tag:blogger.com,1999:blog-60928915734665554872024-03-14T02:32:10.819+07:00Mathematics Olympiad Resourcehigh school,elementary school, algebra, geometry, numbers and many other mathematics olympiad problems and competitionsUnknownnoreply@blogger.comBlogger15125tag:blogger.com,1999:blog-6092891573466555487.post-56069882315993745632011-11-27T10:31:00.002+07:002011-11-27T10:31:33.471+07:00Median of TriangleA median is a line segment drawn from the vertex of a triangle to the<br />
midpoint of the opposite side.<br />
A triangle has an area of 72 cm2<br />
. The length of one side is 12 cm and the<br />
length of the median to this side is 13 cm.<br />
Determine the length of the other two sides of the triangle.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-89011719308117252492011-07-18T19:06:00.001+07:002011-07-18T19:08:19.527+07:00The Case of Confused CashierTaken from South East Asian Mathematics Competition (SEAMC) 2010 in Bangkok, Thailand.<br />
<br />
Mr. Smith went into his local bank with a cheque for an amount in Dollars and Cents. He asked the cashier to give him cash for the amount on the cheque. However, she confused the Dollars and cents. So Mr. Smith received Dollars for the amount of cents on the cheque, and cents for the amount of Dollars (e.g if the cheque was for $22.43, Mr. Smith would have been given $43.22)<br />
Mr. Smith left the bank and bought a newspaper for 50 cents. After this, Mr. Smith realised he had exactly three times as much money left as the value of the original cheque.<br />
How much was the original cheque for?<br />
<br />
For another SEAMC past problems visit the official <a href="http://www.seamc.asia/pastpapers/">site</a>.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-33970185990082951132011-06-04T21:45:00.002+07:002011-06-04T21:50:29.380+07:00Harvard–MIT Mathematics Tournament (Problem and Solution)This high school mathematics tournament is sponsored by Harvard and MIT. HMMT is one of the largest math contests in the United States (based on opinion in <a href="http://web.mit.edu/hmmt/www/">the official site</a>). <br />
<br />
Well, The 2011 Harvard-MIT Mathematics Tournament was held on Saturday, February 12, 2011. All the archives (including problems and solutions) can be download here:<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="http://web.mit.edu/hmmt/www/datafiles/solutions/" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="60" width="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwfETyHT1nsMji_qJ4o0ZH5sHKozZrj87T6Imf0868hUkDJX1v2AT_NABHcHMZeciwXWL7ou_ovLH3UPtSZbsbF58Ucycw7LActh3A3U8W0GhV9lf122-4Yqsk7yqyWtlRwSDziNjGH1Y/s320/harvard-mit.JPG" /></a></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-28197974589314229932011-05-15T07:01:00.001+07:002011-05-15T07:02:27.101+07:00Card ProblemThere are some people playing a card game. On the table there are fifty cards, numbered 1 to 50, all facing up. Each players is allowed to choose a certain number of cards. Ig the sum of the numberson all cards chosen by the player is the highest, then he/she is the winner. There is only one winner.<br />
Questions:<br />
<br />
What is the lowest possible score that makes a player a sure winner if each player has to choose:<br />
<br />
a. two cards<br />
b. three cards<br />
c. five cardsUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-19936247022388425362011-04-24T12:27:00.000+07:002011-04-24T12:27:32.030+07:00International Mathematics Olympiad (IMO) 2011<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMznvqC09t6V_STiaStxLhfeUNFmJ0n5VqqdfuN796p0uf0V2eFBpa-xRN7ytVpCJkzGeqCd6K7CVV8xNq0MHClNpWKqk2iXCC_DSE5rA30jQjflCVB7UVqoqdy75IWjzBvg5-hl4_VFw/s1600/imoamsterdam.jpg" imageanchor="1" style="clear:left; float:left;margin-right:1em; margin-bottom:1em"><img border="0" height="178" width="133" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMznvqC09t6V_STiaStxLhfeUNFmJ0n5VqqdfuN796p0uf0V2eFBpa-xRN7ytVpCJkzGeqCd6K7CVV8xNq0MHClNpWKqk2iXCC_DSE5rA30jQjflCVB7UVqoqdy75IWjzBvg5-hl4_VFw/s400/imoamsterdam.jpg" /></a></div><br />
It is the dream of all mathematics olympiad contestant around the world to be a winner! The 52nd International Mathematical Olympiad (IMO) will be held in the Netherlands in July 2011. <br />
<br />
Deadlines<br />
<br />
28 February 2011: Online confirmation of participation<br />
28 March 2011: Receipt of problem proposals<br />
25 April 2011:<br />
Online registration of (deputy) leader, single rooms and observers (if applicable)<br />
For leaders and observers A: registration of arrival day (12 or 13 July 2011)<br />
Online registration of the number of contestants<br />
30 May 2011:<br />
Online registration of contestants<br />
Full payment of the charges for single rooms and observers in cleared funds<br />
13 June 2011: online registration of all travel details<br />
<br />
See: <a href="https://www.imo2011.nl/">https://www.imo2011.nl/</a><br />
<br />
<a href="http://www.amazon.com/gp/product/0883858231/ref=as_li_ss_tl?ie=UTF8&tag=matheolympres-20&linkCode=as2&camp=217145&creative=399349&creativeASIN=0883858231">USA And International Mathematical Olympiads 2005: Examples-pictures-proofs (Problem Books)</a><img src="http://www.assoc-amazon.com/e/ir?t=&l=as2&o=1&a=0883858231&camp=217145&creative=399349" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /><br />
<br />
Try IMO 2010 problems:<br />
<object id="doc_733418214343176" name="doc_733418214343176" height="500" width="100%" type="application/x-shockwave-flash" data="http://d1.scribdassets.com/ScribdViewer.swf" style="outline:none;"> <param name="movie" value="http://d1.scribdassets.com/ScribdViewer.swf"><param name="wmode" value="opaque"><param name="bgcolor" value="#ffffff"><param name="allowFullScreen" value="true"><param name="allowScriptAccess" value="always"><param name="FlashVars" value="document_id=53712443&access_key=key-13w9i2x69wc1rl4eni7q&page=1&viewMode=list"><embed id="doc_733418214343176" name="doc_733418214343176" src="http://d1.scribdassets.com/ScribdViewer.swf?document_id=53712443&access_key=key-13w9i2x69wc1rl4eni7q&page=1&viewMode=list" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" height="500" width="100%" wmode="opaque" bgcolor="#ffffff"></embed> </object>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-60126819342489370952011-04-19T22:49:00.008+07:002011-05-15T07:31:07.692+07:00Bank Problems (Geometric Series)A bank invites term deposits under the following <span style="color: yellow;">conditions</span><span style="color: black;">:</span><br />
1. The deposit (or initial principal) may be any amount in dollars and cents, with a<br />
minimum of $1.<br />
2. The yearly interest, calculated at the end of each year and added to the principal, is<br />
one cent less than 10% of the current principal, fractions of a cent being discarded.<br />
3.The deposit with accumulated interest is returned at end of the sixth year.<br />
<br />
Find the smallest initial deposit which would result in no fractions of cents being discarded<br />
in any of the six years.<br />
<br />
Hints.<br />
Let $\displaystyle \large {\color{Yellow} x_{n}}$ be the value of the principal at the end of the nth year.<br />
Derive a relationship between $\displaystyle \large {\color{Yellow} x_{n}}$ and $\displaystyle \large {\color{Yellow} x_{n-1}}$ <br />
Guess a relationship between $\displaystyle \large {\color{Yellow} x_{n}}$ and $\displaystyle \large {\color{Yellow} x_{0}}$ ( $\displaystyle \large {\color{Yellow} x_{0}}$ is the initial principal). This relationship should remind you of the compound interest formula.<br />
Prove your guess by mathematical induction.<br />
What's the sum of a geometric series?<br />
Now think in terms of congruences.<br />
<br />
Source: <a href="http://www.amazon.com/gp/product/9814293547/ref=as_li_qf_sp_asin_tl?ie=UTF8&tag=matheolympres-20&linkCode=as2&camp=217145&creative=399349&creativeASIN=9814293547">Lecture Notes on Mathematical Olympiad Courses: For Junior Section Vol 1 (Mathematical Olympiad Series)</a><img src="http://www.assoc-amazon.com/e/ir?t=matheolympres-20&l=as2&o=1&a=9814293547&camp=217145&creative=399349" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-54415196036862802702011-04-16T22:03:00.000+07:002011-04-16T22:03:07.583+07:00Geometry Problem for High School1. ABCD is a square with E insides it. If ABE is a equilateral triangle, then <BEC = ....<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrNsgfgLkYs0jZ6tR2C3P4mJ2qkVGvsU526po-1earlnE8iZtv0nWZzXFhRjuowjHQ3Rt_L8S14iebMb2AOaCZ2pSHlUoNkRP3wGirPAWsY4vQKQwROlj8LNtTmXVP7O2Ng1G2bSjqW8g/s1600/geometry+high+school.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrNsgfgLkYs0jZ6tR2C3P4mJ2qkVGvsU526po-1earlnE8iZtv0nWZzXFhRjuowjHQ3Rt_L8S14iebMb2AOaCZ2pSHlUoNkRP3wGirPAWsY4vQKQwROlj8LNtTmXVP7O2Ng1G2bSjqW8g/s1600/geometry+high+school.jpg" /></a></div><br />
<br />
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</span></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-11857389043981706942011-04-06T20:05:00.004+07:002011-04-23T18:15:16.907+07:00International Mathematics and Science Olympiad (IMSO) for Primary School 2005<iframe src="http://rcm.amazon.com/e/cm?lt1=_blank&bc1=000000&IS2=1&bg1=080808&fc1=000000&lc1=FFF100&t=matheolympres-20&o=1&p=8&l=as1&m=amazon&f=ifr&ref=tf_til&asins=1441920277" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe><br />
1. Complete the magic triangle so that the numbers along each side give the same sum. Use each of the numbers 5,6,7,8,9 and 10 only once. (Give only one solution)<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_cQBNzNh762ju_Aop2-IMP7btBvxsJzIW3kG3dnhTXwFPl2IjXyHqyXLDFPvwxG4Q6iAcXUpTg-f7QN9jsZolFYzSWRsYW2YCQnzKzpGld9tBPf5RdsKxtwwJ7KCKzw8nUEQpTE-JvQQ/s1600/imso2005+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_cQBNzNh762ju_Aop2-IMP7btBvxsJzIW3kG3dnhTXwFPl2IjXyHqyXLDFPvwxG4Q6iAcXUpTg-f7QN9jsZolFYzSWRsYW2YCQnzKzpGld9tBPf5RdsKxtwwJ7KCKzw8nUEQpTE-JvQQ/s320/imso2005+1.jpg" width="320" /></a></div><br />
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2. The height of the ground floor of a building is 4 m. The height of each of the other floors is 3m. The total height of this building is 61 m. Inclusive og the ground floor, how many floors does the building have?<br />
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3. The composition of Scotty Cake for 6 servings is :<br />
<br />
3/4 kg rice flour<br />
45 gr margarin<br />
4 egg<br />
220 gr sugar<br />
300 ml margarin<br />
1/2 tea spoon vanilla<br />
<br />
<br />
How much rice flour is needed to make Scotty cake for 10 servings?<br />
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4. If a positive number B is divided by 2, 3, 4, 6 or 9, the remainder is 1. Find the smallest possible value of B.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-21443798400121326712011-04-05T20:45:00.002+07:002011-04-24T11:43:50.758+07:00Algebra and Number Problem (With Hint)<a href="http://www.amazon.com/gp/product/1441904948/ref=as_li_ss_tl?ie=UTF8&tag=matheolympres-20&linkCode=as2&camp=217145&creative=399349&creativeASIN=1441904948">Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads</a><img src="http://www.assoc-amazon.com/e/ir?t=&l=as2&o=1&a=1441904948&camp=217145&creative=399349" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /><br />
<br />
1. For every positive integers <i>n</i> ,<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhavimZFiJ77iXlCv8MUV1zlFvil6cI-4xwuNvI0mDBIrzGjQDYd_fUHD5PDP1jFO4BP13a5n08PcH4arHKZzv_0vL6lqfS1oeHJIUNPMoEVkEHA2oruZRoic83moPMLZJsyVU5SeqXPAY/s1600/algebra+problem.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhavimZFiJ77iXlCv8MUV1zlFvil6cI-4xwuNvI0mDBIrzGjQDYd_fUHD5PDP1jFO4BP13a5n08PcH4arHKZzv_0vL6lqfS1oeHJIUNPMoEVkEHA2oruZRoic83moPMLZJsyVU5SeqXPAY/s1600/algebra+problem.jpg" /></a></div> divisible by 2000. Proof it.<br />
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Hint: 2000 = 125 x 16<br />
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2. If<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1qJbahfW1PD2HLt72r-ExwRrogRoFuzMS2IqLx06gna4oHbMIcf0-doMtAC30uLkCeNRa6YXVncEKjKdlvOA5lQNosbV34TObUurzBS5bP7PUooEbTbQ2aIaPxmOKM0ixb7Iai-uKU80/s1600/number+problem.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1qJbahfW1PD2HLt72r-ExwRrogRoFuzMS2IqLx06gna4oHbMIcf0-doMtAC30uLkCeNRa6YXVncEKjKdlvOA5lQNosbV34TObUurzBS5bP7PUooEbTbQ2aIaPxmOKM0ixb7Iai-uKU80/s1600/number+problem.jpg" /></a></div> Find <i>a</i> x <i>b</i> x <i>c </i>x <i>d</i><br />
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Hint: <i>a</i> is integer part of 57/17Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-90970078727834502902011-04-05T05:59:00.001+07:002011-04-24T11:42:45.515+07:00Probability Problem<a href="http://www.amazon.com/gp/product/0198501056/ref=as_li_ss_tl?ie=UTF8&tag=matheolympres-20&linkCode=as2&camp=217145&creative=399349&creativeASIN=0198501056">The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965-1996 (Oxford Science Publications)</a><img src="http://www.assoc-amazon.com/e/ir?t=&l=as2&o=1&a=0198501056&camp=217145&creative=399349" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /><br />
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1. A survey of the non-healthy habits of 80 sophomore students of a certain seminary showed the following result.<br />
45 drink alcoholic beverages<br />
42 stay up late<br />
40 smoke cigarettes<br />
25 drink alcohol and smoke<br />
19 stay up late and smoke<br />
22 drink alcohol and stay up late<br />
9 practice clean healthy living by not doing any of the 3<br />
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If a seminarian sophomore is randomly picked, what is the probability that he:<br />
a. is just an insomniac (or just stay up late)<br />
b. smokes and/or drinks but is a sleepyhead (or smokes and/or drinks but sleeps early)<br />
c. he should be kicked out of the seminary (by doing all the three things)<br />
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<br />
2. What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive <i>x</i> or the positive <i>y </i>direction?<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie2rHdl8mzsdHR-YTr9CB75wtheePbAyL5E7mdNqG2DlA-wvS2gW9fS2XiAXwPwQdiCumpzsBtkng-EDsEOCjKxgMNrmuRZ_f5is6kJ8zyopN0fgsF17wGujDW50YwLM2Azf8vOafOH2o/s1600/probability+problem.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="233" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie2rHdl8mzsdHR-YTr9CB75wtheePbAyL5E7mdNqG2DlA-wvS2gW9fS2XiAXwPwQdiCumpzsBtkng-EDsEOCjKxgMNrmuRZ_f5is6kJ8zyopN0fgsF17wGujDW50YwLM2Azf8vOafOH2o/s320/probability+problem.jpg" width="320" /></a></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-25234761423411632332011-04-04T20:58:00.001+07:002011-04-24T11:46:31.989+07:00Geometry Problem for High School<a href="http://www.amazon.com/gp/product/0078778549/ref=as_li_ss_tl?ie=UTF8&tag=matheolympres-20&linkCode=as2&camp=217145&creative=399349&creativeASIN=0078778549">California Geometry: Concepts, Skills, and Problem Solving</a><img src="http://www.assoc-amazon.com/e/ir?t=&l=as2&o=1&a=0078778549&camp=217145&creative=399349" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /><br />
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<br />
<m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%;">1. In circle O, <PRS= 50<sup>0</sup> and </span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpInxDBtyfc1YQzfDe8pNwTyAQPAVliXAIVzaJocu5zOeJflWlIQOaZL5c4kmuQeWEVmsxPJtUFjUKQKdjBOiRJzbeP4dy7vCJOCy9x5Qd0ZnEmVZ_s3e9Y0K7x1zxg_SZ6LzFzI7FTgk/s1600/geometry+problem.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpInxDBtyfc1YQzfDe8pNwTyAQPAVliXAIVzaJocu5zOeJflWlIQOaZL5c4kmuQeWEVmsxPJtUFjUKQKdjBOiRJzbeP4dy7vCJOCy9x5Qd0ZnEmVZ_s3e9Y0K7x1zxg_SZ6LzFzI7FTgk/s1600/geometry+problem.jpg" /></a><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%;"> </span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div style="text-align: left;"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%;">Find the measure of <QPR.</span></div><div style="text-align: left;"><br />
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</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZr86K5SMoR-otvahONeKGLxunKdPHsJMpIGVW-abP4JMX_dicIdj5pMkwjboXGq9Y142g4mO5xC28bYYhRpiCfhfT2CsNpcgXMujmPSbwaNzEfwSOm_5CIgDlLOS1VwXP3rV0KV4KqIE/s1600/geometry+problem2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZr86K5SMoR-otvahONeKGLxunKdPHsJMpIGVW-abP4JMX_dicIdj5pMkwjboXGq9Y142g4mO5xC28bYYhRpiCfhfT2CsNpcgXMujmPSbwaNzEfwSOm_5CIgDlLOS1VwXP3rV0KV4KqIE/s1600/geometry+problem2.jpg" /></a></div><div style="text-align: left;"><br />
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</div><div style="text-align: left;"><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%;"></span></div><div style="text-align: left;"><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%;"></span></div><div class="MsoListParagraph" style="text-indent: -18pt;"><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%;"></span> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><br />
<br />
<br />
<br />
2.<m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:wrapindent m:val="1440"><m:intlim m:val="subSup"></m:intlim></m:wrapindent></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><span style="font: 7pt "Times New Roman";"> </span>Given that <i>HURN</i> is a square of side <i>x</i> and <i>∆HUT</i> is equilateral. What is the area of <i>∆UER</i> in terms of <i>x</i>?<br />
<div class="MsoListParagraph" style="text-indent: -18pt;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0V8wXj0Qsb-ofPuCwblo3oZoiIsB8DW2Y-IAeka9kTQGOq_5-dl66zzNwIHm7xSRItlK81SRSIs1JDreixE_iwdQuiz60iLNm-FuXq-W2qGuq-NAkpMSfhnUVPqAcQ8wOFckooghKwwA/s1600/geometry+problem+square.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0V8wXj0Qsb-ofPuCwblo3oZoiIsB8DW2Y-IAeka9kTQGOq_5-dl66zzNwIHm7xSRItlK81SRSIs1JDreixE_iwdQuiz60iLNm-FuXq-W2qGuq-NAkpMSfhnUVPqAcQ8wOFckooghKwwA/s1600/geometry+problem+square.jpg" /></a></div><div class="MsoListParagraph" style="text-indent: -18pt;"></div><div class="MsoListParagraph" style="text-indent: -18pt;"><br />
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</div><div class="MsoListParagraph" style="text-indent: -18pt;"> From: MSA Math Competition High School</div><div class="MsoListParagraph" style="text-indent: -18pt;"><br />
</div><br />
<div style="text-align: left;"><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%;"> </span><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%;"> </span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div>Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-6092891573466555487.post-43176660829173312202011-04-03T14:59:00.003+07:002011-04-24T11:50:16.165+07:00Math Olympiad Example Problem for Grade 6<a href="http://www.amazon.com/gp/product/0132031191/ref=as_li_ss_tl?ie=UTF8&tag=matheolympres-20&linkCode=as2&camp=217145&creative=399349&creativeASIN=0132031191">Prentice Hall Mathematics California Grade 6 Math</a><img src="http://www.assoc-amazon.com/e/ir?t=&l=as2&o=1&a=0132031191&camp=217145&creative=399349" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /><br />
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<m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">Problems</span></b></div><div class="MsoListParagraphCxSpFirst" style="margin-left: 14.2pt; text-align: justify; text-indent: -14.2pt;"><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">1.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">What are the possible dimensions of a rectangle with integer-valued side lengths in which the numerical value of the area is twice the perimeter?</span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 14.2pt; text-align: justify; text-indent: -14.2pt;"><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">2.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">In celebration of her birthday, Claudine threw a big party. Every two persons shared a bowl of rice, every three persons shared a bowl of fruit salad, and every four persons shared a bowl of soup. There were 130 bowl used together. How many guests were present ?</span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 14.2pt; text-align: justify; text-indent: -14.2pt;"><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">3.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">Calculate:</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyY7Jgz-T4PKSn6VB4ypDCkVSwUOhyphenhyphenr1gjgpyQRBYIrQgd3VwT-JGyRy6KALvdoN-UcWpdZT4gPKaLzxExANOHAUeNprd2GmlUUwAPLu1w5-uWuqv8rdwQZcKRMx0AT9HlL9AQMCJEhDA/s1600/math+olympiad+grade+6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyY7Jgz-T4PKSn6VB4ypDCkVSwUOhyphenhyphenr1gjgpyQRBYIrQgd3VwT-JGyRy6KALvdoN-UcWpdZT4gPKaLzxExANOHAUeNprd2GmlUUwAPLu1w5-uWuqv8rdwQZcKRMx0AT9HlL9AQMCJEhDA/s1600/math+olympiad+grade+6.jpg" /></a></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 14.2pt; text-align: justify;"><table align="left" cellpadding="0" cellspacing="0"><tbody>
<tr> <td height="5" width="197"><br />
</td></tr>
<tr><td><br />
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</tbody></table><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;"></span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 14.2pt; text-align: justify;"><br />
</div><br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 14.2pt; text-align: justify; text-indent: -14.2pt;"><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">4.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">The pages of the Math Book are numbered consecutively, starting with page 1. The book is bound in ten booklets, with equal number of pages in each booklet. If the sum of the numbers on the first page of every booklet is 4150, how many pages does each booklet have?</span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 14.2pt; text-align: justify; text-indent: -14.2pt;"><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">5.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">Angela is fond of making a wish everytime her car’s odometer displays a number read the same forward and backward (palyndrome). At 10:18 am the odometer read 87978 km. Traveling continuosly the odometer displayed the next possible number that in palyndrome at 11:13 am. During this time, what was the car’s average speed in kilometers per hours ?</span><br />
<span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;"> </span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 14.2pt; text-align: justify; text-indent: -14.2pt;"><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">6.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">Eight of the angles of an undecagon have measures whose sum is 1380˚. Of the remaining three angles, two are complementary to each other and two are supplementary to each other. Find the measure of the largest of these three angles.</span></div><div class="MsoListParagraphCxSpLast" style="margin-left: 14.2pt; text-align: justify; text-indent: -14.2pt;"><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">7.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; line-height: 115%;">What is the sum of the numbers less than 200 that has exactly 3 divisors?</span></div><iframe src="http://rcm.amazon.com/e/cm?lt1=_blank&bc1=000000&IS2=1&bg1=020202&fc1=000000&lc1=E9FF00&t=matheolympres-20&o=1&p=8&l=as4&m=amazon&f=ifr&ref=ss_til&asins=0486206645" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-77155795186978944462011-04-03T06:35:00.001+07:002011-04-23T19:10:15.664+07:00Math Olympiad Example Problem for K9<iframe src="http://rcm.amazon.com/e/cm?lt1=_blank&bc1=000000&IS2=1&bg1=040404&fc1=000000&lc1=FFF100&t=matheolympres-20&o=1&p=8&l=as4&m=amazon&f=ifr&ref=ss_til&asins=0967991552" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe><br />
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<m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div class="MsoListParagraph" style="line-height: 150%; margin: 0cm 0cm 0.0001pt 14.2pt; text-indent: -14.2pt;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;">1.<span style="font: 7pt "Times New Roman";"> </span></span><span lang="SV" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;"> <i>ABC</i> is a right triangle with <</span><span lang="EN-US" style="font-family: Symbol; font-size: 12pt; line-height: 150%;"></span><i><span lang="SV" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;">ACB</span></i><span lang="SV" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;">= 74</span><span lang="EN-US" style="font-family: Symbol; font-size: 12pt; line-height: 150%;">°</span><span lang="SV" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;"> and <i>AM</i>=<i>MQ</i>=<i>QP</i>. </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;">Find <QPB</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;">. </span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBdlLPde-kQFl2n3bMZj-EpDDdBIkBxt6pG8aGO_0QJjxHzYBqppbe6G8hMfib9s_HMJ86Qn-O-cZV78_fEqMJLddy_hu4dT9tnl_4tK4vvnOErUyiJBVqxDoysU_5tVoLZKdNcr6DjnM/s1600/math+olympiad+example+problem+1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBdlLPde-kQFl2n3bMZj-EpDDdBIkBxt6pG8aGO_0QJjxHzYBqppbe6G8hMfib9s_HMJ86Qn-O-cZV78_fEqMJLddy_hu4dT9tnl_4tK4vvnOErUyiJBVqxDoysU_5tVoLZKdNcr6DjnM/s320/math+olympiad+example+problem+1.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">math olympiad example problem</td></tr>
</tbody></table><br />
<div class="MsoListParagraph" style="line-height: 150%; margin: 0cm 0cm 0.0001pt 14.2pt; text-indent: -14.2pt;"><br />
</div><br />
<br />
<div class="MsoListParagraph" style="line-height: 150%; margin: 0cm 0cm 0.0001pt 14.2pt; text-indent: -14.2pt;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><span lang="SV" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;">2. <span style="font: 7pt "Times New Roman";"> </span></span><span lang="SV" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;">How many positive integer <i>n</i> , if <i>n</i>-1 is the factor for 3<i>n</i>-6</span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoListParagraph" style="line-height: 150%; margin: 0cm 0cm 0.0001pt 14.2pt; text-indent: -14.2pt;"><span lang="SV" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;">3. <A=60<sup>o</sup> and the radius of big circle is 6. Find the radius of small circle.</span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAtcJo6ghZl4hnyOlPnEYcnuBxLnE24Wd0LimzHo9C2KgxxONSXCE5ASjDdSPMezDXM5xvt2NihIjerm-qCf8zzLFejssJp4D3km-B36T0bPpibeplsgKreOaDHBEDOp2NGMjt5ie5qCI/s1600/math+olympiad+example+problem+2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="220" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAtcJo6ghZl4hnyOlPnEYcnuBxLnE24Wd0LimzHo9C2KgxxONSXCE5ASjDdSPMezDXM5xvt2NihIjerm-qCf8zzLFejssJp4D3km-B36T0bPpibeplsgKreOaDHBEDOp2NGMjt5ie5qCI/s320/math+olympiad+example+problem+2.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">math olympiad example problem</td></tr>
</tbody></table><div class="MsoListParagraph" style="line-height: 150%; margin: 0cm 0cm 0.0001pt 14.2pt; text-indent: -14.2pt;"><span lang="SV" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 150%;"><br />
</span></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-1101133708971538802011-04-03T00:55:00.001+07:002011-04-24T11:53:34.280+07:00Singapore Math Olympiad (SMO) 2011<a href="http://www.amazon.com/gp/product/1441488871/ref=as_li_ss_tl?ie=UTF8&tag=matheolympres-20&linkCode=as2&camp=217145&creative=399349&creativeASIN=1441488871">Competition Math for Middle School</a><img src="http://www.assoc-amazon.com/e/ir?t=&l=as2&o=1&a=1441488871&camp=217145&creative=399349" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /><br />
<br />
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One of Mathematical Olympiad competition in south east Asia. The current name Singapore Mathematical Olympiad is held for Junior, Senior and Open. For 2011, the Singapore Mathematical Olympiad schedule is:<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPr8a-xykyDh90dT2TdRkMsbNgjeQRCwOTfxRwYHjpIgudGxO8Cl1cLr1riVUP-S37v_uEPRC4hrvasoO6-uOuqkOYopjD_AbwLuNfMLJxJkdjKWdUa2_uqZP5QuyKpazqAF_K5xPkKCc/s1600/smo+competition+schedule.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPr8a-xykyDh90dT2TdRkMsbNgjeQRCwOTfxRwYHjpIgudGxO8Cl1cLr1riVUP-S37v_uEPRC4hrvasoO6-uOuqkOYopjD_AbwLuNfMLJxJkdjKWdUa2_uqZP5QuyKpazqAF_K5xPkKCc/s320/smo+competition+schedule.jpg" width="320" /></a></div><span class="body"><br />
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<span class="body">Example problems:</span><br />
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<a href="http://www.scribd.com/doc/52141044/Singapore-National-Mathematical-Olympiad-2010" style="display: block; font: 14px Helvetica,Arial,Sans-serif; margin: 12px auto 6px; text-decoration: underline;" title="View Singapore National Mathematical Olympiad 2010 on Scribd">Singapore National Mathematical Olympiad 2010</a><iframe class="scribd_iframe_embed" data-aspect-ratio="0.772727272727273" data-auto-height="true" frameborder="0" height="600" id="doc_60201" scrolling="no" src="http://www.scribd.com/embeds/52141044/content?start_page=1&view_mode=list&access_key=key-24y9drzhdcxzwp7cdwdp" width="100%"></iframe><script type="text/javascript">
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See also:<br />
<a href="http://sms.math.nus.edu.sg/competitions/CompetitionHomePage.aspx">SMO</a><br />
<a href="http://artofproblemsolving.com/">Art of Problem Solving</a>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6092891573466555487.post-47025118948667862862011-04-02T14:55:00.000+07:002011-04-03T06:10:04.268+07:00Canadian Math Olympiad<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjY4Ly1bNrFLyC6SOJlEmctml6ve1h-zLHuX3yJv3oO3mxhJNJql409bIIqdbhpAZzztGhCV0u5m2ZE0jAKoBtXzlhD0ATQbDqaT44kPPmLmhvngqIjpKjug1K0str2F3F6l0aGMD9dc0k/s1600/cmo.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="37" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjY4Ly1bNrFLyC6SOJlEmctml6ve1h-zLHuX3yJv3oO3mxhJNJql409bIIqdbhpAZzztGhCV0u5m2ZE0jAKoBtXzlhD0ATQbDqaT44kPPmLmhvngqIjpKjug1K0str2F3F6l0aGMD9dc0k/s320/cmo.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">canadian math olympiad</td></tr>
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Resource, problem and sample of solution for competitors see <a href="http://www.math.ca/Competitions/CMO/%20">http://www.math.ca/Competitions/CMO/%20</a> .Unknownnoreply@blogger.com0