User contributions
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- 20:09, 27 May 2012 (diff | hist) . . (+1) . . m 2006 SMT/Advanced Topics Problems (→Problem 2) (current)
- 20:09, 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)
- 19:07, 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...")
- 17:32, 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)
- 16:22, 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)
- 16:02, 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)
- 14:19, 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)
- 13:59, 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)
- 12:31, 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)
- 12:22, 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)
- 11:09, 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)
- 11:02, 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)
- 10:23, 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)
- 10:16, 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...")
- 09:47, 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)
- 09:39, 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)
- 09:33, 27 May 2012 (diff | hist) . . (-28) . . Stanford Mathematics Tournament Problems
- 09:33, 27 May 2012 (diff | hist) . . (+29) . . Stanford Mathematics Tournament Problems
- 09:19, 27 May 2012 (diff | hist) . . (+117) . . m Stanford Mathematics Tournament Problems
- 08:12, 27 May 2012 (diff | hist) . . (+59) . . m Stanford Mathematics Tournament
- 07:56, 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...")
- 22:58, 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> ...")
- 22:41, 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 ...")
- 22:31, 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 <...")
- 22:27, 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 ...")
- 22:21, 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...")
- 22:12, 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...")
- 22:03, 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' </...")
- 21:32, 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...")
- 21:14, 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...")
- 21:03, 26 May 2012 (diff | hist) . . (+893) . . N 1974 AHSME Problems/Problem 20 (Created page with "==Problem== Let <cmath> T=\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}. </cmath> Then <math> \...")
- 20:57, 26 May 2012 (diff | hist) . . (+1,587) . . N 1974 AHSME Problems/Problem 19 (Created page with "==Problem== In the adjoining figure <math> ABCD </math> is a square and <math> CMN </math> is an equilateral triangle. If the area of <math> ABCD </math> is one square inch, then...")
- 19:21, 26 May 2012 (diff | hist) . . (+1,007) . . N 1974 AHSME Problems/Problem 18 (Created page with "==Problem== If <math> \log_8{3}=p </math> and <math> \log_3{5}=q </math>, then, in terms of <math> p </math> and <math> q </math>, <math> \log_{10}{5} </math> equals <math> \mat...")
- 19:09, 26 May 2012 (diff | hist) . . (+491) . . N 1974 AHSME Problems/Problem 17 (Created page with "==Problem== If <math> i^2=-1 </math>, then <math> (1+i)^{20}-(1-i)^{20} </math> equals <math> \mathrm{(A)\ } -1024 \qquad \mathrm{(B) \ }-1024i \qquad \mathrm{(C) \ } 0 \qquad ...")
- 19:06, 26 May 2012 (diff | hist) . . (+1,602) . . N 1974 AHSME Problems/Problem 16 (Created page with "==Problem== A circle of radius <math> r </math> is inscribed in a right isosceles triangle, and a circle of radius <math> R </math> is circumscribed about the triangle. Then <mat...")
- 18:43, 26 May 2012 (diff | hist) . . (+593) . . N 1974 AHSME Problems/Problem 15 (Created page with "==Problem== If <math> x<-2 </math>, then <math> |1-|1+x|| </math> equals <math> \mathrm{(A)\ } 2+x \qquad \mathrm{(B) \ }-2-x \qquad \mathrm{(C) \ } x \qquad \mathrm{(D) \ } ...")
- 18:38, 26 May 2012 (diff | hist) . . (+808) . . N 1974 AHSME Problems/Problem 14 (Created page with "==Problem== Which statement is correct? <math> \mathrm{(A)\ } \text{If } x<0, \text{then } x^2>x. \qquad \mathrm{(B) \ } \text{If } x^2>0, \text{then } x>0. </math> <math> \qqu...")
- 18:33, 26 May 2012 (diff | hist) . . (+1,373) . . N 1974 AHSME Problems/Problem 13 (Created page with "==Problem== Which of the following is equivalent to "If P is true, then Q is false."? <math> \mathrm{(A)\ } \text{``P is true or Q is false."} \qquad </math> <math> \mathrm{(B)...")
- 18:24, 26 May 2012 (diff | hist) . . (+887) . . N 1974 AHSME Problems/Problem 12 (Created page with "==Problem== If <math> g(x)=1-x^2 </math> and <math> f(g(x))=\frac{1-x^2}{x^2} </math> when <math> x\not=0 </math>, then <math> f(1/2) </math> equals <math> \mathrm{(A)\ } 3/4 \...")
- 18:14, 26 May 2012 (diff | hist) . . (+1,011) . . N 1974 AHSME Problems/Problem 11 (Created page with "==Problem== If <math> (a, b) </math> and <math> (c, d) </math> are two points on the line whose equation is <math> y=mx+k </math>, then the distance between <math> (a, b) </math>...")
- 18:07, 26 May 2012 (diff | hist) . . (+270) . . 1974 AHSME Problems/Problem 10
- 18:07, 26 May 2012 (diff | hist) . . (+54) . . 1974 AHSME Problems/Problem 10
- 18:07, 26 May 2012 (diff | hist) . . (-55) . . 1974 AHSME Problems (→See Also)
- 18:06, 26 May 2012 (diff | hist) . . (+394) . . N 1974 AHSME Problems/Problem 10 (Created page with " ==Solution== Expanding, we have <math> 2kx^2-8x-x^2+6=0 </math>, or <math> (2k-1)x^2-8x+6=0 </math>. For this quadratic not to have real roots, it must have a negative discrimi...")
- 18:06, 26 May 2012 (diff | hist) . . (-394) . . 1974 AHSME Problems (→Solution)
- 18:06, 26 May 2012 (diff | hist) . . (+3) . . m 1974 AHSME Problems (→Problem)
- 18:05, 26 May 2012 (diff | hist) . . (+447) . . 1974 AHSME Problems (→Problem 10)
- 17:59, 26 May 2012 (diff | hist) . . (0) . . m 1974 AHSME Problems (→Problem 9)
- 17:56, 26 May 2012 (diff | hist) . . (+1,552) . . N 1974 AHSME Problems/Problem 9 (Created page with "==Problem== The integers greater than one are arranged in five columns as follows: <cmath> \begin{tabular}{c c c c c}\ & 2 & 3 & 4 & 5\\ 9 & 8 & 7 & 6 &\ \\ \ & 10 & 11 & 12 & 1...")
- 17:43, 26 May 2012 (diff | hist) . . (+749) . . N 1974 AHSME Problems/Problem 8 (Created page with "==Problem== What is the smallest prime number dividing the sum <math> 3^{11}+5^{13} </math>? <math> \mathrm{(A)\ } 2 \qquad \mathrm{(B) \ }3 \qquad \mathrm{(C) \ } 5 \qquad \ma...")
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