>== Problem ==<br />
Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <br />
<br />
<cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath><br />
<br />
== Solution ==</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems&diff=323231964 IMO Problems2009-07-15T23:31:29Z<p>Xpmath: Undo revision 32320 by Xpmath (Talk)</p>
<hr />
<div>Problems of the 6th [[IMO]] 1964 in USSR.<br />
<br />
== Day I ==<br />
<br />
=== Problem 1 ===<br />
(a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>.<br />
<br />
(b) Prove that there is no positive integer <math>n</math> for which <math>2^n+1</math> is divisible by <math>7</math>.<br />
<br />
[[1964 IMO Problems/Problem 1 | Solution]]<br />
<br />
=== Problem 2 ===<br />
Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <br />
<br />
<cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath><br />
<br />
[[1964 IMO Problems/Problem 2 | Solution]]<br />
<br />
=== Problem 3 ===<br />
A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Each of these tangents cuts off a triangle from <math>\triangle ABC</math>. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).<br />
<br />
[[1964 IMO Problems/Problem 3 | Solution]]<br />
<br />
== Day II ==<br />
<br />
=== Problem 4 ===<br />
Seventeen people correspond by mail with one another - each one with all<br />
the rest. In their letters only three different topics are discussed. Each pair<br />
of correspondents deals with only one of these topics. Prove that there are<br />
at least three people who write to each other about the same topic.<br />
<br />
[[1964 IMO Problems/Problem 4 | Solution]]<br />
<br />
=== Problem 5 ===<br />
Suppose five points in a plane are situated so that no two of the straight lines<br />
joining them are parallel, perpendicular, or coincident. From each point perpendiculars<br />
are drawn to all the lines joining the other four points. Determine<br />
the maximum number of intersections that these perpendiculars can have.<br />
<br />
[[1964 IMO Problems/Problem 5 | Solution]]<br />
<br />
=== Problem 6 ===<br />
In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0</math> are drawn through <math>A,B</math> and <math>C</math>. These lines intersect the planes <math>BCD, CAD</math> and <math>ABD</math> in points <math>A_1, B_1,</math> and <math>C_1</math>, respectively. Prove that the volume of <math>ABCD</math> is one third the volume of <math>A_1B_1C_1D_0</math>. Is the result true if point <math>D_o</math> is selected anywhere within <math>\triangle ABC</math><br />
<br />
[[1964 IMO Problems/Problem 6 | Solution]]<br />
<br />
== Resources ==<br />
* [[1964 IMO]]<br />
* [http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=16&year=1964 IMO 1964 Problems on the Resources page]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems&diff=323221964 IMO Problems2009-07-15T23:31:17Z<p>Xpmath: Undo revision 32321 by Xpmath (Talk)</p>
<hr />
<div>Problems of the 6th [[IMO]] 1964 in USSR.<br />
<br />
== Day I ==<br />
<br />
== Problem 1 ==<br />
(a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>.<br />
<br />
(b) Prove that there is no positive integer <math>n</math> for which <math>2^n+1</math> is divisible by <math>7</math>.<br />
<br />
[[1964 IMO Problems/Problem 1 | Solution]]<br />
<br />
== Problem 2 ==<br />
Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <br />
<br />
<cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath><br />
<br />
[[1964 IMO Problems/Problem 2 | Solution]]<br />
<br />
== Problem 3 ==<br />
A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Each of these tangents cuts off a triangle from <math>\triangle ABC</math>. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).<br />
<br />
[[1964 IMO Problems/Problem 3 | Solution]]<br />
<br />
== Day II ==<br />
<br />
=== Problem 4 ===<br />
Seventeen people correspond by mail with one another - each one with all<br />
the rest. In their letters only three different topics are discussed. Each pair<br />
of correspondents deals with only one of these topics. Prove that there are<br />
at least three people who write to each other about the same topic.<br />
<br />
[[1964 IMO Problems/Problem 4 | Solution]]<br />
<br />
=== Problem 5 ===<br />
Suppose five points in a plane are situated so that no two of the straight lines<br />
joining them are parallel, perpendicular, or coincident. From each point perpendiculars<br />
are drawn to all the lines joining the other four points. Determine<br />
the maximum number of intersections that these perpendiculars can have.<br />
<br />
[[1964 IMO Problems/Problem 5 | Solution]]<br />
<br />
=== Problem 6 ===<br />
In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0</math> are drawn through <math>A,B</math> and <math>C</math>. These lines intersect the planes <math>BCD, CAD</math> and <math>ABD</math> in points <math>A_1, B_1,</math> and <math>C_1</math>, respectively. Prove that the volume of <math>ABCD</math> is one third the volume of <math>A_1B_1C_1D_0</math>. Is the result true if point <math>D_o</math> is selected anywhere within <math>\triangle ABC</math><br />
<br />
[[1964 IMO Problems/Problem 6 | Solution]]<br />
<br />
== Resources ==<br />
* [[1964 IMO]]<br />
* [http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=16&year=1964 IMO 1964 Problems on the Resources page]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems&diff=323211964 IMO Problems2009-07-15T23:30:21Z<p>Xpmath: /* Day II */</p>
<hr />
<div>Problems of the 6th [[IMO]] 1964 in USSR.<br />
<br />
== Day I ==<br />
<br />
== Problem 1 ==<br />
(a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>.<br />
<br />
(b) Prove that there is no positive integer <math>n</math> for which <math>2^n+1</math> is divisible by <math>7</math>.<br />
<br />
[[1964 IMO Problems/Problem 1 | Solution]]<br />
<br />
== Problem 2 ==<br />
Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <br />
<br />
<cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath><br />
<br />
[[1964 IMO Problems/Problem 2 | Solution]]<br />
<br />
== Problem 3 ==<br />
A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Each of these tangents cuts off a triangle from <math>\triangle ABC</math>. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).<br />
<br />
[[1964 IMO Problems/Problem 3 | Solution]]<br />
<br />
== Day II ==<br />
<br />
== Problem 4 ==<br />
Seventeen people correspond by mail with one another - each one with all<br />
the rest. In their letters only three different topics are discussed. Each pair<br />
of correspondents deals with only one of these topics. Prove that there are<br />
at least three people who write to each other about the same topic.<br />
<br />
[[1964 IMO Problems/Problem 4 | Solution]]<br />
<br />
== Problem 5 ==<br />
Suppose five points in a plane are situated so that no two of the straight lines<br />
joining them are parallel, perpendicular, or coincident. From each point perpendiculars<br />
are drawn to all the lines joining the other four points. Determine<br />
the maximum number of intersections that these perpendiculars can have.<br />
<br />
[[1964 IMO Problems/Problem 5 | Solution]]<br />
<br />
== Problem 6 ==<br />
In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0</math> are drawn through <math>A,B</math> and <math>C</math>. These lines intersect the planes <math>BCD, CAD</math> and <math>ABD</math> in points <math>A_1, B_1,</math> and <math>C_1</math>, respectively. Prove that the volume of <math>ABCD</math> is one third the volume of <math>A_1B_1C_1D_0</math>. Is the result true if point <math>D_o</math> is selected anywhere within <math>\triangle ABC</math><br />
<br />
[[1964 IMO Problems/Problem 6 | Solution]]<br />
<br />
== Resources ==<br />
* [[1964 IMO]]<br />
* [http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=16&year=1964 IMO 1964 Problems on the Resources page]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems&diff=323201964 IMO Problems2009-07-15T23:29:53Z<p>Xpmath: /* Day I */</p>
<hr />
<div>Problems of the 6th [[IMO]] 1964 in USSR.<br />
<br />
== Day I ==<br />
<br />
== Problem 1 ==<br />
(a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>.<br />
<br />
(b) Prove that there is no positive integer <math>n</math> for which <math>2^n+1</math> is divisible by <math>7</math>.<br />
<br />
[[1964 IMO Problems/Problem 1 | Solution]]<br />
<br />
== Problem 2 ==<br />
Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <br />
<br />
<cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath><br />
<br />
[[1964 IMO Problems/Problem 2 | Solution]]<br />
<br />
== Problem 3 ==<br />
A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Each of these tangents cuts off a triangle from <math>\triangle ABC</math>. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).<br />
<br />
[[1964 IMO Problems/Problem 3 | Solution]]<br />
<br />
== Day II ==<br />
<br />
=== Problem 4 ===<br />
Seventeen people correspond by mail with one another - each one with all<br />
the rest. In their letters only three different topics are discussed. Each pair<br />
of correspondents deals with only one of these topics. Prove that there are<br />
at least three people who write to each other about the same topic.<br />
<br />
[[1964 IMO Problems/Problem 4 | Solution]]<br />
<br />
=== Problem 5 ===<br />
Suppose five points in a plane are situated so that no two of the straight lines<br />
joining them are parallel, perpendicular, or coincident. From each point perpendiculars<br />
are drawn to all the lines joining the other four points. Determine<br />
the maximum number of intersections that these perpendiculars can have.<br />
<br />
[[1964 IMO Problems/Problem 5 | Solution]]<br />
<br />
=== Problem 6 ===<br />
In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0</math> are drawn through <math>A,B</math> and <math>C</math>. These lines intersect the planes <math>BCD, CAD</math> and <math>ABD</math> in points <math>A_1, B_1,</math> and <math>C_1</math>, respectively. Prove that the volume of <math>ABCD</math> is one third the volume of <math>A_1B_1C_1D_0</math>. Is the result true if point <math>D_o</math> is selected anywhere within <math>\triangle ABC</math><br />
<br />
[[1964 IMO Problems/Problem 6 | Solution]]<br />
<br />
== Resources ==<br />
* [[1964 IMO]]<br />
* [http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=16&year=1964 IMO 1964 Problems on the Resources page]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_1&diff=323191964 IMO Problems/Problem 12009-07-15T23:29:29Z<p>Xpmath: /* Solution */</p>
<hr />
<div>== Problem ==<br />
(a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>.<br />
<br />
(b) Prove that there is no positive integer <math>n</math> for which <math>2^n+1</math> is divisible by <math>7</math>.<br />
<br />
== Solution ==<br />
We see that <math>2^n</math> is equivalent to <math>2, 4,</math> and <math>1</math> <math>\pmod{7}</math> for <math>n</math> congruent to <math>1</math>, <math>2</math>, and <math>0</math> <math>\pmod{3}</math>, respectively.<br />
<br />
(a) From the statement above, only <math>n</math> divisible by <math>3</math> work.<br />
<br />
(b) Again from the statement above, <math>2^n</math> can never be congruent to <math>-1</math> <math>\pmod{7}</math>, so there are no solutions for <math>n</math>.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems/Problem_1&diff=323181964 IMO Problems/Problem 12009-07-15T23:16:55Z<p>Xpmath: Created page with '== Problem == (a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>. (b) Prove that there is no positive integer <math>n</mat…'</p>
<hr />
<div>== Problem ==<br />
(a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>.<br />
<br />
(b) Prove that there is no positive integer <math>n</math> for which <math>2^n+1</math> is divisible by <math>7</math>.<br />
<br />
== Solution ==</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=1964_IMO_Problems&diff=323171964 IMO Problems2009-07-15T23:13:04Z<p>Xpmath: Created page with 'Problems of the 6th IMO 1964 in USSR. == Day I == === Problem 1 === (a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math…'</p>
<hr />
<div>Problems of the 6th [[IMO]] 1964 in USSR.<br />
<br />
== Day I ==<br />
<br />
=== Problem 1 ===<br />
(a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>.<br />
<br />
(b) Prove that there is no positive integer <math>n</math> for which <math>2^n+1</math> is divisible by <math>7</math>.<br />
<br />
[[1964 IMO Problems/Problem 1 | Solution]]<br />
<br />
=== Problem 2 ===<br />
Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <br />
<br />
<cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath><br />
<br />
[[1964 IMO Problems/Problem 2 | Solution]]<br />
<br />
=== Problem 3 ===<br />
A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Each of these tangents cuts off a triangle from <math>\triangle ABC</math>. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).<br />
<br />
[[1964 IMO Problems/Problem 3 | Solution]]<br />
<br />
== Day II ==<br />
<br />
=== Problem 4 ===<br />
Seventeen people correspond by mail with one another - each one with all<br />
the rest. In their letters only three different topics are discussed. Each pair<br />
of correspondents deals with only one of these topics. Prove that there are<br />
at least three people who write to each other about the same topic.<br />
<br />
[[1964 IMO Problems/Problem 4 | Solution]]<br />
<br />
=== Problem 5 ===<br />
Suppose five points in a plane are situated so that no two of the straight lines<br />
joining them are parallel, perpendicular, or coincident. From each point perpendiculars<br />
are drawn to all the lines joining the other four points. Determine<br />
the maximum number of intersections that these perpendiculars can have.<br />
<br />
[[1964 IMO Problems/Problem 5 | Solution]]<br />
<br />
=== Problem 6 ===<br />
In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0</math> are drawn through <math>A,B</math> and <math>C</math>. These lines intersect the planes <math>BCD, CAD</math> and <math>ABD</math> in points <math>A_1, B_1,</math> and <math>C_1</math>, respectively. Prove that the volume of <math>ABCD</math> is one third the volume of <math>A_1B_1C_1D_0</math>. Is the result true if point <math>D_o</math> is selected anywhere within <math>\triangle ABC</math><br />
<br />
[[1964 IMO Problems/Problem 6 | Solution]]<br />
<br />
== Resources ==<br />
* [[1964 IMO]]<br />
* [http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=16&year=1964 IMO 1964 Problems on the Resources page]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=32246User:Xpmath2009-07-05T13:52:04Z<p>Xpmath: /* Stuff to do during summer */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
<br />
Moems: - 5 - - -<br />
<br />
USAMTS: 17 - 17 10 <br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, <br />
<br />
1st state written, 1st state bracket countdown, 9th state team.<br />
<br />
27th nats written, 17th place team<br />
<br />
144 AMC 10A<br />
<br />
109.5 AMC 12B<br />
<br />
6 AIME II<br />
<br />
<br />
<br />
==Goals for 9th grade==<br />
Make USAMO, Make Red MOP, top 10 MMPC, make CMO, 8+ ARML, Silver USAMTS<br />
<br />
[[Media:Example.ogg]]== Stuff to do during summer==<br />
Sleep.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:5849206328x&diff=32245User:5849206328x2009-07-05T13:51:30Z<p>Xpmath: </p>
<hr />
<div>Instead of talking about myself, I'll find a better use of this page.<br />
<br />
No u wont. Talk.<br />
<br />
Woah I want to talk.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=32081User:Xpmath2009-06-07T16:15:09Z<p>Xpmath: /* To Do List */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
<br />
Moems: - 5 - - -<br />
<br />
USAMTS: 17 - 17 10 <br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, <br />
<br />
1st state written, 1st state bracket countdown, 9th state team.<br />
<br />
27th nats written, 17th place team<br />
<br />
144 AMC 10A<br />
<br />
109.5 AMC 12B<br />
<br />
6 AIME II<br />
<br />
<br />
<br />
==Goals for 9th grade==<br />
Make USAMO, Make Red MOP, top 10 MMPC, make CMO, 8+ ARML, Silver USAMTS<br />
<br />
== Stuff to do during summer==<br />
Finish Volume 2, solve problems</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=32080User:Xpmath2009-06-07T16:14:34Z<p>Xpmath: /* Minor Goals for 8th grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
<br />
Moems: - 5 - - -<br />
<br />
USAMTS: 17 - 17 10 <br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, <br />
<br />
1st state written, 1st state bracket countdown, 9th state team.<br />
<br />
27th nats written, 17th place team<br />
<br />
144 AMC 10A<br />
<br />
109.5 AMC 12B<br />
<br />
6 AIME II<br />
<br />
<br />
<br />
==Goals for 9th grade==<br />
Make USAMO, Make Red MOP, top 10 MMPC, make CMO, 8+ ARML, Silver USAMTS<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=32079User:Xpmath2009-06-07T16:13:10Z<p>Xpmath: /* Major Goals for 8th Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
<br />
Moems: - 5 - - -<br />
<br />
USAMTS: 17 - 17 10 <br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, <br />
<br />
1st state written, 1st state bracket countdown, 9th state team.<br />
<br />
27th nats written, 17th place team<br />
<br />
144 AMC 10A<br />
<br />
109.5 AMC 12B<br />
<br />
6 AIME II<br />
<br />
<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid (didn't take), 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer (didn't take)<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=32078User:Xpmath2009-06-07T16:12:51Z<p>Xpmath: /* Eighth Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
<br />
Moems: - 5 - - -<br />
<br />
USAMTS: 17 - 17 10 <br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, <br />
<br />
1st state written, 1st state bracket countdown, 9th state team.<br />
<br />
27th nats written, 17th place team<br />
<br />
144 AMC 10A<br />
<br />
109.5 AMC 12B<br />
<br />
6 AIME II<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown ('''nope, 27th'''), 144+ AMC 10A-'''yes (144),''' 132+ AMC 12B-'''no(109.5),''' 8+ AIME II-'''no (6),''' 6+ USAMO '''(didn't qualify'''), 6+ ARML ('''not going),''' 60+ USAMTS-'''no (my second round was lost, which probably would've gotten 16+ so I would've gotten 60+ since I had 44 due to being very lazy on round 4)'''<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid (didn't take), 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer (didn't take)<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=32077User:Xpmath2009-06-07T16:11:05Z<p>Xpmath: /* Major Goals for 8th Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
Moems: - 5 - - -<br />
USAMTS: 17 TBD 17 dunno (since I only needed like ~10 on round 4, I decided to only do three problems, but made very stupid mistakes on two, so I'll probably miss bronze by a tiny bit)<br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, 1st state written, 1st state bracket countdown, 9th state team.<br />
I'm going to Nats for the second year in a row. Yay.<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown ('''nope, 27th'''), 144+ AMC 10A-'''yes (144),''' 132+ AMC 12B-'''no(109.5),''' 8+ AIME II-'''no (6),''' 6+ USAMO '''(didn't qualify'''), 6+ ARML ('''not going),''' 60+ USAMTS-'''no (my second round was lost, which probably would've gotten 16+ so I would've gotten 60+ since I had 44 due to being very lazy on round 4)'''<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid (didn't take), 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer (didn't take)<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=31184User:Xpmath2009-04-09T17:40:54Z<p>Xpmath: /* Major Goals for 8th Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
Moems: - 5 - - -<br />
USAMTS: 17 TBD 17 dunno (since I only needed like ~10 on round 4, I decided to only do three problems, but made very stupid mistakes on two, so I'll probably miss bronze by a tiny bit)<br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, 1st state written, 1st state bracket countdown, 9th state team.<br />
I'm going to Nats for the second year in a row. Yay.<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10A-yes (144), 132+ AMC 12B-no(109.5), 8+ AIME II-no (6), 6+ USAMO, 6+ ARML (not going), 60+ USAMTS-no (my second round was lost, which probably would've gotten 16+ so I would've gotten 60+ since I had 44 due to being very lazy on round 4)<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid (didn't take), 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer (didn't take)<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=31107User:Xpmath2009-04-05T01:19:23Z<p>Xpmath: /* Major Goals for 8th Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
Moems: - 5 - - -<br />
USAMTS: 17 TBD 17 dunno (since I only needed like ~10 on round 4, I decided to only do three problems, but made very stupid mistakes on two, so I'll probably miss bronze by a tiny bit)<br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, 1st state written, 1st state bracket countdown, 9th state team.<br />
I'm going to Nats for the second year in a row. Yay.<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10A-yes (144), 132+ AMC 12B-no(109.5), 8+ AIME II-no (6), 6+ USAMO, 6+ ARML (not going), 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid (didn't take), 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer (didn't take)<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=31106User:Xpmath2009-04-05T01:19:04Z<p>Xpmath: /* Minor Goals for 8th grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
Moems: - 5 - - -<br />
USAMTS: 17 TBD 17 dunno (since I only needed like ~10 on round 4, I decided to only do three problems, but made very stupid mistakes on two, so I'll probably miss bronze by a tiny bit)<br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, 1st state written, 1st state bracket countdown, 9th state team.<br />
I'm going to Nats for the second year in a row. Yay.<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10-yes (144), 132+ AMC 12-no(109.5), 8+ AIME-no (6), 6+ USAMO, 6+ ARML (not going), 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid (didn't take), 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer (didn't take)<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=31105User:Xpmath2009-04-05T01:18:48Z<p>Xpmath: /* Major Goals for 8th Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
Moems: - 5 - - -<br />
USAMTS: 17 TBD 17 dunno (since I only needed like ~10 on round 4, I decided to only do three problems, but made very stupid mistakes on two, so I'll probably miss bronze by a tiny bit)<br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, 1st state written, 1st state bracket countdown, 9th state team.<br />
I'm going to Nats for the second year in a row. Yay.<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10-yes (144), 132+ AMC 12-no(109.5), 8+ AIME-no (6), 6+ USAMO, 6+ ARML (not going), 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=30727User:Xpmath2009-03-15T16:48:14Z<p>Xpmath: /* Eighth Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
So I didn't take very many competitions.<br />
Mandelbrot: - 7 11 - -<br />
Moems: - 5 - - -<br />
USAMTS: 17 TBD 17 dunno (since I only needed like ~10 on round 4, I decided to only do three problems, but made very stupid mistakes on two, so I'll probably miss bronze by a tiny bit)<br />
<br />
Mathcounts: 1st chapter written, 1st chapter bracket countdown, 3rd chapter team, 1st state written, 1st state bracket countdown, 9th state team.<br />
I'm going to Nats for the second year in a row. Yay.<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10-yep, 132+ AMC 12-no, but didn't expect to, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=30520User:Xpmath2009-02-27T20:32:25Z<p>Xpmath: /* Minor Goals for 8th grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
Bad year for me somewhat, so far. 7/14 on round 2 on Mandelbrot. You know what? I'm not going to say I made stupid mistakes this time. It doesn't matter at all. 17 on USAMTS round 1, expected 17-19 on round 2. Too bad that my solutions were lost and I didn't save a real copy, just a rough draft. I'll have to make it up on rounds 3 and 4. Missed Mandelbrot round 3 as well, along with MOEMS round 3....<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10-yep, 132+ AMC 12-no, but didn't expect to, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal (didn't take), perfect Fryer<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=30519User:Xpmath2009-02-27T20:32:03Z<p>Xpmath: /* Major Goals for 8th Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
Bad year for me somewhat, so far. 7/14 on round 2 on Mandelbrot. You know what? I'm not going to say I made stupid mistakes this time. It doesn't matter at all. 17 on USAMTS round 1, expected 17-19 on round 2. Too bad that my solutions were lost and I didn't save a real copy, just a rough draft. I'll have to make it up on rounds 3 and 4. Missed Mandelbrot round 3 as well, along with MOEMS round 3....<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10-yep, 132+ AMC 12-no, but didn't expect to, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal, perfect Fryer<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=30430User:Xpmath2009-02-20T21:43:23Z<p>Xpmath: /* Minor Goals for 8th grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
Bad year for me somewhat, so far. 7/14 on round 2 on Mandelbrot. You know what? I'm not going to say I made stupid mistakes this time. It doesn't matter at all. 17 on USAMTS round 1, expected 17-19 on round 2. Too bad that my solutions were lost and I didn't save a real copy, just a rough draft. I'll have to make it up on rounds 3 and 4. Missed Mandelbrot round 3 as well, along with MOEMS round 3....<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10-yep, 132+ AMC 12, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first four rounds), perfect Pascal, perfect Fryer<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=30108User:Xpmath2009-02-11T21:06:24Z<p>Xpmath: /* Major Goals for 8th Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
Bad year for me somewhat, so far. 7/14 on round 2 on Mandelbrot. You know what? I'm not going to say I made stupid mistakes this time. It doesn't matter at all. 17 on USAMTS round 1, expected 17-19 on round 2. Too bad that my solutions were lost and I didn't save a real copy, just a rough draft. I'll have to make it up on rounds 3 and 4. Missed Mandelbrot round 3 as well, along with MOEMS round 3....<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10-yep, 132+ AMC 12, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first three rounds), perfect Pascal, perfect Fryer<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=2003_AMC_10A_Problems/Problem_3&diff=297032003 AMC 10A Problems/Problem 32009-01-24T22:42:44Z<p>Xpmath: /* Solution */</p>
<hr />
<div>== Problem ==<br />
A solid [[rectangular prism|box]] is <math>15</math> cm by <math>10</math> cm by <math>8</math> cm. A new solid is formed by removing a [[cube]] <math>3</math> cm on a side from each corner of this box. What [[percent]] of the original volume is removed? <br />
<br />
<math> \mathrm{(A) \ } 4.5\qquad \mathrm{(B) \ } 9\qquad \mathrm{(C) \ } 12\qquad \mathrm{(D) \ } 18\qquad \mathrm{(E) \ } 24 </math><br />
<br />
== Solution ==<br />
The volume of the original box is <math>15cm\cdot10cm\cdot8cm=1200cm^{3}</math> <br />
<br />
The volume of each cube that is removed is <math>3cm\cdot3cm\cdot3cm=27cm^{3}</math><br />
<br />
Since there are <math>8</math> corners on the box, <math>8</math> cubes are removed. <br />
<br />
So the total volume removed is <math>8\cdot27cm^{3}=216cm^{3}</math>. <br />
<br />
Therefore, the desired percentage is <math>\frac{216}{1200}\cdot100 = 18\% \rightarrow D</math>.<br />
<br />
== See also ==<br />
{{AMC10 box|year=2003|ab=A|num-b=2|num-a=4}}<br />
<br />
[[Category:Introductory Geometry Problems]]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=29598User:Xpmath2009-01-16T23:53:36Z<p>Xpmath: /* The Problem Solver's Resource To Do List */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
Bad year for me somewhat, so far. 7/14 on round 2 on Mandelbrot. You know what? I'm not going to say I made stupid mistakes this time. It doesn't matter at all. 17 on USAMTS round 1, expected 17-19 on round 2. Too bad that my solutions were lost and I didn't save a real copy, just a rough draft. I'll have to make it up on rounds 3 and 4. Missed Mandelbrot round 3 as well, along with MOEMS round 3....<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10, 132+ AMC 12, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first three rounds), perfect Pascal, perfect Fryer<br />
<br />
== To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?) to [[User:Temperal/The Problem Solver's Resource]]<br />
<br />
Write non computation MC problems.</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Temperal/The_Problem_Solver%27s_Resource6&diff=29469User:Temperal/The Problem Solver's Resource62009-01-11T16:44:44Z<p>Xpmath: </p>
<hr />
<div>__NOTOC__<br />
{{User:Temperal/testtemplate|page 6}}<br />
==<span style="font-size:20px; color: blue;">Beginner/Intermediate Number Theory</span>==<br />
This section covers [[number theory]], specifically [[Fermat's Little Theorem]], [[Wilson's Theorem]],[[Euler's Totient Theorem]], [[Quadratic residues]], and the [[Euclidean algorithm]].<br />
<br />
To use this page, we recommend knowing the basics of [[Linear congruence]], [[Modular arithmetic]], and have a grasp of basic number theory needed for the AMC 10 and 12.<br />
<br />
==Definitions==<br />
*<math>n\equiv a\pmod{b}</math> if <math>n</math> is the remainder when <math>a</math> is divided by <math>b</math> to give an integral amount. Also, this means b divides (n-a).<br />
*<math>a|b</math> (or <math>a</math> divides <math>b</math>) if <math>b=ka</math> for some [[integer]] <math>k</math>.<br />
*<math>\phi</math> is the greek letter phi. <math>\phi(n)</math> is the number of integers less than or equal to m that are at the same time relatively prime to n. If the prime factorization of n is <math>p_1^{e_1}p_2^{e_2}...p_n^{e_n}</math>, <math>\phi(n)=n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)...\left(1-\frac{1}{p_n}\right)</math>.<br />
<br />
==Special Notation==<br />
Occasionally, if two equivalent expressions are both modulated by the same number, the entire equation will be followed by the modulo.<br />
<br />
<math>(a_1, a_2,...a_n)</math> refers to the greatest common factor of <math>a_1, a_2, ...a_n</math> and <math>[a_1, a_2, ...a_n]</math> refers to the lowest common multiple of <math>a_1, a_2,...a_n</math>.<br />
<br />
==Properties==<br />
For any number there will be only one congruent number modulo <math>m</math> between <math>0</math> and <math>m-1</math>.<br />
<br />
If <math>a\equiv b \pmod{m}</math> and <math>c \equiv d \pmod{m}</math>, then <math>(a+c) \equiv (b+d) \pmod {m}</math>. <br />
<br />
*<math>a \pmod{m} + b \pmod{m} \equiv (a + b) \pmod{m}</math><br />
<br />
*<math>a \pmod{m} - b \pmod{m} \equiv (a - b) \pmod{m}</math><br />
<br />
*<math>a \pmod{m} \cdot b \pmod{m} \equiv (a \cdot b) \pmod{m} </math><br />
<br />
*<math>\frac{a}{e}\equiv \frac{b}{e}\pmod {\frac{m}{\gcd(m,e)}}</math>, where <math>e</math> is a positive integer that divides <math>{a}</math> and <math>b</math>.<br />
<br />
*<math>a^e\equiv{b^e}\pmod{m}</math><br />
<br />
===Fundamental Theorem of Arithmetic===<br />
The Fundamenal Theorem of Arithmetic is fairly clear, yet is extremely important. It states that any integer n greater than one has a unique representation as a product of primes. It has a very interesting proof; attempt to prove it using contradiction.<br />
<br />
===Fermat's Little Theorem===<br />
For a prime <math>p</math> and a number <math>a</math> such that <math>(a,b)=1</math>, <math>a^{p-1}\equiv 1 \pmod{p}</math>. A frequently used result of this is <math>a^p\equiv a\pmod{p}</math>.<br />
<br />
====Example Problem 1====<br />
Find all primes p such that <math>p|2^p+1</math>.<br />
<br />
=====Solution=====<br />
Firstly, p=2 clearly does not work. Now, as all other primes are odd, <math>(2, p)=1</math> and hence <math>2^p\equiv2\pmod{p}</math>. After adding one, we have <math>3\equiv0\pmod{p}</math> since p divides <math>2^p+1</math>. However, that means p must divide 3, so the only prime possible is 3. Indeed, <math>2^3+1=9</math> is a multiple of 3.<br />
<br />
===Wilson's Theorem===<br />
For a prime <math>p</math>, <math> (p-1)! \equiv -1 \pmod p</math>.<br />
<br />
====Example Problem 2====<br />
Let <math>a</math> be an integer such that <math>\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{23}=\frac{a}{23!}</math>. Find the remainder when <math>a</math> is divided by <math>13</math>.<br />
<br />
=====Solution=====<br />
After multiplying through by <math>23!</math>, we know that every term on the left-hand-side will be divisible by 13 except for <math>\frac{23!}{13}</math>. We wish to find the remainder when <math>23\cdot22\cdot21...\cdot1</math> is divided by 13. From Wilson's Theorem, we know that <math>12!\equiv-1\pmod{13}</math> so we consider (mod 13). Thus, the remainder is <math>10\cdot9\cdot8...\cdot1\cdot12!\equiv10!\cdot{-1}\pmod{13}</math> which comes out to be 7. Thus, our answer is 7.<br />
<br />
===Euler's Phi Theorem===<br />
If <math>(a,m)=1</math>, then <math>a^{\phi{m}}\equiv1\pmod{m}</math>, where <math>\phi{m}</math> is the number of relatively prime numbers lower than <math>m</math>. This is mostly a generalization of Fermat's Little Theorem, although much more useful.<br />
<br />
===Quadratic Residues===<br />
An integer n is a quadratic residue (mod m) if and only if there exists an integer p such that <math>p^2\equiv n\pmod{m}</math>.<br />
Some useful facts are that all quadratic residues are <math>0</math> or <math>1\pmod{4}</math> and <math>0</math>, <math>1</math>, or <math>4</math> <math>\pmod{8}</math>. All cubic residues (mod 9) are 0, 1, or -1.<br />
<br />
====Example Problem 3====<br />
Does there exist an integer such that its cube is equal to <math>3n^2 + 3n + 7</math>, where n is an integer? (IMO longlist 1967)<br />
<br />
=====Solution=====<br />
Consider <math>3n^2 + 3n + 7</math> (mod 9), and n (mod 3). If n is divisible by 3, <math>3n^2 + 3n</math> is clearly divisible by 9. If n is congruent to 1 (mod 3), <math>3n^2 + 3n</math> is congruent to 6 (mod 9). If n is congruent to 2 (mod 3), then <math>3n^2 + 3n\equiv3(n)(n + 1)\pmod{9}</math>. As n+1 is divisible by 3, it is congruent to 0 (mod 9). Hence, <math>3n^2 + 3n + 7</math> is either 7 or 4 (mod 9). However, all cubes are 0,1, or -1 (mod 9), so there does not exist such an integer.<br />
<br />
===Solving Linear Congruences===<br />
As mentioned at the top, you should at least know how to solve simple linear congruences, with just one [[linear congruence]]. However, solving with two or more congruences is more complex, and many times there is not even a solution. The [[Chinese Remainder Theorem]] shows when the congruences do have a unique solution. *to be continued*<br />
<br />
===Euclidean Algorithm===<br />
<br />
[[User:Temperal/The Problem Solver's Resource5|Back to page 5]] | [[User:Temperal/The Problem Solver's Resource7|Continue to page 7]]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=29468User:Xpmath2009-01-11T16:40:57Z<p>Xpmath: /* The Problem Solver's Resource To Do List */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
Bad year for me somewhat, so far. 7/14 on round 2 on Mandelbrot. You know what? I'm not going to say I made stupid mistakes this time. It doesn't matter at all. 17 on USAMTS round 1, expected 17-19 on round 2. Too bad that my solutions were lost and I didn't save a real copy, just a rough draft. I'll have to make it up on rounds 3 and 4. Missed Mandelbrot round 3 as well, along with MOEMS round 3....<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10, 132+ AMC 12, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first three rounds), perfect Pascal, perfect Fryer<br />
<br />
==The Problem Solver's Resource To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations. Add FTA, division algorithm (?).<br />
<br />
[[User:Temperal/The Problem Solver's Resource]]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Temperal/The_Problem_Solver%27s_Resource6&diff=29464User:Temperal/The Problem Solver's Resource62009-01-11T15:47:49Z<p>Xpmath: /* Properties */</p>
<hr />
<div>__NOTOC__<br />
{{User:Temperal/testtemplate|page 6}}<br />
==<span style="font-size:20px; color: blue;">Beginner/Intermediate Number Theory</span>==<br />
This section covers [[number theory]], specifically [[Fermat's Little Theorem]], [[Wilson's Theorem]],[[Euler's Totient Theorem]], [[Quadratic residues]], and the [[Euclidean algorithm]].<br />
<br />
To use this page, we recommend knowing the basics of [[Linear congruence]], [[Modular arithmetic]], and have a grasp of basic number theory needed for the AMC 10 and 12.<br />
<br />
==Definitions==<br />
*<math>n\equiv a\pmod{b}</math> if <math>n</math> is the remainder when <math>a</math> is divided by <math>b</math> to give an integral amount. Also, this means b divides (n-a).<br />
*<math>a|b</math> (or <math>a</math> divides <math>b</math>) if <math>b=ka</math> for some [[integer]] <math>k</math>.<br />
*<math>\phi</math> is the greek letter phi. <math>\phi(n)</math> is the number of integers less than or equal to m that are at the same time relatively prime to n. If the prime factorization of n is <math>p_1^{e_1}p_2^{e_2}...p_n^{e_n}</math>, <math>\phi(n)=n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)...\left(1-\frac{1}{p_n}\right)</math>.<br />
<br />
==Special Notation==<br />
Occasionally, if two equivalent expressions are both modulated by the same number, the entire equation will be followed by the modulo.<br />
<br />
<math>(a_1, a_2,...a_n)</math> refers to the greatest common factor of <math>a_1, a_2, ...a_n</math> and <math>[a_1, a_2, ...a_n]</math> refers to the lowest common multiple of <math>a_1, a_2,...a_n</math>.<br />
<br />
==Properties==<br />
For any number there will be only one congruent number modulo <math>m</math> between <math>0</math> and <math>m-1</math>.<br />
<br />
If <math>a\equiv b \pmod{m}</math> and <math>c \equiv d \pmod{m}</math>, then <math>(a+c) \equiv (b+d) \pmod {m}</math>. <br />
<br />
*<math>a \pmod{m} + b \pmod{m} \equiv (a + b) \pmod{m}</math><br />
<br />
*<math>a \pmod{m} - b \pmod{m} \equiv (a - b) \pmod{m}</math><br />
<br />
*<math>a \pmod{m} \cdot b \pmod{m} \equiv (a \cdot b) \pmod{m} </math><br />
<br />
*<math>\frac{a}{e}\equiv \frac{b}{e}\pmod {\frac{m}{\gcd(m,e)}}</math>, where <math>e</math> is a positive integer that divides <math>{a}</math> and <math>b</math>.<br />
<br />
*<math>a^e\equiv{b^e}\pmod{m}</math><br />
<br />
<br />
===Fermat's Little Theorem===<br />
For a prime <math>p</math> and a number <math>a</math> such that <math>(a,b)=1</math>, <math>a^{p-1}\equiv 1 \pmod{p}</math>. A frequently used result of this is <math>a^p\equiv a\pmod{p}</math>.<br />
<br />
====Example Problem 1====<br />
Find all primes p such that <math>p|2^p+1</math>.<br />
<br />
=====Solution=====<br />
Firstly, p=2 clearly does not work. Now, as all other primes are odd, <math>(2, p)=1</math> and hence <math>2^p\equiv2\pmod{p}</math>. After adding one, we have <math>3\equiv0\pmod{p}</math> since p divides <math>2^p+1</math>. However, that means p must divide 3, so the only prime possible is 3. Indeed, <math>2^3+1=9</math> is a multiple of 3.<br />
<br />
===Wilson's Theorem===<br />
For a prime <math>p</math>, <math> (p-1)! \equiv -1 \pmod p</math>.<br />
<br />
====Example Problem 2====<br />
Let <math>a</math> be an integer such that <math>\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{23}=\frac{a}{23!}</math>. Find the remainder when <math>a</math> is divided by <math>13</math>.<br />
<br />
=====Solution=====<br />
After multiplying through by <math>23!</math>, we know that every term on the left-hand-side will be divisible by 13 except for <math>\frac{23!}{13}</math>. We wish to find the remainder when <math>23\cdot22\cdot21...\cdot1</math> is divided by 13. From Wilson's Theorem, we know that <math>12!\equiv-1\pmod{13}</math> so we consider (mod 13). Thus, the remainder is <math>10\cdot9\cdot8...\cdot1\cdot12!\equiv10!\cdot{-1}\pmod{13}</math> which comes out to be 7. Thus, our answer is 7.<br />
<br />
===Euler's Phi Theorem===<br />
If <math>(a,m)=1</math>, then <math>a^{\phi{m}}\equiv1\pmod{m}</math>, where <math>\phi{m}</math> is the number of relatively prime numbers lower than <math>m</math>. This is mostly a generalization of Fermat's Little Theorem, although much more useful.<br />
<br />
===Quadratic Residues===<br />
An integer n is a quadratic residue (mod m) if and only if there exists an integer p such that <math>p^2\equiv n\pmod{m}</math>.<br />
Some useful facts are that all quadratic residues are <math>0</math> or <math>1\pmod{4}</math> and <math>0</math>, <math>1</math>, or <math>4</math> <math>\pmod{8}</math>. All cubic residues (mod 9) are 0, 1, or -1.<br />
<br />
====Example Problem 3====<br />
Does there exist an integer such that its cube is equal to <math>3n^2 + 3n + 7</math>, where n is an integer? (IMO longlist 1967)<br />
<br />
=====Solution=====<br />
Consider <math>3n^2 + 3n + 7</math> (mod 9), and n (mod 3). If n is divisible by 3, <math>3n^2 + 3n</math> is clearly divisible by 9. If n is congruent to 1 (mod 3), <math>3n^2 + 3n</math> is congruent to 6 (mod 9). If n is congruent to 2 (mod 3), then <math>3n^2 + 3n\equiv3(n)(n + 1)\pmod{9}</math>. As n+1 is divisible by 3, it is congruent to 0 (mod 9). Hence, <math>3n^2 + 3n + 7</math> is either 7 or 4 (mod 9). However, all cubes are 0,1, or -1 (mod 9), so there does not exist such an integer.<br />
<br />
===Solving Linear Congruences===<br />
As mentioned at the top, you should at least know how to solve simple linear congruences, with just one [[linear congruence]]. However, solving with two or more congruences is more complex, and many times there is not even a solution. The [[Chinese Remainder Theorem]] shows when the congruences do have a unique solution. *to be continued*<br />
<br />
===Euclidean Algorithm===<br />
<br />
[[User:Temperal/The Problem Solver's Resource5|Back to page 5]] | [[User:Temperal/The Problem Solver's Resource7|Continue to page 7]]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=29462User:Xpmath2009-01-11T15:46:23Z<p>Xpmath: /* Minor Goals for 8th grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
<br />
55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
<br />
==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
<br />
Bad year for me somewhat, so far. 7/14 on round 2 on Mandelbrot. You know what? I'm not going to say I made stupid mistakes this time. It doesn't matter at all. 17 on USAMTS round 1, expected 17-19 on round 2. Too bad that my solutions were lost and I didn't save a real copy, just a rough draft. I'll have to make it up on rounds 3 and 4. Missed Mandelbrot round 3 as well, along with MOEMS round 3....<br />
<br />
==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10, 132+ AMC 12, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
<br />
==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot (taken out due to me unable to take two of the first three rounds), perfect Pascal, perfect Fryer<br />
<br />
==The Problem Solver's Resource To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations.<br />
<br />
[[User:Temperal/The Problem Solver's Resource]]</div>Xpmathhttps://artofproblemsolving.com/wiki/index.php?title=User:Xpmath&diff=29461User:Xpmath2009-01-11T15:45:55Z<p>Xpmath: /* Eighth Grade */</p>
<hr />
<div>==Introduction==<br />
<br />
So. I finally decide to use this page, just to record my failures at math. It'll be sort of a history for me to look back upon. Oh yeah, I'm also adding stuff at the end.<br />
<br />
==Fourth Grade==<br />
<br />
My first "actual" math competition was in fourth grade, when I took the MML and scored a 29/30 (surprising, since I thought I had failed). <br />
<br />
==Fifth Grade==<br />
Then, in fifth grade, I took it again (fifth grade contest though) and got a 27/30, which was kind of disappointing. I also took the Gauss contest for seventh graders, which is Canadian, and I got a 134/150. Meh.<br />
<br />
==Sixth Grade==<br />
In sixth grade, I actually started competition math. I got a 17/40 on MMPC Part 1, allowing me to go to Part II, where I failed with a 0, even though my solution for 2b was pretty much the same as the official one. I made the school Mathcounts team, and got 8th at Chapter, where our team came 2nd. At state, I came 22nd and our team came 3rd. I got a 109.5 AMC 10A (all luck) and only like 76.5 10B, ugh. <br />
<br />
I did manage to get 40/40 on 6th grade MML and a 150 on the 7th grade Gauss. I also got 38/40 on the Fryer competition (9th grade), another Canadian one, but proof oriented. 27/80 on the COMC though. Yuck. Also got a 142/150 on the 9th grade Canadian Pascal competition, and a 26/42 (since I missed the first round, so not out of 56) on Mandelbrot regional. Oh, and 23/25 on MOEMS, and 23/25 on AMC 8.<br />
<br />
==Seventth Grade==<br />
My 7th grade year , where I moved to Ohio, but still took a lot of the same competitions. I got 24/40 on MMPC Part 1 and 13 on Part 2, giving me 102nd place. I also won Chapter Mathcounts and 4th at state (team came 2nd chapter, 16th state), so I went to Nationals. I got 129 on 10A, 108 on 12B, and an unfortunate 4 on AIME II. I missed Mandelbrot round 5, giving me a 33/70 overall. I got a 24 on MOEMS and 22 on AMC 8.<br />
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55/80 on the COMC, 38/40 on Fryer, 144 on Gauss 7. So I scored lower on the AMC 8 and Gauss 7, tied on Fryer, and improved in everything else.<br />
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==Eighth Grade==<br />
This year, I didn't go to ICAE (where I take most of my math competitions) until the Winter session, so I missed a bunch of competitions. I missed MMPC (darn), AMC 8 (who cares?), Mandelbrot round 1 (darn, round 1 was easy), and MOEMS (who cares?). Oh, I also missed COMC, which is bad because I could solve every question besides 4b and 4c. Darn.<br />
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Bad year for me somewhat, so far. 7/14 on round 2 on Mandelbrot. You know what? I'm not going to say I made stupid mistakes this time. It doesn't matter at all. 17 on USAMTS round 1, expected 17-19 on round 2. Too bad that my solutions were lost and I didn't save a real copy, just a rough draft. I'll have to make it up on rounds 3 and 4. Missed Mandelbrot round 3 as well, along with MOEMS round 3....<br />
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==Major Goals for 8th Grade==<br />
National Countdown, 144+ AMC 10, 132+ AMC 12, 8+ AIME, 6+ USAMO, 6+ ARML, 60+ USAMTS<br />
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==Minor Goals for 8th grade==<br />
85+ Euclid, 40+ Mandelbrot, perfect Pascal, perfect Fryer<br />
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==The Problem Solver's Resource To Do List==<br />
Add to the linear congruences part and post euclidean algorithm; some stuff related to proofs. Also figure out where to put diophantine equations.<br />
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[[User:Temperal/The Problem Solver's Resource]]</div>Xpmath