https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Lol+man000&feedformat=atomAoPS Wiki - User contributions [en]2021-04-20T14:32:50ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=Resources_for_Physics_Competitions&diff=122200Resources for Physics Competitions2020-05-09T17:08:41Z<p>Lol man000: Blanked the page</p>
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<div></div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Resources_for_Physics_Competitions&diff=122199Resources for Physics Competitions2020-05-09T17:08:00Z<p>Lol man000: Created page with "[size=150]A Comprehensive List of Physics Olympiad Resources[/size] [b]Introductory Physics Books[/b] [list] [*] [b][url=https://www.amazon.com/s?k=conceptual+physics&ref=nb_..."</p>
<hr />
<div>[size=150]A Comprehensive List of Physics Olympiad Resources[/size]<br />
<br />
[b]Introductory Physics Books[/b]<br />
[list]<br />
[*] [b][url=https://www.amazon.com/s?k=conceptual+physics&ref=nb_sb_noss]Conceptual Physics[/url][/b] by Paul G. Hewitt (Algebra-based). A comprehensive book on algebra-based physics. Good for people who haven't had exposure to calculus yet. <br />
[*][b][url=https://www.amazon.com/Physics-Scientists-Engineers-Strategic-Approach/dp/0133942651/ref=sr_1_1?keywords=knight+physics&qid=1583572681&sr=8-1]Physics for Scientists and Engineers[/url][/b] by Randall D. Knight (Calculus-based).<br />
[*] [b][url = https://www.amazon.com/Fundamentals-Physics-10th-David-Halliday-ebook/dp/B07889MJMT/ref=sr_1_1?crid=185GPX3XV54QA&dchild=1&keywords=fundamentals+of+physics+10th+edition+halliday+and+resnick&qid=1588993335&sprefix=Fundamentals+of+Physics+%2Caps%2C206&sr=8-1]Fundamentals of Physics[/url][/b] by Halliday Resnick Walker (Calculus-based). Easier version of Halliday Resnick Krane (HRK, see below).<br />
[*] [b][url=https://www.amazon.com/Physics-1-Robert-Resnick/dp/0471320579/?pldnSite=1]Physics[/url][/b] by Halliday Resnick Krane (Calculus-based) Harder version of HRW with about 1/3 more harder material added to each chapter. Previous editions were edited by former USAPhO coach. This book covers almost all the material required for physics olympiads and is recommended by many coaches and teachers alike. <br />
[/list]<br />
<br />
[b]Subject Specific Books[/b]<br />
[list]<br />
[*] [b][url=https://www.amazon.com/Introduction-Electrodynamics-David-J-Griffiths/dp/1108420419]Introduction to Electrodynamics[/url][/b] by David J. Griffiths.<br />
[*] [b][url=https://www.amazon.com/Electricity-Magnetism-Edward-M-Purcell/dp/1107014026/]Electricity and Magnetism[/url][/b] by Purcell and Morin.<br />
[*] [b][url = https://www.amazon.com/Introduction-Classical-Mechanics-Problems-Solutions/dp/0521876222]An Introduction to Classical Mechanics[/url][/b] by David Morin.<br />
[*] [b][url=https://www.amazon.com/Introduction-Mechanics-Daniel-Kleppner/dp/0521198119]An Introduction to Mechanics[/url][/b] by Kleppner and Kolenkow.<br />
[*] [b][url=https://www.amazon.com/Optics-5th-Eugene-Hecht/dp/0133977226]Optics[/url][/b] by Eugene Hecht.<br />
[*] [b][url=https://www.amazon.com/Concepts-Thermal-Physics-Stephen-Blundell-ebook/dp/B00O148EZO/ref=sr_1_1?crid=1AWIVCZ2WGVLC&dchild=1&keywords=blundell+and+blundell&qid=1589001543&s=books&sprefix=Blundell+and+Bl%2Cstripbooks%2C183&sr=1-1]Concepts in Thermal Physics[/url][/b] by Stephen J. Blundell, Katherine M. Blundell.<br />
[*] [b][url=https://www.amazon.com/Modern-Physics-Kenneth-S-Krane/dp/1118061144/ref=sr_1_1?dchild=1&keywords=Modern+Physics+Krane&qid=1589001641&s=books&sr=1-1]Modern Physics[/url][/b] by Kenneth S. Krane.<br />
[*] [b][url=https://www.amazon.com/Thermodynamics-Dover-Books-Physics-Enrico-ebook/dp/B008TVLP6K/ref=sr_1_1?crid=MRYFX64UIT12&dchild=1&keywords=fermi+thermodynamics&qid=1589001700&s=books&sprefix=Fermi+Thermo%2Cstripbooks%2C172&sr=1-1]Thermodynamics[/url][/b] by Enrico Fermi.<br />
[*] [b][url=https://www.amazon.com/Vibrations-Waves-P-French-ebook/dp/B078JLQW49/ref=sr_1_2?dchild=1&keywords=Vibrations+and+Waves&qid=1589001816&s=books&sr=1-2]Vibrations and Waves[/url][/b] by A.P French.<br />
[*] [b][url=http://physics.weber.edu/thermal/]Thermal Physics[/url][/b] by Daniel Schroeder. <br />
[*] [b][url= https://www.mheducation.co.in/concepts-of-modern-physics-sie-9789351341857-india] Concepts of Modern physics[/url][/b] by Beiser.<br />
[*] [b][url= https://www.amazon.com/Fluid-Mechanics-8-Ed-WHITE/dp/9385965492/ref=dp_ob_image_bk ]Fluid mechanics[/url][/b] by Frank White.<br />
[*] [b][url= https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927]Introduction Quantum Mechanics[/url][/b] by David Griffiths. This book contains a brilliant discussion of quantum mechanics in a very approachable and keen way.<br />
<br />
[/list]<br />
[b]Problem Books/Handouts[/b]<br />
[list]<br />
[*] [b][url=https://smile.amazon.com/Thinking-Physics-Understandable-Practical-Reality/dp/0935218084]Thinking Physics[/url][/b] by Lewis Carroll Epstein (a book of conceptual problems for beginners and intermediate-levels)<br />
[*] [b][url=https://smile.amazon.com/Problems-Solutions-Introductory-Mechanics-David/dp/1482086921]Problems and Solutions in Introductory Mechanics[/url][/b] by David Morin (A good book for preparing to the F=ma exam and for practicing basic mechanics)<br />
[*] [b][url=https://smile.amazon.com/200-Puzzling-Physics-Problems-Solutions/dp/0521774802]200 Puzzling Physics Problems[/url][/b] by Gnadig (USAPhO / IPhO level problems)<br />
[*] [b][url=https://www.amazon.com/P%C3%A9ter-Gn%C3%A4dig-ebook/dp/B01DPNK4D6/ref=sr_1_1?dchild=1&keywords=200+More+Puzzling+physics+problems&qid=1589002162&s=books&sr=1-1]200 More Puzzling Physics Problems[/url][/b] by Peter Gnadig.<br />
[*] [b][url=https://smile.amazon.com/Creative-Physics-Problems-Solutions-Learning/dp/1843318695]300 Creative Physics Problems with Solutions[/url][/b] by Holics (USAPhO / IPhO level problems)<br />
[*] [b][url=https://smile.amazon.com/Physics-Degree-G-Thomas/dp/9056992775]Physics to a Degree[/url][/b] by Thomas and Raine (USAPhO / IPhO level problems)<br />
[*] [b][url=https://smile.amazon.com/Thinking-Like-Physicist-Undergraduates-1987-07-01/dp/B01K0RZDYK]Thinking Like a Physicist[/url][/b] by Thompson (USAPhO / IPhO level problems)<br />
[*] [b][url=https://www.amazon.in/Pathfinder-Olympiad-Tiwari-Singh-Jangid/dp/9332568715]Pathfinder for Olympiad & JEE:Physics[/url][/b] by Arwind Tiwari/Sachin Singh.<br />
[*] [b][url=https://www.amazon.in/Problems-GENERAL-PHYSICS-I-Irodov/dp/9351762564/ref=sr_1_1?crid=6VC3LERN4FDZ&dchild=1&keywords=irodov+physics&qid=1588994723&s=books&sprefix=irodov+%2Cstripbooks%2C257&sr=1-1]Problems in General Physics[/url][/b] by I.E Irodov.<br />
[*] [b][url=https://www.amazon.in/Science-Everyone-Aptitude-Problem-Physics/dp/9350941449/ref=sr_1_1?dchild=1&keywords=krotov&qid=1588994821&s=books&sr=1-1]Aptitude Test Problems in Physics[/url][/b] by S.S Krotov.<br />
[*] [b][url=https://www.ioc.ee/~kalda/ipho/]Jaan Kalda's Handouts[/url][/b] by Jaan Kalda (IPhO Level Problems)<br />
[*] [b][url=https://physoly.tech/kalda/]Solutions to Jaan Kalda's Handouts[/url][/b]<br />
[*] [b][url=https://artofproblemsolving.com/community/q1h1416845p7977573]Lagrangian Mechanics in Action[/url][/b] by AstrapiGnosis<br />
[*] [b][url=https://drive.google.com/file/d/1zBnBI3xEclkgIG_PNylPEHv6dL21Tyfk/view]F=ma Solutions Manual[/url][/b] by Branislav Kisaˇcanin and Eric K. Zhang.<br />
[*] [b][url=https://www.amazon.com/Physics-Olympiad-Basic-Advanced-Exercises/dp/981455667X]Physics Olympiad - Basic to Advanced Exercises[/url][/b] by The Committee Of Japan Physics Olympiad Japan <br />
[*] [b][url=https://www.amazon.com/Competitive-Physics-Mechanics-General-Aspects-ebook/dp/B07HM93NJC/ref=sr_1_2?dchild=1&keywords=Competitive+Physics&qid=1589003000&s=books&sr=1-2]Competitive Physics: Mechanics and Waves[/url][/b] by Wang and Ricardo<br />
[*] [b][url=https://www.amazon.com/Competitive-Physics-Thermodynamics-Electromagnetism-Relativity/dp/9813238534/ref=sr_1_1?dchild=1&keywords=Competitive+Physics&qid=1589003000&s=books&sr=1-1]Competitive Physics: Thermodynamics, Electromagnetism and Relativity[/url][/b] by Wang and Ricardo.<br />
[*] [b][url=http://www.feynmanlectures.caltech.edu/]Feynman's Lectures on Physics[/url][/b].<br />
[/list]<br />
<br />
<br />
[b]List of Physics Contests[/b]<br />
[list]<br />
[*] [b][url=https://opho.physoly.tech/]OPhO[/url][/b]<br />
[*] [b][url=https://ortvay.elte.hu/main.html]Rudolf Ortvay Competition in Physics[/url][/b]<br />
[*] [b][url=https://eupho2019.lu.lv/]EuPhO[/url][/b]<br />
[*] [b][url=https://www.aapt.org/physicsteam/2020/pastexams.cfm]F=ma Exam[/url][/b]<br />
[*] [b][url=https://www.aapt.org/physicsteam/2020/pastexams.cfm]USAPhO[/url][/b]<br />
[*] [b][url=https://www.aapt.org/programs/physicsbowl/]Physics Bowl[/url][/b]<br />
[*] [b][url=https://uwaterloo.ca/sir-isaac-newton-exam/]Sir Isaac Newton Exam[/url][/b]<br />
[*] [b][url=https://fykos.org/en]FYKOS Internet Physics Competition[/url][/b]<br />
[*] [b][url=http://liquids.seas.harvard.edu/oleg/competition/prev.html]BAUPC[/url][/b]<br />
[*] [b][url=https://www.ioc.ee/~kalda/ipho/E_S.html]NBPhO[/url][/b]<br />
[*] [b][url=https://physprob.com/]IPhO[/url][/b]<br />
[*] [b][url=https://physicscup.ee/]Physics Cup[/url][/b]<br />
[*] [b][url=https://olympiads.hbcse.tifr.res.in/how-to-prepare/past-papers/]INPhO[/url][/b]<br />
[*] [b][url=http://hkpho.phys.ust.hk/panpearl_2016.html]HKPhO[/url][/b]<br />
[*] [b][url=https://izho.kz/problems/]IZhO[/url][/b]<br />
[*] [b][url=https://apho2020.tw/site/page.aspx?pid=901&sid=1316&lang=en]APhO[/url][/b]<br />
[*] [b][url=https://www.bpho.org.uk/]BPhO[/url][/b]<br />
[*] [b][url=http://hkpho.phys.ust.hk/panpearl_2016.html ]Pan Pearl River Delta Physics Olympiad[/url][/b]<br />
[*] [b][url= https://www.asi.edu.au/programs/past-exams/physics-olympiad-past-exams/]AuPhO[/url][/b]<br />
[*] [b][url= http://pupc.princeton.edu/Archive.php]Princeton University Physics Competition[/url][/b]<br />
[*] [b][url= https://www.ioc.ee/~kalda/ipho/GPhO/]Gulf Physics Olympiad [/url][/b]<br />
[*] [b][url= https://online.fyziklani.cz/en/]Online Physics Brawl[/url][/b]<br />
[*] [b][url= https://tjphysicsolympiad.com/]TJPhO[/url][/b]<br />
[*] [b][url= http://www.uphysicsc.com/]The University Physics Competition[/url][/b]<br />
[*] [b][url= http://thworldcup.com/]ThWorldCup[/url][/b]<br />
[*] [b][url= http://physicsu.org/explorer]PUEC[/url][/b]<br />
[*] [b][url= http://www.jpho.jp/index_challenge.html]JPhO[/url][/b] (in Japanese)<br />
<br />
[/list]<br />
<br />
[b]Other Resources[/b]<br />
[list]<br />
[*] [b][url=https://discord.gg/3wGtwA5]Physics Olympiad Discord Server[/url][/b].<br />
[*] [b][url=https://www.nsta.org/publications/quantum.aspx]Quantum Magazine[/url][/b].<br />
[*] [b][url=https://www.bpho.org.uk/resources/upgrade-your-physics]Upgrade Your Physics[/url][/b] by BPhO. <br />
[*] [b][url=https://ocw.mit.edu/courses/physics/8-01sc-classical-mechanics-fall-2016/]MIT OCW 8.01[/url][/b] (Classical Mechanics)<br />
[*] [b][url=https://ocw.mit.edu/courses/physics/8-02-physics-ii-electricity-and-magnetism-spring-2007/]MIT OCW 8.02[/url][/b] (Electricity and Magnetism)<br />
[*] [b][url=https://artofproblemsolving.com/school/woot-physics]Physics WOOT[/url][/b] created by AoPS.<br />
[*] [b][url=https://artofproblemsolving.com/school/course/fma]F=ma Problem Series Class[/url][/b] created by AoPS.<br />
[*] [b][url=https://knzhou.github.io/]Kevin Zhou's Tutoring Program[/url][/b] (high level)<br />
[*] [b][url=https://www.awesomemath.org/academy/online-courses/]AwesomeMath Physics Classes[/url][/b].<br />
[*] [b][url=https://isaacphysics.org/]Isaac Physics[/url][/b].<br />
[*] [b][url=https://everaise.org/physics-mechanics/]Everaise Academy Physics Classes[/url][/b] (these are free, directed to people who are starting physics competitions)<br />
[*] [b][url=https://physoly.tech/]Physics Olympiad Hub[/url][/b]<br />
[*] [b][url=https://www.youtube.com/view_play_list?p=CCD6C043FEC59772]Leonard Susskind - Modern Physics: Special Relativity Video Lectures[/url][/b]<br />
[*] [b][url=https://nptel.ac.in/courses/115/106/115106119/]NPTEL Waves and Oscillations[/url][/b]<br />
[*] [b][url=https://artofproblemsolving.com/community/c164]AoPS Physics Forums[/url][/b] :P<br />
[/list]</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Online_Physics_Olympiad&diff=120917Online Physics Olympiad2020-04-13T15:01:52Z<p>Lol man000: /* Submission of Test Papers */</p>
<hr />
<div>== Introduction ==<br />
The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team consisting of 1-3 high school students. Undergraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes.<br />
<br />
Visit the official website at: https://physoly.tech/opho/<br />
<br />
== Open Contest == <br />
Thegch consists of 30+ numerical questions from various categories in physics including mechanics, electromagnetism, thermodynamics, relativity, waves, and more. Teams will work to compete over the course of five days to qualify for the \textit{Invitational Contest}, which will be held the following week. Please see Section <math>3</math> for more details. Competitors will submit their solutions via an on-line submission portal. Difficulty of the contest will be ranging from AP Physics to IPhO. <br />
<br />
== Submission Portal ==<br />
<br />
On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, for any decimal answers, please round your answer to three significant digits!! Generally, more digits are better than less digits.<br />
<br />
== Scoring ==<br />
The base score for each problem is dependent on the difficulty which in turn is decided by the number of people who successfully answered it. Each incorrect attempt will decrease the base score and teams will be awarded bonus points for correctly solving it quickly. <br />
<br />
The scoring mechanism is heavily based off of the one at HMMT:<br />
<cmath><br />
w(n, N) = (0.9)^{i}[\exp(n/30) + \max(8 - \lfloor \ln{N} \rfloor, 2)] + \frac{3}{10}k,<br />
</cmath><br />
where <math>i \in \{0,1,2\}</math> (represents whether a team got it on the first try, second try, or third try) and <math>k \in \{0, 1, 2, \cdots , 10\}</math> which gives a bonus to the first <math>10</math> teams who submit a solution to a problem correctly . The cumulative score of a submission will be determined by the sum of these values. With this scoring system, ties will be very unlikely. Note that the scoring system is subject to change, so if there is any type of edits we want to make we will do so before the start of the contest.<br />
<br />
== Invitational Contest ==<br />
Approximately the top <math>10</math> teams from the Open Contest will be invited to compete in the Invitational Exam. The Invitational Competition will be a three day Olympiad style physics competition. Invitees will be required to write their solutions either handwritten or on a LaTeX compiler (we prefer the latter because many times handwritten solutions are hard to read). For information on an online LaTeX compiler, please visit http://www.overleaf.com.<br />
<br />
== Submission of Test Papers ==<br />
If a team qualifies for the Open Contest, we will e-mail the Invitational Contest to them from opho@physoly.tech. Once a team is finished with write-up of their solutions, they will be asked to submit them to a survey, which will be provided to them via e-mail.<br />
<br />
== Scoring == <br />
Scoring for the invitational competition will be done by the OPhO Lead Organizers. They will each grade a submission's solution out of the points value of the individual problem and then sum all of your scores together. The cumulative sum of your scores over the entire exam will be the submission's final score which will be used to determine prizes.</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Online_Physics_Olympiad&diff=120916Online Physics Olympiad2020-04-13T15:00:51Z<p>Lol man000: /* Scoring */</p>
<hr />
<div>== Introduction ==<br />
The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team consisting of 1-3 high school students. Undergraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes.<br />
<br />
Visit the official website at: https://physoly.tech/opho/<br />
<br />
== Open Contest == <br />
Thegch consists of 30+ numerical questions from various categories in physics including mechanics, electromagnetism, thermodynamics, relativity, waves, and more. Teams will work to compete over the course of five days to qualify for the \textit{Invitational Contest}, which will be held the following week. Please see Section <math>3</math> for more details. Competitors will submit their solutions via an on-line submission portal. Difficulty of the contest will be ranging from AP Physics to IPhO. <br />
<br />
== Submission Portal ==<br />
<br />
On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, for any decimal answers, please round your answer to three significant digits!! Generally, more digits are better than less digits.<br />
<br />
== Scoring ==<br />
The base score for each problem is dependent on the difficulty which in turn is decided by the number of people who successfully answered it. Each incorrect attempt will decrease the base score and teams will be awarded bonus points for correctly solving it quickly. <br />
<br />
The scoring mechanism is heavily based off of the one at HMMT:<br />
<cmath><br />
w(n, N) = (0.9)^{i}[\exp(n/30) + \max(8 - \lfloor \ln{N} \rfloor, 2)] + \frac{3}{10}k,<br />
</cmath><br />
where <math>i \in \{0,1,2\}</math> (represents whether a team got it on the first try, second try, or third try) and <math>k \in \{0, 1, 2, \cdots , 10\}</math> which gives a bonus to the first <math>10</math> teams who submit a solution to a problem correctly . The cumulative score of a submission will be determined by the sum of these values. With this scoring system, ties will be very unlikely. Note that the scoring system is subject to change, so if there is any type of edits we want to make we will do so before the start of the contest.<br />
<br />
== Invitational Contest ==<br />
Approximately the top <math>10</math> teams from the Open Contest will be invited to compete in the Invitational Exam. The Invitational Competition will be a three day Olympiad style physics competition. Invitees will be required to write their solutions either handwritten or on a LaTeX compiler (we prefer the latter because many times handwritten solutions are hard to read). For information on an online LaTeX compiler, please visit http://www.overleaf.com.<br />
<br />
== Submission of Test Papers ==<br />
If a team qualifies for the Open Contest, we will e-mail the Invitational Contest to them from \url{opho@physoly.tech}. Once a team is finished with write-up of their solutions, they will be asked to submit them to a survey, which will be provided to them via e-mail.<br />
<br />
== Scoring == <br />
Scoring for the invitational competition will be done by the OPhO Lead Organizers. They will each grade a submission's solution out of the points value of the individual problem and then sum all of your scores together. The cumulative sum of your scores over the entire exam will be the submission's final score which will be used to determine prizes.</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Online_Physics_Olympiad&diff=120915Online Physics Olympiad2020-04-13T14:46:17Z<p>Lol man000: /* Introduction */</p>
<hr />
<div>== Introduction ==<br />
The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team consisting of 1-3 high school students. Undergraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes.<br />
<br />
Visit the official website at: https://physoly.tech/opho/<br />
<br />
== Open Contest == <br />
Thegch consists of 30+ numerical questions from various categories in physics including mechanics, electromagnetism, thermodynamics, relativity, waves, and more. Teams will work to compete over the course of five days to qualify for the \textit{Invitational Contest}, which will be held the following week. Please see Section <math>3</math> for more details. Competitors will submit their solutions via an on-line submission portal. Difficulty of the contest will be ranging from AP Physics to IPhO. <br />
<br />
== Submission Portal ==<br />
<br />
On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, for any decimal answers, please round your answer to three significant digits!! Generally, more digits are better than less digits.<br />
<br />
== Scoring ==<br />
The base score for each problem is dependent on the difficulty which in turn is decided by the number of people who successfully answered it. Each incorrect attempt will decrease the base score and teams will be awarded bonus points for correctly solving it quickly. \\<br />
<br />
The scoring mechanism is heavily based off of the one at HMMT:<br />
<cmath><br />
w(n, N) = (0.9)^{i}[\exp(n/30) + \max(8 - \lfloor \ln{N} \rfloor, 2)] + \frac{3}{10}k,<br />
</cmath><br />
where <math>i \in \{0,1,2\}</math> (represents whether a team got it on the first try, second try, or third try) and <math>k \in \{0, 1, 2, \cdots , 10\}</math> which gives a bonus to the first <math>10</math> teams who submit a solution to a problem correctly . The cumulative score of a submission will be determined by the sum of these values. With this scoring system, ties will be very unlikely. Note that the scoring system is subject to change, so if there is any type of edits we want to make we will do so before the start of the contest.<br />
<br />
== Invitational Contest ==<br />
Approximately the top <math>10</math> teams from the Open Contest will be invited to compete in the Invitational Exam. The Invitational Competition will be a three day Olympiad style physics competition. Invitees will be required to write their solutions either handwritten or on a LaTeX compiler (we prefer the latter because many times handwritten solutions are hard to read). For information on an online LaTeX compiler, please visit http://www.overleaf.com.<br />
<br />
== Submission of Test Papers ==<br />
If a team qualifies for the Open Contest, we will e-mail the Invitational Contest to them from \url{opho@physoly.tech}. Once a team is finished with write-up of their solutions, they will be asked to submit them to a survey, which will be provided to them via e-mail.<br />
<br />
== Scoring == <br />
Scoring for the invitational competition will be done by the OPhO Lead Organizers. They will each grade a submission's solution out of the points value of the individual problem and then sum all of your scores together. The cumulative sum of your scores over the entire exam will be the submission's final score which will be used to determine prizes.</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Online_Physics_Olympiad&diff=120914Online Physics Olympiad2020-04-13T14:45:47Z<p>Lol man000: /* Invitational Contest */</p>
<hr />
<div>== Introduction ==<br />
The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team consisting of 1-3 high school students. Undergraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes.<br />
<br />
== Open Contest == <br />
Thegch consists of 30+ numerical questions from various categories in physics including mechanics, electromagnetism, thermodynamics, relativity, waves, and more. Teams will work to compete over the course of five days to qualify for the \textit{Invitational Contest}, which will be held the following week. Please see Section <math>3</math> for more details. Competitors will submit their solutions via an on-line submission portal. Difficulty of the contest will be ranging from AP Physics to IPhO. <br />
<br />
== Submission Portal ==<br />
<br />
On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, for any decimal answers, please round your answer to three significant digits!! Generally, more digits are better than less digits.<br />
<br />
== Scoring ==<br />
The base score for each problem is dependent on the difficulty which in turn is decided by the number of people who successfully answered it. Each incorrect attempt will decrease the base score and teams will be awarded bonus points for correctly solving it quickly. \\<br />
<br />
The scoring mechanism is heavily based off of the one at HMMT:<br />
<cmath><br />
w(n, N) = (0.9)^{i}[\exp(n/30) + \max(8 - \lfloor \ln{N} \rfloor, 2)] + \frac{3}{10}k,<br />
</cmath><br />
where <math>i \in \{0,1,2\}</math> (represents whether a team got it on the first try, second try, or third try) and <math>k \in \{0, 1, 2, \cdots , 10\}</math> which gives a bonus to the first <math>10</math> teams who submit a solution to a problem correctly . The cumulative score of a submission will be determined by the sum of these values. With this scoring system, ties will be very unlikely. Note that the scoring system is subject to change, so if there is any type of edits we want to make we will do so before the start of the contest.<br />
<br />
== Invitational Contest ==<br />
Approximately the top <math>10</math> teams from the Open Contest will be invited to compete in the Invitational Exam. The Invitational Competition will be a three day Olympiad style physics competition. Invitees will be required to write their solutions either handwritten or on a LaTeX compiler (we prefer the latter because many times handwritten solutions are hard to read). For information on an online LaTeX compiler, please visit http://www.overleaf.com.<br />
<br />
== Submission of Test Papers ==<br />
If a team qualifies for the Open Contest, we will e-mail the Invitational Contest to them from \url{opho@physoly.tech}. Once a team is finished with write-up of their solutions, they will be asked to submit them to a survey, which will be provided to them via e-mail.<br />
<br />
== Scoring == <br />
Scoring for the invitational competition will be done by the OPhO Lead Organizers. They will each grade a submission's solution out of the points value of the individual problem and then sum all of your scores together. The cumulative sum of your scores over the entire exam will be the submission's final score which will be used to determine prizes.</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Online_Physics_Olympiad&diff=120913Online Physics Olympiad2020-04-13T14:45:31Z<p>Lol man000: /* Scoring */</p>
<hr />
<div>== Introduction ==<br />
The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team consisting of 1-3 high school students. Undergraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes.<br />
<br />
== Open Contest == <br />
Thegch consists of 30+ numerical questions from various categories in physics including mechanics, electromagnetism, thermodynamics, relativity, waves, and more. Teams will work to compete over the course of five days to qualify for the \textit{Invitational Contest}, which will be held the following week. Please see Section <math>3</math> for more details. Competitors will submit their solutions via an on-line submission portal. Difficulty of the contest will be ranging from AP Physics to IPhO. <br />
<br />
== Submission Portal ==<br />
<br />
On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, for any decimal answers, please round your answer to three significant digits!! Generally, more digits are better than less digits.<br />
<br />
== Scoring ==<br />
The base score for each problem is dependent on the difficulty which in turn is decided by the number of people who successfully answered it. Each incorrect attempt will decrease the base score and teams will be awarded bonus points for correctly solving it quickly. \\<br />
<br />
The scoring mechanism is heavily based off of the one at HMMT:<br />
<cmath><br />
w(n, N) = (0.9)^{i}[\exp(n/30) + \max(8 - \lfloor \ln{N} \rfloor, 2)] + \frac{3}{10}k,<br />
</cmath><br />
where <math>i \in \{0,1,2\}</math> (represents whether a team got it on the first try, second try, or third try) and <math>k \in \{0, 1, 2, \cdots , 10\}</math> which gives a bonus to the first <math>10</math> teams who submit a solution to a problem correctly . The cumulative score of a submission will be determined by the sum of these values. With this scoring system, ties will be very unlikely. Note that the scoring system is subject to change, so if there is any type of edits we want to make we will do so before the start of the contest.<br />
<br />
== Invitational Contest ==<br />
Approximately the top <math>10</math> teams from the Open Contest will be invited to compete in the Invitational Exam. The Invitational Competition will be a three day Olympiad style physics competition. Invitees will be required to write their solutions either handwritten or on a LaTeX compiler (we prefer the latter because many times handwritten solutions are hard to read). For information on an online LaTeX compiler, please visit \url{http://www.overleaf.com}. <br />
<br />
== Submission of Test Papers ==<br />
If a team qualifies for the Open Contest, we will e-mail the Invitational Contest to them from \url{opho@physoly.tech}. Once a team is finished with write-up of their solutions, they will be asked to submit them to a survey, which will be provided to them via e-mail.<br />
<br />
== Scoring == <br />
Scoring for the invitational competition will be done by the OPhO Lead Organizers. They will each grade a submission's solution out of the points value of the individual problem and then sum all of your scores together. The cumulative sum of your scores over the entire exam will be the submission's final score which will be used to determine prizes.</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Online_Physics_Olympiad&diff=120912Online Physics Olympiad2020-04-13T14:45:15Z<p>Lol man000: /* Submission Portal */</p>
<hr />
<div>== Introduction ==<br />
The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team consisting of 1-3 high school students. Undergraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes.<br />
<br />
== Open Contest == <br />
Thegch consists of 30+ numerical questions from various categories in physics including mechanics, electromagnetism, thermodynamics, relativity, waves, and more. Teams will work to compete over the course of five days to qualify for the \textit{Invitational Contest}, which will be held the following week. Please see Section <math>3</math> for more details. Competitors will submit their solutions via an on-line submission portal. Difficulty of the contest will be ranging from AP Physics to IPhO. <br />
<br />
== Submission Portal ==<br />
<br />
On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, for any decimal answers, please round your answer to three significant digits!! Generally, more digits are better than less digits.<br />
<br />
== Scoring ==<br />
The base score for each problem is dependent on the difficulty which in turn is decided by the number of people who successfully answered it. Each incorrect attempt will decrease the base score and teams will be awarded bonus points for correctly solving it quickly. \\<br />
<br />
The scoring mechanism is heavily based off of the one at HMMT:<br />
\[<br />
w(n, N) = (0.9)^{i}[\exp(n/30) + \max(8 - \lfloor \ln{N} \rfloor, 2)] + \frac{3}{10}k,<br />
\]<br />
where <math>i \in \{0,1,2\}</math> (represents whether a team got it on the first try, second try, or third try) and <math>k \in \{0, 1, 2, \cdots , 10\}</math> which gives a bonus to the first <math>10</math> teams who submit a solution to a problem correctly . The cumulative score of a submission will be determined by the sum of these values. With this scoring system, ties will be very unlikely. Note that the scoring system is subject to change, so if there is any type of edits we want to make we will do so before the start of the contest.<br />
<br />
== Invitational Contest ==<br />
Approximately the top <math>10</math> teams from the Open Contest will be invited to compete in the Invitational Exam. The Invitational Competition will be a three day Olympiad style physics competition. Invitees will be required to write their solutions either handwritten or on a LaTeX compiler (we prefer the latter because many times handwritten solutions are hard to read). For information on an online LaTeX compiler, please visit \url{http://www.overleaf.com}. <br />
<br />
== Submission of Test Papers ==<br />
If a team qualifies for the Open Contest, we will e-mail the Invitational Contest to them from \url{opho@physoly.tech}. Once a team is finished with write-up of their solutions, they will be asked to submit them to a survey, which will be provided to them via e-mail.<br />
<br />
== Scoring == <br />
Scoring for the invitational competition will be done by the OPhO Lead Organizers. They will each grade a submission's solution out of the points value of the individual problem and then sum all of your scores together. The cumulative sum of your scores over the entire exam will be the submission's final score which will be used to determine prizes.</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Online_Physics_Olympiad&diff=120911Online Physics Olympiad2020-04-13T14:44:36Z<p>Lol man000: /* Submission Portal */</p>
<hr />
<div>== Introduction ==<br />
The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team consisting of 1-3 high school students. Undergraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes.<br />
<br />
== Open Contest == <br />
Thegch consists of 30+ numerical questions from various categories in physics including mechanics, electromagnetism, thermodynamics, relativity, waves, and more. Teams will work to compete over the course of five days to qualify for the \textit{Invitational Contest}, which will be held the following week. Please see Section <math>3</math> for more details. Competitors will submit their solutions via an on-line submission portal. Difficulty of the contest will be ranging from AP Physics to IPhO. <br />
<br />
== Submission Portal ==<br />
On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, <math>\textbf{for any decimal answers, please round your answer to three significant digits}</math>!! Generally, more digits are better than less digits.<br />
<br />
== Scoring ==<br />
The base score for each problem is dependent on the difficulty which in turn is decided by the number of people who successfully answered it. Each incorrect attempt will decrease the base score and teams will be awarded bonus points for correctly solving it quickly. \\<br />
<br />
The scoring mechanism is heavily based off of the one at HMMT:<br />
\[<br />
w(n, N) = (0.9)^{i}[\exp(n/30) + \max(8 - \lfloor \ln{N} \rfloor, 2)] + \frac{3}{10}k,<br />
\]<br />
where <math>i \in \{0,1,2\}</math> (represents whether a team got it on the first try, second try, or third try) and <math>k \in \{0, 1, 2, \cdots , 10\}</math> which gives a bonus to the first <math>10</math> teams who submit a solution to a problem correctly . The cumulative score of a submission will be determined by the sum of these values. With this scoring system, ties will be very unlikely. Note that the scoring system is subject to change, so if there is any type of edits we want to make we will do so before the start of the contest.<br />
<br />
== Invitational Contest ==<br />
Approximately the top <math>10</math> teams from the Open Contest will be invited to compete in the Invitational Exam. The Invitational Competition will be a three day Olympiad style physics competition. Invitees will be required to write their solutions either handwritten or on a LaTeX compiler (we prefer the latter because many times handwritten solutions are hard to read). For information on an online LaTeX compiler, please visit \url{http://www.overleaf.com}. <br />
<br />
== Submission of Test Papers ==<br />
If a team qualifies for the Open Contest, we will e-mail the Invitational Contest to them from \url{opho@physoly.tech}. Once a team is finished with write-up of their solutions, they will be asked to submit them to a survey, which will be provided to them via e-mail.<br />
<br />
== Scoring == <br />
Scoring for the invitational competition will be done by the OPhO Lead Organizers. They will each grade a submission's solution out of the points value of the individual problem and then sum all of your scores together. The cumulative sum of your scores over the entire exam will be the submission's final score which will be used to determine prizes.</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Online_Physics_Olympiad&diff=120910Online Physics Olympiad2020-04-13T14:43:39Z<p>Lol man000: Created page with "== Introduction == The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team cons..."</p>
<hr />
<div>== Introduction ==<br />
The Online Physics Olympiad (OPhO) is one of the largest online run physics olympiads in the world. This contest is a team based contest with each team consisting of 1-3 high school students. Undergraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes.<br />
<br />
== Open Contest == <br />
Thegch consists of 30+ numerical questions from various categories in physics including mechanics, electromagnetism, thermodynamics, relativity, waves, and more. Teams will work to compete over the course of five days to qualify for the \textit{Invitational Contest}, which will be held the following week. Please see Section <math>3</math> for more details. Competitors will submit their solutions via an on-line submission portal. Difficulty of the contest will be ranging from AP Physics to IPhO. <br />
<br />
== Submission Portal ==<br />
On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediately be logged by the program. Most importantly, \textbf{for any decimal answers, please round your answer to three significant digits}!! Generally, more digits are better than less digits.<br />
<br />
== Scoring ==<br />
The base score for each problem is dependent on the difficulty which in turn is decided by the number of people who successfully answered it. Each incorrect attempt will decrease the base score and teams will be awarded bonus points for correctly solving it quickly. \\<br />
<br />
The scoring mechanism is heavily based off of the one at HMMT:<br />
\[<br />
w(n, N) = (0.9)^{i}[\exp(n/30) + \max(8 - \lfloor \ln{N} \rfloor, 2)] + \frac{3}{10}k,<br />
\]<br />
where <math>i \in \{0,1,2\}</math> (represents whether a team got it on the first try, second try, or third try) and <math>k \in \{0, 1, 2, \cdots , 10\}</math> which gives a bonus to the first <math>10</math> teams who submit a solution to a problem correctly . The cumulative score of a submission will be determined by the sum of these values. With this scoring system, ties will be very unlikely. Note that the scoring system is subject to change, so if there is any type of edits we want to make we will do so before the start of the contest.<br />
<br />
== Invitational Contest ==<br />
Approximately the top <math>10</math> teams from the Open Contest will be invited to compete in the Invitational Exam. The Invitational Competition will be a three day Olympiad style physics competition. Invitees will be required to write their solutions either handwritten or on a LaTeX compiler (we prefer the latter because many times handwritten solutions are hard to read). For information on an online LaTeX compiler, please visit \url{http://www.overleaf.com}. <br />
<br />
== Submission of Test Papers ==<br />
If a team qualifies for the Open Contest, we will e-mail the Invitational Contest to them from \url{opho@physoly.tech}. Once a team is finished with write-up of their solutions, they will be asked to submit them to a survey, which will be provided to them via e-mail.<br />
<br />
== Scoring == <br />
Scoring for the invitational competition will be done by the OPhO Lead Organizers. They will each grade a submission's solution out of the points value of the individual problem and then sum all of your scores together. The cumulative sum of your scores over the entire exam will be the submission's final score which will be used to determine prizes.</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Physics_competitions&diff=120909Physics competitions2020-04-13T14:36:02Z<p>Lol man000: /* International Physics competitions */</p>
<hr />
<div>This is a resources page for students interested in '''Physics competitions'''. Please add quality resources.<br />
<br />
<br />
== International Physics competitions ==<br />
* [[International Physics Olympiad]] [http://www.jyu.fi/ipho website]<br />
* [[Online Physics Olympiad]] [https://physoly.tech/opho/]<br />
* [[International Physics Online Olympiad (IPhOO)]] [http://onlinescienceolympiads.org website]<br />
* [[Rudolf Ortvay Problem Solving Contest in Physics]] [http://ortvay.elte.hu/ website]<br />
* [[The University Physics Competition]] [http://www.uphysicsc.com website]<br />
* [[Online Physics Brawl]] – next on '''28th November 2018''' [http://physicsbrawl.org website]<br />
* [[FYKOS – The Internet Physics Competition]] [http://fykos.org website]<br />
* [[Physics League Across Numerous Countries for Kick-ass Students (PLANCKS)]] [http://plancks.info/ website]<br />
* [[Princeton University Physics Competition]] [http://physics.princeton.edu/pupc/ website]<br />
<br />
== National Physics competitions ==<br />
=== Canada ===<br />
* [[Canadian Association of Physicists High School Competition]] [http://physics.usask.ca/~pywell/HighSchool/index.html website]<br />
<br />
<br />
=== United States ===<br />
* [[Unites States Physics Olympiad]] [http://www.aapt.org/Contests/olympiad.cfm website] <br />
<br><br />
* [[American Association of PhysicsTeachers Physics Bowl]] [http://www.aapt.org/Contests/physicsbowl.cfm website]<br />
* [[Auburn Physics Invitation]] [http://www.physics.auburn.edu/~msimon/InvBro99-2K.html website]<br />
* [[Iowa State Physics Olympics]] [http://www.educ.drake.edu/gerlovich/physics%20olympics/physics_olympics.html website]<br />
* [[NJAAPT Physics Olympics]] [http://www.njaapt.org/PhysicsOlympics/2005-2006/NJ%20Physics%20Olympics%202005-2006.htm website]<br />
* [[Princeton University Physics Competition]] [http://physics.princeton.edu/pupc/ website]<br />
* [[The Raytheon/TAPT Annual High School Physics Competition]]<br />
* [[St. Louis Area Physics Teachers Physics Competition]] [http://www.slapt.org/ website]<br />
* [[San Diego COE/SDSA Physics Team Competition]] [http://www.sdsa.org/Physics/about.html website]<br />
* [[Unites States Physics Olympiad]] [http://www.aapt.org/Contests/olympiad.cfm website] <br />
* [[University of Alabama High School Physics contest]] [http://bama.ua.edu/~physics/Contest2006.html website]<br />
* [[University of Miami Physics Competition]] [http://www.physics.miami.edu/competition/ website]<br />
* [[University of Michigan Physics Olympiad]] [http://phys-advlab.physics.lsa.umich.edu/ website]<br />
* [[UNC-Charlotte Physics Competition]] [http://education.uncc.edu/aewickli/supercomp1.htm#Physics website]<br />
* [[University of Northern Iowa Regional Physics Olympics]] [http://www.physics.uni.edu/uni_aea267_olympics.shtml website]<br />
* [[Utah Physics Olympiad]] [http://departments.weber.edu/sciencecenter/ScienceOlympiad/Olympiadpage.htm website]<br />
* [[Western Kentucky Physics Olympics]] [http://physics.wku.edu/olympics/events.html website]<br />
* [[Yale Physics Olympics]] [http://wnsl.physics.yale.edu/events/olympics/ website]<br />
<br />
== Regional Physics competitions ==<br />
* [[Asian Physics Olympiad]] [http://www.apho.org/en/home/index.php?charencode=en website]<br />
*[[Ibero-American Physics Olympiad]] - [http://oc.uan.edu.co/oibf/oibf.htm website]<br />
<br />
== Resources ==<br />
==Past Contests==<br />
*[[Boston Area Undergraduate Physics Competition]] [http://liquids.deas.harvard.edu/oleg/competition/ website]<br />
=== Books ===<br />
<br />
<br />
=== Online Resources ===<br />
* [[AoPS]] hosts both an [http://www.artofproblemsolving.com/Forum/index.php?f=405 Introductory Physics Forum] as well as an [http://www.artofproblemsolving.com/Forum/index.php?f=332 Advanced Physics Forum].<br />
* [[AoPS]] also teaches [https://artofproblemsolving.com/school/woot-physics PhysicsWOOT]—like WOOT, but for physics.<br />
* [http://www.physicsforums.com/ Physics Forums] -- One of the largest educational forums on the web!<br />
* [http://physicsweb.org/ PhysicsWeb]<br />
* [http://www.luiseduardo.com.br/ Physics Challenges - Problems] -- Collection of Challenging Physics Problems<br />
<br />
== See also ==<br />
* [[Physics books]]<br />
* [[Physics scholarships]]<br />
* [[Science competitions]]<br />
* [[Mathematics competitions]]<br />
* [[Physics]]</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=2003_AMC_10B_Problems/Problem_20&diff=1128712003 AMC 10B Problems/Problem 202019-12-15T05:18:08Z<p>Lol man000: /* Solution 3 */</p>
<hr />
<div>{{duplicate|[[2003 AMC 12B Problems|2003 AMC 12B #14]] and [[2003 AMC 10B Problems|2003 AMC 10B #20]]}}<br />
<br />
==Problem==<br />
In rectangle <math>ABCD, AB=5</math> and <math>BC=3</math>. Points <math>F</math> and <math>G</math> are on <math>\overline{CD}</math> so that <math>DF=1</math> and <math>GC=2</math>. Lines <math>AF</math> and <math>BG</math> intersect at <math>E</math>. Find the area of <math>\triangle AEB</math>.<br />
<center><asy><br />
unitsize(8mm);<br />
defaultpen(linewidth(.8pt)+fontsize(10pt));<br />
dotfactor=0;<br />
<br />
pair A=(0,0), B=(5,0), C=(5,3), D=(0,3);<br />
pair F=(1,3), G=(3,3);<br />
pair E=(5/3,5);<br />
<br />
draw(A--B--C--D--cycle);<br />
draw(A--E);<br />
draw(B--E);<br />
<br />
pair[] ps={A,B,C,D,E,F,G}; dot(ps);<br />
label("$A$",A,SW);<br />
label("$B$",B,SE);<br />
label("$C$",C,NE);<br />
label("$D$",D,NW);<br />
label("$E$",E,N);<br />
label("$F$",F,SE);<br />
label("$G$",G,SW);<br />
label("$1$",midpoint(D--F),N);<br />
label("$2$",midpoint(G--C),N);<br />
label("$5$",midpoint(A--B),S);<br />
label("$3$",midpoint(A--D),W);<br />
</asy></center><br />
<math>\textbf{(A) } 10 \qquad\textbf{(B) } \frac{21}{2} \qquad\textbf{(C) } 12 \qquad\textbf{(D) } \frac{25}{2} \qquad\textbf{(E) } 15</math><br />
<br />
==Solution 1==<br />
<br />
<math>\triangle EFG \sim \triangle EAB</math> because <math>FG \parallel AB.</math> The ratio of <math>\triangle EFG</math> to <math>\triangle EAB</math> is <math>2:5</math> since <math>AB=5</math> and <math>FG=2</math> from subtraction. If we let <math>h</math> be the height of <math>\triangle EAB,</math><br />
<br />
<cmath>\frac{2}{5} = \frac{h-3}{h}</cmath><br />
<cmath>2h = 5h-15</cmath><br />
<cmath>3h = 15</cmath><br />
<cmath>h = 5</cmath><br />
<br />
The height is <math>5</math> so the area of <math>\triangle EAB</math> is <math>\frac{1}{2}(5)(5) = \boxed{\textbf{(D)}\ \frac{25}{2}}</math>.<br />
<br />
==Solution 2==<br />
<br />
We can look at this diagram as if it were a coordinate plane with point <math>A</math> being <math>(0,0)</math>. This means that the equation of the line <math>AE</math> is <math>y=3x</math> and the equation of the line <math>EB</math> is <math>y=\frac{-3}{2}x+\frac{15}{2}</math>. From this we can set of the follow equation to find the <math>x</math> coordinate of point <math>E</math>:<br />
<br />
<cmath>3x=\frac{-3}{2}x+\frac{15}{2}</cmath><br />
<cmath>6x=-3x+15</cmath><br />
<cmath>9x=15</cmath><br />
<cmath>x=\frac{5}{3}</cmath><br />
<br />
We can plug this into one of our original equations to find that the <math>y</math> coordinate is <math>5</math>, meaning the area of <math>\triangle EAB</math> is <math>\frac{1}{2}(5)(5) = \boxed{\textbf{(D)}\ \frac{25}{2}}</math><br />
<br />
==Solution 3==<br />
At points <math>A</math> and <math>B</math>, segment <math>AE</math> is 5 units from segment <math>BE</math>. At points <math>F</math> and <math>G</math>, the segments are 2 units from each other. This means that collectively, the two lines closed the distance between them by 3 units over a height of 3 units. Therefore, to close the next two units of distance, they will have to travel a height of 2 units.<br />
<br />
Then calculate the area of trapezoid <math>FGBA</math> and triangle <math>EGF</math> separately and add them. The area of the trapezoid is <math>\frac {2+5}{2}\cdot 3 = \frac {21}{2}</math> and the area of the triangle is <math>\frac{1}{2}\cdot 2 \cdot 2 = 2</math>. <math>\frac{21}{2}+2=\boxed{\textbf{(D)}\ \frac{25}{2}}</math><br />
<br />
==Solution 4==<br />
Since <math>\Delta{ABE}\sim{\Delta{FGE}}</math> then <math>[AFGB]\sim{[FXYG]}</math>, where <math>X</math> and <math>Y</math> are ponts on <math>EF</math> and <math>EG</math> respectivley which make the areas similar. This process can be done over and over again multiple times by the ratio of <math>\frac{FG}{AB}=\frac{2}{5}</math>, or something like this<br />
<cmath>[AEB]=[AFGB]+[FXYZ]+...</cmath><cmath>[AEB]=[AFGB]+\frac{2}{5}[AFGB]+(\frac{2}{5})^2[AFGB]+...</cmath>we have to find the ratio of the areas when the sides have shrunk by length <math>\frac{2}{5}l</math><br />
[asy]<br />
unitsize(0.6 cm);<br />
<br />
pair A, B, C, D, E, F, G;<br />
<br />
A = (0,0);<br />
B = (5,0);<br />
C = (5,3);<br />
D = (0,3);<br />
F = (1,3);<br />
G = (3,3);<br />
E = extension(A,F,B,G);<br />
<br />
draw(A--B--C--D--cycle);<br />
draw(A--E--B);<br />
<br />
label("<math>A</math>", A, SW);<br />
label("<math>B</math>", B, SE);<br />
label("<math>C</math>", C, NE);<br />
label("<math>D</math>", D, NW);<br />
label("<math>E</math>", E, N);<br />
label("<math>F</math>", F, SE);<br />
label("<math>G</math>", G, SW);<br />
label("<math>2/5</math>", (D + F)/2, N);<br />
label("<math>4/5</math>", (G + C)/2, N);<br />
label("<math>6/5</math>", (B + C)/2, dir(0));<br />
label("<math>6/5</math>", (A + D)/2, W);<br />
label("<math>2</math>", (A + B)/2, S);<br />
[/asy]<br />
Let <math>[AFGB]'</math> be the area of the shape whose length is <math>\frac{2}{5}l</math><br />
<cmath>[AFGB]'=[ADCB]-[ADF]-[BCG]</cmath><cmath>[AFGB]'=12/5-6/25-12/25</cmath><cmath>[AFGB]'=42/25</cmath>Now comparing the ratios of <math>[AFGB]'</math> to <math>[AFGB]</math> we get<br />
<cmath>\frac{[AFGB]'}{[AFGB]}=\frac{42}{25}/\frac{21}{2}\implies \frac{[AFGB]'}{[AFGB]}=\frac{4}{25}</cmath>By applying an infinite summation<br />
<cmath>[AEB]=\sum_{n=0}^{\infty} \frac{21}{2}\cdot{(\frac{4}{25})^n}</cmath><cmath>S=\frac{a_1}{1-r}</cmath><cmath>\boxed{[AEB]=\frac{25}{2}}</cmath><br />
<br />
==See Also==<br />
<br />
{{AMC12 box|year=2003|ab=B|num-b=13|num-a=15}}<br />
{{AMC10 box|year=2003|ab=B|num-b=19|num-a=21}}<br />
{{MAA Notice}}</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=Mock_F%3Dma_Contests&diff=109772Mock F=ma Contests2019-09-11T23:03:53Z<p>Lol man000: /* Mock F=ma */</p>
<hr />
<div>== Mock F=ma ==<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author(s)'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock F=ma #1'''<br />
| Lol_man000, monkeycalculator, cmsgr8er<br />
| 2019<br />
| [https://artofproblemsolving.com/community/c164h1892482_mock_fma_exam Initial Discussion]<br />
| [https://latex.artofproblemsolving.com/miscpdf/hpofzsfb.pdf?t=1568219936181 Problems]<br />
| Coming<br />
| Coming</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_10B_Problems/Problem_25&diff=1075022002 AMC 10B Problems/Problem 252019-07-08T18:52:12Z<p>Lol man000: /* Solution 3 */</p>
<hr />
<div>== Problem ==<br />
When <math>15</math> is appended to a list of integers, the mean is increased by <math>2</math>. When <math>1</math> is appended to the enlarged list, the mean of the enlarged list is decreased by <math>1</math>. How many integers were in the original list?<br />
<br />
<math> \mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 5\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 8 </math><br />
<br />
== Solution 1==<br />
Let <math>x</math> be the sum of the integers and <math>y</math> be the number of elements in the list. Then we get the equations <math>\dfrac{x+15}{y+1}=\dfrac{x}{y}+2</math> and <math>\dfrac{x+15+1}{y+1+1}=\dfrac{x+16}{y+2}=\frac{x}{y}+2-1=\frac{x}{y}+1</math>. With a lot of algebra, the solution is found to be <math>y= \boxed{\textbf{(A)}\ 4} </math>.<br />
<br />
==Solution 2==<br />
We let <math>m</math> be the original number of elements in the set and we let <math>n</math> be the original average of the terms of the original list. Then we have <math>mn</math> is the sum of all the elements of the list. So we have two equations: <cmath>mn+15=(m+2)(n+1)=mn+m+2n+2</cmath> and <cmath>mn+16=(m+1)(n+2)=mn+2m+n+2.</cmath>Simplifying both equations and we get,<br />
<cmath>13=m+2n</cmath><br />
<cmath>14=2m+n</cmath><br />
Solving for <math>m</math> and <math>n</math>, we get <math>m=5</math> and <math>n=\boxed{\textbf{(A)}4}</math>.<br />
<br />
==Solution 3==<br />
Warning: This solution will rarley ever work in any other case however seeing that you can so easily plug and chug in probem 25 it is funny to see this<br />
<br />
Plug and chug random numbers with the answer choices we can start with <math>4</math> numbers. You see that if you have 4 5s and you add 15 to the set the resulting mean will be 7 we can verify this with math<br />
<cmath>\frac{5+5+5+5+15}{5}=7</cmath><br />
adding in 1 to the set you result in the mean to be 6.<br />
<cmath>\frac{5+5+5+5+15+1}{6}=6</cmath><br />
Thus we conclude that 4 is the correct choice or <math>\boxed{\textbf{(A)}}</math><br />
<br />
== See also ==<br />
{{AMC10 box|year=2002|ab=B|num-b=24|after=Last problem}}<br />
{{MAA Notice}}</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_10B_Problems/Problem_25&diff=1075012002 AMC 10B Problems/Problem 252019-07-08T18:51:25Z<p>Lol man000: /* Solution 3 */</p>
<hr />
<div>== Problem ==<br />
When <math>15</math> is appended to a list of integers, the mean is increased by <math>2</math>. When <math>1</math> is appended to the enlarged list, the mean of the enlarged list is decreased by <math>1</math>. How many integers were in the original list?<br />
<br />
<math> \mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 5\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 8 </math><br />
<br />
== Solution 1==<br />
Let <math>x</math> be the sum of the integers and <math>y</math> be the number of elements in the list. Then we get the equations <math>\dfrac{x+15}{y+1}=\dfrac{x}{y}+2</math> and <math>\dfrac{x+15+1}{y+1+1}=\dfrac{x+16}{y+2}=\frac{x}{y}+2-1=\frac{x}{y}+1</math>. With a lot of algebra, the solution is found to be <math>y= \boxed{\textbf{(A)}\ 4} </math>.<br />
<br />
==Solution 2==<br />
We let <math>m</math> be the original number of elements in the set and we let <math>n</math> be the original average of the terms of the original list. Then we have <math>mn</math> is the sum of all the elements of the list. So we have two equations: <cmath>mn+15=(m+2)(n+1)=mn+m+2n+2</cmath> and <cmath>mn+16=(m+1)(n+2)=mn+2m+n+2.</cmath>Simplifying both equations and we get,<br />
<cmath>13=m+2n</cmath><br />
<cmath>14=2m+n</cmath><br />
Solving for <math>m</math> and <math>n</math>, we get <math>m=5</math> and <math>n=\boxed{\textbf{(A)}4}</math>.<br />
<br />
==Solution 3==<br />
Warning: This solution will rarley ever work in any other case however seeing that you can so easily plug and chug in probem 25 it is funny to see this<br />
<br />
Plug and chug random numbers with the answer choices we can start with <math>4</math> numbers. You see that if you have 4 5s and you add 15 the resulting mean will be 7 we can verify this with math<br />
<cmath>\frac{5+5+5+5+15}{5}=7</cmath><br />
adding in 1 to the set you result in the mean to be 6.<br />
<cmath>\frac{5+5+5+5+15+1}{6}=6</cmath><br />
Thus we conclude that 4 is the correct choice or <math>\boxed{\textbf{(A)}}</math><br />
<br />
== See also ==<br />
{{AMC10 box|year=2002|ab=B|num-b=24|after=Last problem}}<br />
{{MAA Notice}}</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_10B_Problems/Problem_25&diff=1075002002 AMC 10B Problems/Problem 252019-07-08T18:51:12Z<p>Lol man000: /* Solution 3 */</p>
<hr />
<div>== Problem ==<br />
When <math>15</math> is appended to a list of integers, the mean is increased by <math>2</math>. When <math>1</math> is appended to the enlarged list, the mean of the enlarged list is decreased by <math>1</math>. How many integers were in the original list?<br />
<br />
<math> \mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 5\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 8 </math><br />
<br />
== Solution 1==<br />
Let <math>x</math> be the sum of the integers and <math>y</math> be the number of elements in the list. Then we get the equations <math>\dfrac{x+15}{y+1}=\dfrac{x}{y}+2</math> and <math>\dfrac{x+15+1}{y+1+1}=\dfrac{x+16}{y+2}=\frac{x}{y}+2-1=\frac{x}{y}+1</math>. With a lot of algebra, the solution is found to be <math>y= \boxed{\textbf{(A)}\ 4} </math>.<br />
<br />
==Solution 2==<br />
We let <math>m</math> be the original number of elements in the set and we let <math>n</math> be the original average of the terms of the original list. Then we have <math>mn</math> is the sum of all the elements of the list. So we have two equations: <cmath>mn+15=(m+2)(n+1)=mn+m+2n+2</cmath> and <cmath>mn+16=(m+1)(n+2)=mn+2m+n+2.</cmath>Simplifying both equations and we get,<br />
<cmath>13=m+2n</cmath><br />
<cmath>14=2m+n</cmath><br />
Solving for <math>m</math> and <math>n</math>, we get <math>m=5</math> and <math>n=\boxed{\textbf{(A)}4}</math>.<br />
<br />
==Solution 3==<br />
Warning:This solution will rarley ever work in any other case however seeing that you can so easily plug and chug in probem 25 it is funny to see this<br />
<br />
Plug and chug random numbers with the answer choices we can start with <math>4</math> numbers. You see that if you have 4 5s and you add 15 the resulting mean will be 7 we can verify this with math<br />
<cmath>\frac{5+5+5+5+15}{5}=7</cmath><br />
adding in 1 to the set you result in the mean to be 6.<br />
<cmath>\frac{5+5+5+5+15+1}{6}=6</cmath><br />
Thus we conclude that 4 is the correct choice or <math>\boxed{\textbf{(A)}}</math><br />
<br />
== See also ==<br />
{{AMC10 box|year=2002|ab=B|num-b=24|after=Last problem}}<br />
{{MAA Notice}}</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_10B_Problems/Problem_25&diff=1074992002 AMC 10B Problems/Problem 252019-07-08T18:50:35Z<p>Lol man000: /* Solution 2 */</p>
<hr />
<div>== Problem ==<br />
When <math>15</math> is appended to a list of integers, the mean is increased by <math>2</math>. When <math>1</math> is appended to the enlarged list, the mean of the enlarged list is decreased by <math>1</math>. How many integers were in the original list?<br />
<br />
<math> \mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 5\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 8 </math><br />
<br />
== Solution 1==<br />
Let <math>x</math> be the sum of the integers and <math>y</math> be the number of elements in the list. Then we get the equations <math>\dfrac{x+15}{y+1}=\dfrac{x}{y}+2</math> and <math>\dfrac{x+15+1}{y+1+1}=\dfrac{x+16}{y+2}=\frac{x}{y}+2-1=\frac{x}{y}+1</math>. With a lot of algebra, the solution is found to be <math>y= \boxed{\textbf{(A)}\ 4} </math>.<br />
<br />
==Solution 2==<br />
We let <math>m</math> be the original number of elements in the set and we let <math>n</math> be the original average of the terms of the original list. Then we have <math>mn</math> is the sum of all the elements of the list. So we have two equations: <cmath>mn+15=(m+2)(n+1)=mn+m+2n+2</cmath> and <cmath>mn+16=(m+1)(n+2)=mn+2m+n+2.</cmath>Simplifying both equations and we get,<br />
<cmath>13=m+2n</cmath><br />
<cmath>14=2m+n</cmath><br />
Solving for <math>m</math> and <math>n</math>, we get <math>m=5</math> and <math>n=\boxed{\textbf{(A)}4}</math>.<br />
<br />
==Solution 3==<br />
Warning:This solution will rarley ever work however seeing that you can so easily plug and chug in probem 25 it is funny to see this<br />
<br />
Plug and chug random numbers with the answer choices we can start with <math>4</math> numbers. You see that if you have 4 5s and you add 15 the resulting mean will be 7 we can verify this with math<br />
<cmath>\frac{5+5+5+5+15}{5}=7</cmath><br />
adding in 1 to the set you result in the mean to be 6.<br />
<cmath>\frac{5+5+5+5+15+1}{6}=6</cmath><br />
Thus we conclude that 4 is the correct choice or <math>\boxed{\textbf{(A)}}</math><br />
<br />
== See also ==<br />
{{AMC10 box|year=2002|ab=B|num-b=24|after=Last problem}}<br />
{{MAA Notice}}</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=File:Airplane_problem.png&diff=105837File:Airplane problem.png2019-05-17T17:08:33Z<p>Lol man000: Qasnqijnss</p>
<hr />
<div>== Summary ==<br />
Qasnqijnss</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=2005_AMC_8_Problems/Problem_2&diff=985042005 AMC 8 Problems/Problem 22018-11-04T20:26:51Z<p>Lol man000: /* Solution */</p>
<hr />
<div>==Problem==<br />
<br />
Karl bought five folders from Pay-A-Lot at a cost of <math> \textdollar 2.50 </math> each.<br />
Pay-A-Lot had a 20%-off sale the following day. How much could<br />
Karl have saved on the purchase by waiting a day?<br />
<br />
<math> \textbf{(A)}\ \textdollar 1.00 \qquad\textbf{(B)}\ \textdollar 2.00 \qquad\textbf{(C)}\ \textdollar 2.50\qquad\textbf{(D)}\ \textdollar 2.75 \qquad\textbf{(E)}\ \textdollar 5.00 </math><br />
<br />
==Solution==<br />
Karl paid <math>5 \cdot 2.50 = \textdollar 12.50</math>. <math>20 \%</math> of this cost that he saved is <math>12.50 \cdot .2 = \boxed{\textbf{(C)}\ \textdollar 2.50}</math>.<br />
<br />
==Solution 2==<br />
Each folder can also be <math> 5/2</math> dollars, and <math>20\%</math> can be shown as <math>(1/5)</math>. We can multiply <math>(5/2) \cdot (1/5) = (1/2)</math>. <math>(1/2)</math> is also <math>50</math> cents or the amount of money that is saved after the <math>20\%</math> discount. So each folder is <math>2.50-0.5 = \textdollar2</math>.Since Karl bought 5 folders all of the folders after the discount is <math>(5)(2) = 10</math>, and the money bought before the discount is <math>(5)(2.50) = \textdollar12.50</math>. To find the money Karl saves all we have to do is subtract <math>12.50 - 10 = 2.50</math>. Thus the answer is <math>\boxed{\textbf{(C)}\ \textdollar 2.50}</math>.<br />
<br />
==See Also==<br />
{{AMC8 box|year=2005|num-b=1|num-a=3}}<br />
{{MAA Notice}}</div>Lol man000https://artofproblemsolving.com/wiki/index.php?title=2013_AMC_8_Problems/Problem_1&diff=985032013 AMC 8 Problems/Problem 12018-11-04T20:04:14Z<p>Lol man000: /* Solution */</p>
<hr />
<div>==Problem==<br />
Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?<br />
<br />
<math>\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5</math><br />
<br />
==Solution==<br />
In order to have the model cars in complete rows of 6, Danica must have a number of cars that is a multiple of 6. The smallest multiple of 6 which is larger than 23 is 24, so she'll need to buy <math>\boxed{\textbf{(A)}\ 1}</math> more model car.<br />
<br />
==See Also==<br />
{{AMC8 box|year=2013|before=First Problem|num-a=2}}<br />
{{MAA Notice}}</div>Lol man000