26 May 2012

• 20:0320:03, 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> \..."
• 19:5719:57, 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..."
• 18:2118:21, 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..."
• 18:0918:09, 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 ..."
• 18:0618:06, 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..."
• 17:4317:43, 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) \ } ..."
• 17:3817:38, 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..."
• 17:3317:33, 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)..."
• 17:2417:24, 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 \..."
• 17:1417:14, 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>..."
• 17:0717:07, 26 May 2012 diff hist +270 1974 AHSME Problems/Problem 10 No edit summary
• 17:0717:07, 26 May 2012 diff hist +54 1974 AHSME Problems/Problem 10 No edit summary
• 17:0717:07, 26 May 2012 diff hist −55 1974 AHSME Problems →See Also
• 17:0617:06, 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..."
• 17:0617:06, 26 May 2012 diff hist −394 1974 AHSME Problems →Solution
• 17:0617:06, 26 May 2012 diff hist +3 m 1974 AHSME Problems →Problem
• 17:0517:05, 26 May 2012 diff hist +447 1974 AHSME Problems →Problem 10
• 16:5916:59, 26 May 2012 diff hist 0 m 1974 AHSME Problems →Problem 9
• 16:5616:56, 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..."
• 16:4316:43, 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..."
• 16:3816:38, 26 May 2012 diff hist +1,066 N 1974 AHSME Problems/Problem 7 Created page with "==Problem== A town's population increased by <math> 1,200 </math> people, and then this new population decreased by <math> 11\% </math>. The town now had <math> 32 </math> less p..."
• 16:3416:34, 26 May 2012 diff hist +1,305 N 1974 AHSME Problems/Problem 6 Created page with "==Problem== For positive real numbers <math> x </math> and <math> y </math> define <math> x*y=\frac{x\cdot y}{x+y} </math>' then <math> \mathrm{(A)\ } \text{``*" is commutative ..."
• 15:1015:10, 26 May 2012 diff hist +1,082 N 1974 AHSME Problems/Problem 5 Created page with "==Problem== Given a quadrilateral <math> ABCD </math> inscribed in a circle with side <math> AB </math> extended beyond <math> B </math> to point <math> E </math>, if <math> \mea..."
• 15:0415:04, 26 May 2012 diff hist +471 N 1974 AHSME Problems/Problem 4 Created page with "==Problem== What is the remainder when <math> x^{51}+51 </math> is divided by <math> x+1 </math>? <math> \mathrm{(A)\ } 0 \qquad \mathrm{(B) \ }1 \qquad \mathrm{(C) \ } 49 \qqu..."
• 14:5614:56, 26 May 2012 diff hist +858 N 1974 AHSME Problems/Problem 3 Created page with "==Problem== The coefficient of <math> x^7 </math> in the polynomial expansion of <cmath> (1+2x-x^2)^4 </cmath> is <math> \mathrm{(A)\ } -8 \qquad \mathrm{(B) \ }12 \qquad \ma..."
• 14:4914:49, 26 May 2012 diff hist +790 N 1974 AHSME Problems/Problem 2 Created page with "==Problem== Let <math> x_1 </math> and <math> x_2 </math> be such that <math> x_1\not=x_2 </math> and <math> 3x_i^2-hx_i=b </math>, <math> i=1, 2 </math>. Then <math> x_1+x_2 </m..."
• 14:4614:46, 26 May 2012 diff hist +819 N 1974 AHSME Problems/Problem 1 Created page with "==Problem== If <math> x\not=0 </math> or <math> 4 </math> and <math> y\not=0 </math> or <math> 6 </math>, then <math> \frac{2}{x}+\frac{3}{y}=\frac{1}{2} </math> is equivalent to..."
• 14:4214:42, 26 May 2012 diff hist −2 m 1985 AHSME Problems/Problem 1 →Problem 1
• 14:3614:36, 26 May 2012 diff hist +1,311 1974 AHSME Problems No edit summary
• 14:3214:32, 26 May 2012 diff hist +13,504 N 1974 AHSME Problems Created page with "==Problem 1== If <math> x\not=0 </math> or <math> 4 </math> and <math> y\not=0 </math> or <math> 6 </math>, then <math> \frac{2}{x}+\frac{3}{y}=\frac{1}{2} </math> is equivalent ..."
• 12:3412:34, 26 May 2012 diff hist +1,757 N 1974 AHSME Created page with "'''1974 AHSME''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *[[1974 AHSME Prob..."

25 February 2012

• 09:2509:25, 25 February 2012 diff hist 0 m 1985 AIME Problems →Problem 8

2 January 2012

• 13:1213:12, 2 January 2012 diff hist +2,762 N Mock Geometry AIME 2011 Problems/Problem 11 Created page with "==Problem== <math>C</math> is on a semicircle with diameter <math>AB</math> and center <math>O.</math> Circle radius <math>r_1</math> is tangent to <math>OA,OC,</math> and arc <..." current
• 11:2611:26, 2 January 2012 diff hist +354 m Mock Geometry AIME 2011 Problems/Problem 4 No edit summary

1 January 2012

• 22:5722:57, 1 January 2012 diff hist +21 m Mock Geometry AIME 2011 Problems/Problem 4 No edit summary
• 22:0922:09, 1 January 2012 diff hist +1,773 Mock Geometry AIME 2011 Problems/Problem 5 No edit summary
• 21:0521:05, 1 January 2012 diff hist −14 m Mock Geometry AIME 2011 Problems/Problem 3 →Solution
• 21:0521:05, 1 January 2012 diff hist +326 m Mock Geometry AIME 2011 Problems/Problem 3 No edit summary

30 December 2011

• 15:3715:37, 30 December 2011 diff hist +1,016 N Mock Geometry AIME 2011 Problems/Problem 2 Created page with "==Problem== Eleven nonparallel lines lie on a plane, and their pairwise intersections meet at angles of integer degree. How many possible values are there for the smallest of th..."
• 15:2815:28, 30 December 2011 diff hist +1,628 Mock Geometry AIME 2011 Problems/Problem 1 No edit summary
• 15:0715:07, 30 December 2011 diff hist +634 N Mock Geometry AIME 2011 Problems/Problem 1 Created page with "==Problem== Let <math>ABCD</math> be a unit square, and let <math>AB_1C_1D_1</math> be its image after a <math>30</math> degree rotation about point <math>A.</math> The area of ..."
• 14:5714:57, 30 December 2011 diff hist +791 m Mock Geometry AIME 2011 Problems No edit summary
• 14:5614:56, 30 December 2011 diff hist +56 m Mock Geometry AIME 2011 Problems →Problem 1

27 November 2011

• 11:0811:08, 27 November 2011 diff hist +1,614 N 1983 AHSME Created page with "'''1983 AHSME''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *[[1983 AHSME Problems..."
• 11:0611:06, 27 November 2011 diff hist −39 m 1984 AHSME No edit summary

26 November 2011

• 14:1114:11, 26 November 2011 diff hist +801 N 1985 AHSME Problems/Problem 7 Created page with "==Problem== In some computer languages (such as APL), when there are no parentheses in an algebraic expression, the operations are grouped from left to right. Thus, <math> a\time..."
• 14:0714:07, 26 November 2011 diff hist +2,123 N 1985 AHSME Problems/Problem 30 Created page with "==Problem== Let <math> \lfloor x \rfloor </math> be the greatest integer less than or equal to <math> x </math>. Then the number of real solutions to <math> 4x^2-40\lfloor x \rfl..."
• 13:2713:27, 26 November 2011 diff hist +893 N 1985 AHSME Problems/Problem 10 Created page with "==Problem== An arbitrary circle can intersect the graph <math> y=\sin x </math> in <math> \mathrm{(A) } \text{at most }2\text{ points} \qquad \mathrm{(B) }\text{at mos..."

11 November 2011

• 23:5323:53, 11 November 2011 diff hist +2,359 N 1985 AHSME Problems/Problem 29 Created page with "==Problem== In their base <math> 10 </math> representation, the integer <math> a </math> consists of a sequence of <math> 1985 </math> eights and the integer <math> b </math> con..."
• 22:0222:02, 11 November 2011 diff hist +2,543 N 1985 AHSME Problems/Problem 28 Created page with "==Problem== In <math> \triangle ABC </math>, we have <math> \angle C=3\angle A, a=27, </math> and <math> c=48 </math>. What is <math> b </math>? <asy> defaultpen(linewidth(0.7)+..."