{"id":124,"date":"2019-09-30T01:57:54","date_gmt":"2019-09-30T01:57:54","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/lilijia\/?p=124"},"modified":"2019-09-30T01:57:54","modified_gmt":"2019-09-30T01:57:54","slug":"aops_cp-week-4","status":"publish","type":"post","link":"https:\/\/blog.newtonchineseschool.org\/lilijia\/2019\/09\/30\/aops_cp-week-4\/","title":{"rendered":"AOPS_CP Week 4"},"content":{"rendered":"<p>AOPS-CP Week 4: Chapter 3: Correcting for Overcounting<\/p>\n<p><strong>Lesson Review<\/strong><\/p>\n<p>1. <strong>Permutations with repeated elements<\/strong>:<\/p>\n<p><a href=\"https:\/\/www.ck12.org\/probability\/permutations-with-repetition\/lesson\/Permutations-with-Repetition-BSC-PST\/\">https:\/\/www.ck12.org\/probability\/permutations-with-repetition\/lesson\/Permutations-with-Repetition-BSC-PST\/<\/a><\/p>\n<p><a href=\"https:\/\/www.mathwarehouse.com\/probability\/permutations-repeated-items.php\">https:\/\/www.mathwarehouse.com\/probability\/permutations-repeated-items.php<\/a><\/p>\n<p>2. <strong>Counting pairs of items<\/strong> (understand why we need to divide by 2)<\/p>\n<p>Formula to find the sum of n numbers (understand how we derived it step by step).<\/p>\n<p>1+2+3+&#8230;+(n-1) + n = n (n+1) \/2<\/p>\n<p>3. <strong>Counting with symmetries<\/strong><\/p>\n<p>a) <strong>rotational symmetry<\/strong> (round table seats) = n!\/n = (n-1)!<\/p>\n<p>b) <strong>reflective symmetry<\/strong> (flipping over, key chain)\u00a0= n!\/2n = (n-1)!\/2<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Homework<\/strong>:<\/p>\n<p>Page 52: 3.2.1, 3.2.2., 3.2.3, 3.2.5<\/p>\n<p>Page 57: 3.3.1, 3.3.3, *3.3.5 (it&#8217;s a bonus, but not difficult. Just try!)<\/p>\n<p>Page 61: 3.4.1, 3.4.3<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Final Tips:<\/strong><\/p>\n<p>Please do not try to remember the formulas by heart, instead, try to <strong>understand<\/strong> them, and <strong>learn how to derive<\/strong> them.<\/p>\n<p>We value procedures. Please <strong>show all your steps\/procedures<\/strong> in math problem solving: both in classwork and homework. You will benefit from it in the long run.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>AOPS-CP Week 4: Chapter 3: Correcting for Overcounting Lesson Review 1. Permutations with repeated elements: https:\/\/www.ck12.org\/probability\/permutations-with-repetition\/lesson\/Permutations-with-Repetition-BSC-PST\/ https:\/\/www.mathwarehouse.com\/probability\/permutations-repeated-items.php 2. Counting pairs of items (understand why we need to divide by 2) Formula to find the sum of n numbers (understand how we derived it step by step). 1+2+3+&#8230;+(n-1) + n = n (n+1) \/2 3. Counting [&hellip;]<\/p>\n","protected":false},"author":157,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/124"}],"collection":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/users\/157"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/comments?post=124"}],"version-history":[{"count":1,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/124\/revisions"}],"predecessor-version":[{"id":126,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/124\/revisions\/126"}],"wp:attachment":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/media?parent=124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/categories?post=124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/tags?post=124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}