Arcadia Posted March 25, 2013 Share Posted March 25, 2013 1997-2012 questions and solutions http://www.samf.ac.z...tionPapers.aspx ETA: 9th Chinese Girls’ Mathematics Olympiad(2010) 11th Chinese Girls Math Olympiad Guangzhou (2010) Mathematical Olympiad in China(273 pages) http://www.bmoc.math...home/egmo.shtml 2011 and 2012 have solutions http://www.bmoc.math...t no solutions. British Math Olympiad no solutions http://www.bamo.org/archives Bay Area Mathematical Olympiad problems and solutions http://www.egmo2012....uk/competition/ European Girls Math Olympiad 2012 New Zealand Math Olympiad Committee page (questions and solutions to assignments) http://cms.math.ca/Competitions/CMO/ Canadian Mathematical Olympiad International Math Olympiad problems 1959-2012 Asia Pacific Math Olympiadproblems and solution Problems from Olympiads archive http://www.imomath.com/index.php?mod=23 Western Australia Junior Math Olympiad http://enrichmaths.sponsored.uwa.edu.au/home/wajo/qnsandsolns Non olympiad link William Lowell Putnam Mathematics Competition University of Illinois Undergrad Math Contest Quote Link to comment Share on other sites More sharing options...
crazyforlatin Posted March 25, 2013 Share Posted March 25, 2013 My iPad is full of PDFs, partly thanks to you. I need a bigger one. Thanks for the link! Quote Link to comment Share on other sites More sharing options...
lewelma Posted March 25, 2013 Share Posted March 25, 2013 Oh, we will enjoy these! Thanks! 3 months to countdown over here.... Quote Link to comment Share on other sites More sharing options...
lewelma Posted March 25, 2013 Share Posted March 25, 2013 Well, I have to say that I am feeling a lot better about how hard we are having to work over here. This is the juniors set that my ds would have had to solve last year. Not at all like the South African problem sets -- there is definitely a difference between a 1 hour exam and a 1 month exam! The proofs are about to kill me (well, except geometry); even the the solutions for the "show" and "find" questions are proofs. J1. From a square of side length 1, four identical triangles are removed, one at each corner, leaving a regular octagon. What is the area of the octagon? J2. Show the the sum of any three consecutive positive integers is a divisor of the sum of their cubes. J3. Find all triples of positive integers (x, y, z) with xy/z+yz/x+zx/y= 3 J4. A pair of numbers are twin primes if they differ by two, and both are prime. Prove that, except for the pair {3, 5}, the sum of any pair of twin primes is a multiple of 12. J5. Let ABCD be a quadrilateral in which every angle is smaller than 180. If the bisectors of angles DAB and DCB are parallel, prove that ADC = ABC. J6. The vertices of a regular 2012-gon are labelled with the numbers 1 through 2012 in some order. Call a vertex a peak if its label is larger than the label of its two neighbours, and a valley if its label is smaller than the label of its two neighbours. Show that the total number of peaks is equal to the total number of valleys. Quote Link to comment Share on other sites More sharing options...
2smartones Posted March 25, 2013 Share Posted March 25, 2013 Wow... very cool! I'm remembering how much I loved math as a kid, and regretting that my rural, poor, nothing of a high school & college had anything like this. The most math I ever took was college algebra 101. (Even though I minored in science!) Supposedly, schools were better back then than they are today, too. LOL! Quote Link to comment Share on other sites More sharing options...
Luckymama Posted March 25, 2013 Share Posted March 25, 2013 Always good to find more practice for the AMCs----thanks :) Quote Link to comment Share on other sites More sharing options...
Arcadia Posted March 25, 2013 Author Share Posted March 25, 2013 Oh, we will enjoy these! Thanks! 3 months to countdown over here.... More for your boy :) http://www.bmoc.maths.org/home/egmo.shtml 2011 and 2012 have solutions http://www.bmoc.maths.org/ problems but no solutions. Two New Zealanders made it pass British Mathematical Olympiad Round 2 ETA: Updated original posts with more links Quote Link to comment Share on other sites More sharing options...
lewelma Posted March 26, 2013 Share Posted March 26, 2013 Arcadia, you are so good at finding things. Do you know of any sites that have simple problems (with solutions) for proofs by induction? My ds needs to do about 20 easy ones to really get the hang of it, and most of what I have found is really difficult mathematically. I just found out that a 14 year old NZer earned a bronze at the IMO last year. Wow! Quote Link to comment Share on other sites More sharing options...
Arcadia Posted March 26, 2013 Author Share Posted March 26, 2013 Do you know of any sites that have simple problems (with solutions) for proofs by induction? My ds needs to do about 20 easy ones to really get the hang of it, and most of what I have found is really difficult mathematically. http://onlinemathcir...7-induction.pdf This one has seven olympiad level problems with solutions. http://www.math.northwestern.edu/putnam/konter/induction2011_heavy.pdf http://www.math.northwestern.edu/~mlerma/problem_solving/putnam/training-induc.pdf ETA: New Zealand links http://www.mathsolympiad.org.nz/wp-content/uploads/2009/03/induction.pdf http://www.stat.auckland.ac.nz/~stats325/notes/ch4.pdf Quote Link to comment Share on other sites More sharing options...
lewelma Posted March 26, 2013 Share Posted March 26, 2013 Cool! I will look at them tonight. Off to tutor 11th grade English (don't ask how *I* ended up being an English tutor!?!?!) ETA: OMG!!! These are great!!!!! Thanks so much. Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.