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• 17:08, 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...")
• 14:07, 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)
• 11:22, 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)
• 11:00, 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)
• 10:38, 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)
• 09:35, 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)
• 09:30, 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)
• 08:52, 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)
• 08:40, 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)
• 08:31, 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...")
• 08:03, 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)
• 07:55, 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)
• 07:43, 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)
• 07:31, 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)
• 07:01, 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)
• 20:38, 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)
• 20:14, 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)
• 19:58, 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)
• 19:20, 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)
• 19:12, 27 May 2012 (diff | hist) . . (-2)‎ . . m 2006 SMT/Advanced Topics Problems/Problem 1 ‎ (→‎Problem 1) (current)
• 19:09, 27 May 2012 (diff | hist) . . (+1)‎ . . m 2006 SMT/Advanced Topics Problems ‎ (→‎Problem 2) (current)
• 19:09, 27 May 2012 (diff | hist) . . (+2,090)‎ . . N 2006 SMT/Advanced Topics Problems/Problem 2 ‎ (Created page with "==Problem== Define <math> A=\left(\,\begin{matrix}0 & 1\\ 3 &0\end{matrix}\right) </math>. Find a vertical vector <math> v </math> such that <math> (A^8+A^6+A^4+A^2+I)v=\left(\be...") (current)
• 18:07, 27 May 2012 (diff | hist) . . (+1,052)‎ . . N 2006 SMT/Advanced Topics Problems/Problem 1 ‎ (Created page with "==Problem 1== A college student is about to break up with her boyfriend, a mathematics major who is apparently more interested in math than her. Frustrated, she cries, ”You mat...")
• 16:32, 27 May 2012 (diff | hist) . . (+5,805)‎ . . N 2006 SMT/Team Problems ‎ (Created page with "==Problem 1== Given <math> \triangle ABC </math>, where <math> A </math> is at <math> (0,0) </math>, <math> B </math> is at <math> (20,0) </math>, and <math> C </math> is on the ...") (current)
• 15:22, 27 May 2012 (diff | hist) . . (+1,060)‎ . . N 2006 SMT/Team ‎ (Created page with "'''2006 SMT Team''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *[[2006 SMT/Te...") (current)
• 15:02, 27 May 2012 (diff | hist) . . (+9,798)‎ . . N 2006 SMT/General Problems ‎ (Created page with "==Problem 1== After a cyclist has gone <math> \frac{2}{3} </math> of his route, he gets a flat tire. Finishing on foot, he spends twice as long walking as he did riding. How many...") (current)
• 13:19, 27 May 2012 (diff | hist) . . (+1,641)‎ . . N 2006 SMT/General ‎ (Created page with "'''2006 SMT General''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *[[2006 SMT...") (current)
• 12:59, 27 May 2012 (diff | hist) . . (+3,358)‎ . . N 2006 SMT/Calculus Problems ‎ (Created page with "==Problem 1== Evaluate: <cmath> \lim_{x\to0}\frac{\frac{d}{dx}\frac{\sin x}{x}}{x} </cmath> Solution ==Problem 2== Given the equation ...") (current)
• 11:31, 27 May 2012 (diff | hist) . . (+858)‎ . . N 2006 SMT/Calculus ‎ (Created page with "'''2006 SMT Calculus''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *[[2006 SM...") (current)
• 11:22, 27 May 2012 (diff | hist) . . (+5,385)‎ . . N 2006 SMT/Geometry Problems ‎ (Created page with "==Problem 1== 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. [[2006 SMT/G...") (current)
• 10:09, 27 May 2012 (diff | hist) . . (+858)‎ . . N 2006 SMT/Geometry ‎ (Created page with "'''2006 SMT Geometry''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *[[2006 SM...") (current)
• 10:02, 27 May 2012 (diff | hist) . . (+3,081)‎ . . N 2006 SMT/Algebra Problems ‎ (Created page with "==Problem 1== 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}+...") (current)
• 09:23, 27 May 2012 (diff | hist) . . (+845)‎ . . N 2006 SMT/Algebra ‎ (Created page with "'''2006 SMT Algebra''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *[[2006 SMT/...") (current)
• 09:16, 27 May 2012 (diff | hist) . . (+4,073)‎ . . N 2006 SMT/Advanced Topics Problems ‎ (Created page with "==Problem 1== A college student is about to break up with her boyfriend, a mathematics major who is apparently more interested in math than her. Frustrated, she cries, ”You mat...")
• 08:47, 27 May 2012 (diff | hist) . . (+941)‎ . . N 2006 SMT/Advanced Topics ‎ (Created page with "'''2006 SMT Advanced Topics''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *[[2...") (current)
• 08:39, 27 May 2012 (diff | hist) . . (+404)‎ . . N 2006 SMT ‎ (Created page with "'''2006 SMT''' problems and solutions by category. *Advanced Topics *Algebra *[[2006 SMT/Ge...") (current)
• 08:33, 27 May 2012 (diff | hist) . . (-28)‎ . . Stanford Mathematics Tournament Problems ‎
• 08:33, 27 May 2012 (diff | hist) . . (+29)‎ . . Stanford Mathematics Tournament Problems ‎
• 08:19, 27 May 2012 (diff | hist) . . (+117)‎ . . m Stanford Mathematics Tournament Problems ‎
• 07:12, 27 May 2012 (diff | hist) . . (+59)‎ . . m Stanford Mathematics Tournament ‎
• 06:56, 27 May 2012 (diff | hist) . . (+1,241)‎ . . N 1974 AHSME Problems/Problem 30 ‎ (Created page with "==Problem== A line segment is divided so that the lesser part is to the greater part as the greater part is to the whole. If <math> R </math> is the ratio of the lesser part to t...")
• 21:58, 26 May 2012 (diff | hist) . . (+1,079)‎ . . N 1974 AHSME Problems/Problem 29 ‎ (Created page with "==Problem== For <math> p=1, 2, \cdots, 10 </math> let <math> S_p </math> be the sum of the first <math> 40 </math> terms of the arithmetic progression whose first term is <math> ...")
• 21:41, 26 May 2012 (diff | hist) . . (+1,728)‎ . . N 1974 AHSME Problems/Problem 28 ‎ (Created page with "==Problem== Which of the following is satisfied by all numbers <math> x </math> of the form <cmath> x=\frac{a_1}{3}+\frac{a_2}{3^2}+\cdots+\frac{a_{25}}{3^{25}} </cmath> where ...")
• 21:31, 26 May 2012 (diff | hist) . . (+770)‎ . . N 1974 AHSME Problems/Problem 27 ‎ (Created page with "==Problem== If <math> f(x)=3x+2 </math> for all real <math> x </math>, then the statement: "<math> |f(x)+4|<a </math> whenever <math> |x+2|<b </math> and <math> a>0 </math> and <...")
• 21:27, 26 May 2012 (diff | hist) . . (+816)‎ . . N 1974 AHSME Problems/Problem 26 ‎ (Created page with "==Problem== The number of distinct positive integral divisors of <math> (30)^4 </math> excluding <math> 1 </math> and <math> (30)^4 </math> is <math> \mathrm{(A)\ } 100 \qquad ...")
• 21:21, 26 May 2012 (diff | hist) . . (+1,510)‎ . . N 1974 AHSME Problems/Problem 25 ‎ (Created page with "==Problem== In parallelogram <math> ABCD </math> of the accompanying diagram, line <math> DP </math> is drawn bisecting <math> BC </math> at <math> N </math> and meeting <math> A...")
• 21:12, 26 May 2012 (diff | hist) . . (+1,109)‎ . . N 1974 AHSME Problems/Problem 24 ‎ (Created page with "==Problem== A fair die is rolled six times. The probability of rolling at least a five at least five times is <math> \mathrm{(A)\ } \frac{13}{729} \qquad \mathrm{(B) \ }\frac{1...")
• 21:03, 26 May 2012 (diff | hist) . . (+2,053)‎ . . N 1974 AHSME Problems/Problem 23 ‎ (Created page with "==Problem == In the adjoining figure <math> TP </math> and <math> T'Q </math> are parallel tangents to a circle of radius <math> r </math>, with <math> T </math> and <math> T' </...")
• 20:32, 26 May 2012 (diff | hist) . . (+1,141)‎ . . N 1974 AHSME Problems/Problem 22 ‎ (Created page with "==Problem== The minimum of <math> \sin\frac{A}{2}-\sqrt{3}\cos\frac{A}{2} </math> is attained when <math> A </math> is <math> \mathrm{(A)\ } -180^\circ \qquad \mathrm{(B) \ }60...")
• 20:14, 26 May 2012 (diff | hist) . . (+1,124)‎ . . N 1974 AHSME Problems/Problem 21 ‎ (Created page with "==Problem== In a geometric series of positive terms the difference between the fifth and fourth terms is <math> 576 </math>, and the difference between the second and first terms...")

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