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- == Problem == {{AIME box|year=2005|n=II|num-b=3|num-a=5}}3 KB (377 words) - 18:36, 1 January 2024
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- ...d only once. In particular, memorizing a formula for PIE is a bad idea for problem solving. ==== Problem ====9 KB (1,703 words) - 01:20, 7 December 2024
- ...ts are perpendicular. Drawing all four semi-axes divides the ellipse into 4 [[congruent (geometry)|congruent]] quarters. pair P=(3,12/5), F1=(-4,0), F2=(4,0);5 KB (892 words) - 21:52, 1 May 2021
- ...aginary part of a complex number is real: for example, <math>\Im(3 + 4i) = 4</math>. So, if <math>z\in \mathbb C</math>, we can write <math>z=\mathrm{R *[[2007 AMC 12A Problems/Problem 18]]5 KB (860 words) - 15:36, 10 December 2023
- ...Cameron Matthews. In 2003, Crawford became the first employee of [[Art of Problem Solving]] where he helped to write and teach most of the online classes dur * Perfect score on the [[AIME]] as a freshman.2 KB (362 words) - 11:20, 27 September 2024
- For example, <math>1, 2, 4, 8</math> is a geometric sequence with common ratio <math>2</math> and <mat * [[1965 AHSME Problems/Problem 36 | 1965 AHSME Problem 36]]4 KB (649 words) - 21:09, 19 July 2024
- An equation of form <math>x^4+y^4=z^2</math> has no [[integer]] solutions, as follows: If <math>\gcd(x_0,y_0)=1</math>, we then proceed with casework, in <math>\mod 4</math>.9 KB (1,434 words) - 01:15, 4 July 2024
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2004 AIME II Problems]]1 KB (135 words) - 12:24, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME I Problems]]1 KB (154 words) - 12:30, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AIME I Problems]]1 KB (135 words) - 12:31, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME II Problems]]1 KB (135 words) - 12:30, 22 March 2011
- {{AIME Problems|year=2006|n=I}} == Problem 1 ==7 KB (1,173 words) - 03:31, 4 January 2023
- == Problem == ...cient]] <math>{n \choose 6} = \frac{n\cdot(n-1)\cdot(n-2)\cdot(n-3)\cdot(n-4)\cdot(n-5)}{6\cdot5\cdot4\cdot3\cdot2\cdot1}</math>.1 KB (239 words) - 11:54, 31 July 2023
- == Problem == *Person 2: <math>\frac{6 \cdot 4 \cdot 2}{6 \cdot 5 \cdot 4} = \frac 25</math>4 KB (628 words) - 11:28, 14 April 2024
- == Problem == An [[infinite]] [[geometric series]] has sum 2005. A new series, obtained by squaring each term of the original series, has 13 KB (581 words) - 21:19, 22 September 2024
- == Problem == ...og_a b + 6\log_b a=5, 2 \leq a \leq 2005, </math> and <math> 2 \leq b \leq 2005. </math>3 KB (547 words) - 19:15, 4 April 2024
- {{AIME Problems|year=2005|n=II}} == Problem 1 ==7 KB (1,119 words) - 21:12, 28 February 2020
- == Problem == Let <math> x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}. </math> Find <math>(x+1)^{48}</math2 KB (279 words) - 12:33, 27 October 2019
- == Problem == ...> C_3. </math> The radii of <math> C_1 </math> and <math> C_2 </math> are 4 and 10, respectively, and the [[center]]s of the three circles are all [[co4 KB (693 words) - 13:03, 28 December 2021
- == Problem == ...well, so exactly those values of <math>n</math> congruent to <math>1 \pmod 4</math> work. There are <math>\boxed{250}</math> of them in the given range6 KB (1,154 words) - 03:30, 11 January 2024
- == Problem == ..., D=(0,0), E=(2.5-0.5*sqrt(7),9), F=(6.5-0.5*sqrt(7),9), G=(4.5,9), O=(4.5,4.5); draw(A--B--C--D--A);draw(E--O--F);draw(G--O); dot(A^^B^^C^^D^^E^^F^^G^^13 KB (2,080 words) - 13:14, 23 July 2024
