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- 18:08, 15 January 2013 (diff | hist) . . (+2,548) . . N Mock Geometry AIME 2011 Problems/Problem 12 (Created page with "==Problem== A triangle has the property that its sides form an arithmetic progression, and that the angle opposite the longest side is three times the angle opposite the shortes...")
- 15:07, 28 May 2012 (diff | hist) . . (+3,793) . . N 2006 SMT/Geometry Problems/Problem 4 (Created page with "==Problem== The distance <math> AB </math> is <math> l </math>. Find the area of the locus of points <math> X </math> such that <math> 15^\circ\le\angle AXB\le30^\circ </math> an...") (current)
- 12:22, 28 May 2012 (diff | hist) . . (+1,363) . . N 2006 SMT/Geometry Problems/Problem 3 (Created page with "==Problem== Circle <math> \gamma </math> is centered at <math> (0, 3) </math> with radius <math> 1 </math>. Circle <math> \delta </math> is externally tangent to circle <math> \g...") (current)
- 12:00, 28 May 2012 (diff | hist) . . (+1,991) . . N 2006 SMT/Geometry Problems/Problem 2 (Created page with "==Problem== Given square <math> ABCD </math> of side length <math> 1 </math>, with <math> E </math> on <math> \overline{CD} </math> and <math> F </math> in the interior of the sq...") (current)
- 11:38, 28 May 2012 (diff | hist) . . (+1,860) . . N 2006 SMT/Geometry Problems/Problem 1 (Created page with "==Problem== Given a cube, determine the ratio of the volume of the octahedron formed by connecting the centers of each face of the cube to the volume of the cube. ==Solution== ...") (current)
- 10:35, 28 May 2012 (diff | hist) . . (+703) . . N 2006 SMT/Algebra Problems/Problem 10 (Created page with "==Problem== Evaluate: <math> \sum_{k=1}^{\infty}\frac{k}{a^{k-1}} </math> for all <math> |a|<1 </math>. ==Solution== Let <math> S=\sum_{k=1}^{\infty}\frac{k}{a^{k-1}}=\frac{1}{a...") (current)
- 10:30, 28 May 2012 (diff | hist) . . (+1,131) . . N 2006 SMT/Algebra Problems/Problem 9 (Created page with "==Problem== Principal Skinner is thinking of two integers <math> m </math> and <math> n </math> and bets Superintendent Chalmers that he will not be able to determine these integ...") (current)
- 09:52, 28 May 2012 (diff | hist) . . (+1,306) . . N 2006 SMT/Algebra Problems/Problem 8 (Created page with "==Problem== Evaluate: <cmath> \sum_{x=2}^{10}\frac{2}{x(x^2-1)}. </cmath> ==Solution== Since the denominator of the fraction is factorable, we try partial fraction decompositio...") (current)
- 09:40, 28 May 2012 (diff | hist) . . (+802) . . N 2006 SMT/Algebra Problems/Problem 7 (Created page with "==Problem== Find all solutions to <math> aabb=n^4-6n^3 </math>, where <math> a </math> and <math> b </math> are nonzero digits, and <math> n </math> is an integer. (<math> a </ma...") (current)
- 09:31, 28 May 2012 (diff | hist) . . (+1,360) . . N 2006 SMT/Algebra Problems/Problem 6 (Created page with "==Problem== Let <math> a, b, c </math> be real numbers satisfying: <cmath> ab-a=b+119 </cmath> <cmath> bc-b=c+59 </cmath> <cmath> ca-c=a+71 </cmath> Determine all possible valu...")
- 09:03, 28 May 2012 (diff | hist) . . (+1,778) . . N 2006 SMT/Algebra Problems/Problem 5 (Created page with "==Problem== Jerry is bored one day, so he makes an array of Cocoa pebbles. He makes <math> 8 </math> equal rows with the pebbles remaining in a box. When Kramer drops by and eats...") (current)
- 08:55, 28 May 2012 (diff | hist) . . (+1,250) . . N 2006 SMT/Algebra Problems/Problem 4 (Created page with "==Problem== Simplify: <math> \frac{a^3}{(a-b)(a-c)}+\frac{b^3}{(b-a)(b-c)}+\frac{c^3}{(c-a)(c-b)} </math> ==Solution== Firstly, we notice that the factors in the denominators ar...") (current)
- 08:43, 28 May 2012 (diff | hist) . . (+1,313) . . N 2006 SMT/Algebra Problems/Problem 3 (Created page with "==Problem== A Gaussian prime is a Gaussian integer <math> z=a+bi </math> (where <math> a </math> and <math> b </math> are integers) with no Guassian integer factors of smaller ab...") (current)
- 08:31, 28 May 2012 (diff | hist) . . (+1,291) . . N 2006 SMT/Algebra Problems/Problem 2 (Created page with "==Problem== Find the minimum value of <math> 2x^2+2y^2+5z^2-2xy-4yz-4x-2z+15 </math> for real numbers <math> x, y, z </math>. ==Solution== ===Solution 1=== Notice that <math> 2x...") (current)
- 08:01, 28 May 2012 (diff | hist) . . (+1,399) . . N 2006 SMT/Algebra Problems/Problem 1 (Created page with "==Problem== A finite sequence of positive integers <math> m_i </math> for <math> i=1, 2, \cdots, 2006 </math> are defined so that <math> m_1=1 </math> and <math> m_i=10m_{i-1}+1 ...") (current)
- 21:38, 27 May 2012 (diff | hist) . . (+1,713) . . N 2006 SMT/Advanced Topics Problems/Problem 7 (Created page with "==Problem== A lattice point in the plane is a point whose coordinates are both integers. Given a set of <math> 100 </math> distinct lattice points in the plane, find the smallest...") (current)
- 21:14, 27 May 2012 (diff | hist) . . (+1,334) . . N 2006 SMT/Advanced Topics Problems/Problem 6 (Created page with "==Problem== Ten teams of five runners each compete in a cross-country race. A runner finishing in <math> n\text{th} </math> place contributes <math> n </math> points to his team,...") (current)
- 20:58, 27 May 2012 (diff | hist) . . (+1,065) . . N 2006 SMT/Advanced Topics Problems/Problem 5 (Created page with "==Problem== Evaluate: <math> \sum_{k=1}^{\infty}\frac{1}{k\sqrt{k+2}+(k+2)\sqrt{k}} </math> ==Solution== We try to rationalize the denominators. We have <math> \frac{1}{k\sqrt{k...") (current)
- 20:20, 27 May 2012 (diff | hist) . . (+434) . . N 2006 SMT/Advanced Topics Problems/Problem 3 (Created page with "==Problem== Simplify: <math> \sum_{k=10}^{2006}\binom{k}{10} </math> (Your answer should contain no summations but may still contain binomial coefficients/combinations). ==Solut...") (current)
- 20:12, 27 May 2012 (diff | hist) . . (-2) . . m 2006 SMT/Advanced Topics Problems/Problem 1 (→Problem 1) (current)
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