{"id":9636,"date":"2017-05-11t12:52:34","date_gmt":"2017-05-11t19:52:34","guid":{"rendered":"\/\/www.catharsisit.com\/hs\/?p=9636"},"modified":"2018-10-26t06:28:58","modified_gmt":"2018-10-26t13:28:58","slug":"ap-calculus-ab-cram-sheet","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-ab-cram-sheet\/","title":{"rendered":"ap calculus ab cram sheet"},"content":{"rendered":"<p>so the ap calculus ab exam is coming up.  are you prepared?  with this calculus ab cram sheet, you can check that you have the skills necessary to score a 5 on the test.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2016\/06\/sat-note-taking-600x400.jpg\" alt=\"student taking notes - ap calculus ab cram sheet\" width=\"600\" height=\"400\" class=\"aligncenter size-large wp-image-7341\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2016\/06\/sat-note-taking-600x400.jpg 600w, \/\/www.catharsisit.com\/hs\/files\/2016\/06\/sat-note-taking-300x200.jpg 300w, \/\/www.catharsisit.com\/hs\/files\/2016\/06\/sat-note-taking-768x512.jpg 768w, \/\/www.catharsisit.com\/hs\/files\/2016\/06\/sat-note-taking-1536x1023.jpg 1536w, \/\/www.catharsisit.com\/hs\/files\/2016\/06\/sat-note-taking.jpg 1600w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<h2>about the test<\/h2>\n<p>the ap calculus ab exam is a 3 hour and 15 minute standardized test.  a high score (4-5) typically qualifies you to receive college credit or equivalency for one full semester of calculus.  so it&#8217;s really important to do well on the test if you want a jump start on your college career.<\/p>\n<p>click here to learn more about the format of the exam: <a href=\"\/\/www.catharsisit.com\/hs\/ap\/format-ap-calculus-ab-test\/\">what is the format of the ap calculus ab test?<\/a>.<\/p>\n<h3>general tips<\/h3>\n<ul>\n<li>each section has two parts: <em>calculator<\/em> and <em>no calculator<\/em>.  make sure you have a good graphing calculator and are familiar with its features.<\/li>\n<li><strong>multiple choice:<\/strong> there are a total of 45 multiple choice questions in one hour and 45 minutes.  that gives an average of 2 minutes and 20 seconds per problem.<\/li>\n<li>be sure to fill in your answers to the multiple choice problems completely on the bubble sheet.<\/li>\n<li>it doesn&#8217;t hurt your score to guess if you have no idea how to do a problem.  but try to <em>eliminate<\/em> wrong answers first.<\/li>\n<li>pace yourself.  do not spend too much time on any given multiple choice problem.  if you find yourself spending too much time on a question, skip it and move on.<\/li>\n<li>on your first pass through the problems, answer what you can.  then take a second pass, if time permits.  <\/li>\n<li>on your second pass, make sure that your bubble sheet accurately records what you think the answers are.  also, spend some time on more challenging questions that you couldn&#8217;t crack the first time around.<\/li>\n<li><strong>free response:<\/strong>  there are 6 free response problems in 90 minutes.  so you have 15 minutes per question on average.<\/li>\n<li>each free response question has 3 or 4 parts.<\/li>\n<li>in the free response section, spend enough time to clearly write out each step.  most of your points will be earned by showing and carrying out proper methods for each problem. <em>explain<\/em>, <em>communicate<\/em>, and <em>justify<\/em>.<\/li>\n<li>after answering each question, re-read the question statement to ensure that you&#8217;ve understood what they were asking.<\/li>\n<\/ul>\n<figure id=\"attachment_5777\" aria-describedby=\"caption-attachment-5777\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2016\/02\/sat_testtaking-600x274.jpg\" alt=\"students taking a test\" width=\"600\" height=\"274\" class=\"size-large wp-image-5777\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2016\/02\/sat_testtaking-600x274.jpg 600w, \/\/www.catharsisit.com\/hs\/files\/2016\/02\/sat_testtaking-300x137.jpg 300w, \/\/www.catharsisit.com\/hs\/files\/2016\/02\/sat_testtaking.jpg 640w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-5777\" class=\"wp-caption-text\">the ap calculus ab exam is not your typical high school exam.  it&#8217;s a standardized test, much like the sat or act, but specialized to calculus!<\/figcaption><\/figure>\n<h3>what topics are covered?<\/h3>\n<p>a detailed list of what&#8217;s on the test can be found here: <a href=\"\/\/www.catharsisit.com\/hs\/ap\/topics-ap-calculus-ab-exam\/\">what topics are on the ap calculus ab exam?<\/a>.  in what follows, we will highlight a few of the definitions, properties, theorems, and formulas that may be useful on the test.<\/p>\n<p>basically, the ap calculus ab exam covers three <strong>big ideas<\/strong> from calculus.<\/p>\n<ol>\n<li>limits and continuity<\/li>\n<li>derivatives and their applications<\/li>\n<li>integrals and their applications<\/li>\n<\/ol>\n<h2>ap calculus ab cram sheet<\/h2>\n<p>nothing can take the place of consistent study and review over a period of many weeks or months.  <em>cramming<\/em> the night before will not help you to raise your score.<\/p>\n<figure id=\"attachment_6356\" aria-describedby=\"caption-attachment-6356\" style=\"width: 320px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2016\/03\/cramming.gif\" alt=\"homer simpson cramming for a test -magoosh\" width=\"320\" height=\"240\" class=\"size-full wp-image-6356\" \/><figcaption id=\"caption-attachment-6356\" class=\"wp-caption-text\">don&#8217;t be like homer simpson. cramming won&#8217;t work for the ap calculus ab exam.<\/figcaption><\/figure>\n<p>so think of the following ap calculus ab cram sheet as a way to summarize and review what you (should) have been studying throughout the year.<\/p>\n<h3>pre-calculus concepts<\/h3>\n<p>mathematics tends to build upon earlier mathematics, and calculus is no different.  <\/p>\n<ul>\n<li><strong>general problem solving strategies<\/strong>.  this includes using context clues and identifying the <em>givens<\/em> and the <em>goals<\/em> of a problem.<\/li>\n<li><strong>logic<\/strong>. strong  helps to piece together various approaches to a given problem and helps in using theorems and properties.<\/li>\n<li><strong>arithmetic<\/strong>.  a large part of the exam does not allow a calculator.  you&#8217;ll have to know how to add, subtract, multiply and divide numbers, including fractions and decimals.  so if you&#8217;ve relied on your calculator all throughout high school, now is the time to get back to basics.\n<li><strong>algebra<\/strong>.  this includes simplifying and interpreting algebraic <em>expressions<\/em> as well as setting up and solving algebraic <em>equations<\/em>. (yes, there&#8217;s a difference &mdash; an equation has an equals sign, while an expression does not.)  be familiar with the properties of exponents, logarithms, radicals, etc.\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/algebra_rules.gif\" alt=\"common algebra rules\" width=\"551\" height=\"79\" class=\"aligncenter size-full wp-image-9638\" \/><\/p>\n<\/li>\n<li><strong>geometry<\/strong>.  know your basic perimeter, area, volume, and related formulas.  follow <a href=\"http:\/\/mdk12.msde.maryland.gov\/instruction\/curriculum\/hsa\/geometry\/math_reference_sheet.html\" target=\"_blank\" rel=\"noopener noreferrer\">this link<\/a> for a comprehensive formula sheet.\n<\/li>\n<li><strong>trigonometry<\/strong>.  definitions must be memorized (&#8220;<em>soh cah toa<\/em>&#8220;) as well as the most often used trig identities. see <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-review-trigonometric-identities\/\">ap calculus review: trigonometric identities<\/a> for more details.<\/li>\n<li><strong>pre-calculus<\/strong>.  know how to graph functions and how to interpret graphs.  be very familiar with linear functions, especially the concept of <strong>slope<\/strong>.\n<\/ul>\n<h3>big idea 1.  limits and continuity<\/h3>\n<ul>\n<li>know how to find limits algebraically or by estimating from numerical or graphical data.<\/li>\n<li>definition of continuity in terms of limits.  check out <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-exam-review-limits-continuity\/\">limits and continuity<\/a>.<\/li>\n<li><strong>intermediate value theorem (ivt)<\/strong><br \/>\n<blockquote><p>if <em>f<\/em> is continuous on a closed interval [<em>a<\/em>, <em>b<\/em>], and if <em>l<\/em> is any number between <em>f<\/em>(<em>a<\/em>) and <em>f<\/em>(<em>b<\/em>), then there is at least one value <em>x<\/em> = <em>c<\/em> on the interval such that <em>f<\/em>(<em>c<\/em>) = <em>l<\/em>.<\/p><\/blockquote>\n<\/li>\n<li><strong>extreme value theorem (evt)<\/strong><br \/>\n<blockquote><p>if <em>f<\/em> is continuous on a closed interval [<em>a<\/em>, <em>b<\/em>], then <em>f<\/em> attains both an absolute maximum and minimum value on the interval.<\/p><\/blockquote>\n<\/li>\n<li>limits whose values are infinite and their relationship to <a href=\"\/\/www.catharsisit.com\/hs\/ap\/find-vertical-asymptotes-function\/\">vertical asymptotes<\/a><\/li>\n<li>limits as <em>x<\/em> &rarr; &plusmn;&infin; and their relationship to <a href=\"\/\/www.catharsisit.com\/hs\/ap\/find-horizontal-asymptotes\/\">horizontal asymptotes<\/a>\n<\/li>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/oblique-asymptotes\/\">oblique asymptotes<\/a><\/li>\n<\/ul>\n<h3>big idea 2.  derivatives and their applications<\/h3>\n<ul>\n<li>limit definition of the <a href=\"\/\/www.catharsisit.com\/hs\/ap\/derivatives-ap-calculus-ab-bc-exams\/\">derivative<\/a>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/limit_def_derivative.gif\" alt=\"limit definition of the derivative\" width=\"220\" height=\"39\" class=\"aligncenter size-full wp-image-9639\" \/><\/p>\n<\/li>\n<li>if a function is <strong>differentiable<\/strong> at a point, then it must also be <strong>continuous<\/strong> at that point.  but not necessarily the reverse &mdash; for example, |<em>x<\/em>| is continuous at <em>x<\/em> = 0, but not differentiable there.<\/li>\n<li>basic derivative rules.\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/basic_differentiation_rules.gif\" alt=\"basic derivative rules\" width=\"279\" height=\"125\" class=\"aligncenter size-full wp-image-9640\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/sum_and_difference_rules.gif\" alt=\"sum and difference rules\" width=\"247\" height=\"81\" class=\"aligncenter size-full wp-image-9119\" \/>\n<\/li>\n<li>derivatives of trigonometric, exponential, and logarithmic functions.\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/derivatives_trig_exp_log.gif\" alt=\"derivatives of trig, exponential, and log functions\" width=\"304\" height=\"157\" class=\"aligncenter size-full wp-image-9641\" \/>\n<\/li>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-review-product-rule\/\">product rule<\/a> and <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-review-quotient-rule\/\">quotient rule<\/a>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/product_rule.gif\" alt=\"product rule\" width=\"275\" height=\"19\" class=\"aligncenter size-full wp-image-9206\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/quotientrule1.gif\" alt=\"quotient rule formula\" width=\"252\" height=\"47\" class=\"aligncenter size-full wp-image-9280\" \/><\/p>\n<\/li>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/mastering-chain-rule\/\">chain rule<\/a>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/chainrule.gif\" alt=\"statement of the chain rule\" width=\"206\" height=\"20\" class=\"aligncenter size-full wp-image-9293\" \/><\/p>\n<li>the <strong>tangent line<\/strong> to the curve <em>y<\/em> = <em>f<\/em>(<em>x<\/em>) at a point <em>x<\/em> = <em>a<\/em> is measured by the derivative: <em>f<\/em>&nbsp;&#039;(<em>a<\/em>).\n<\/li>\n<li>if <em>s<\/em>(<em>t<\/em>) is a <strong>position<\/strong> function, then\n<ul>\n<li><strong>velocity<\/strong> is <em>v<\/em>(<em>t<\/em>) = <em>s<\/em>&nbsp;&#039;(<em>t<\/em>), and<\/li>\n<li><strong>acceleration<\/strong> is <em>a<\/em>(<em>t<\/em>) = <em>s<\/em>&nbsp;&#039;&#039;(<em>t<\/em>).<\/li>\n<\/ul>\n<li><em>further topics and applications:<\/em>\n<ul>\n<li>implicit differentiation, <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-exam-review-analysis-graphs\/\">analysis of graphs<\/a>, including intervals of increase\/decrease, relative minima\/maxima, intervals of concavity, and inflection points.<\/li>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-review-mean-value-theorem\/\">mean value theorem<\/a> and rolle&#8217;s theorem<\/li>\n<li>optimization\n<li>related rates<\/li>\n<li>elementary differential equations and slope fields<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>big idea 3.  integrals and their applications<\/h3>\n<ul>\n<li>rules and formulas of <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-exam-review-antidifferentiation\/\">antidifferentiation<\/a>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8694\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/power_rule_integral.gif\" alt=\"power rule for integrals\" width=\"388\" height=\"44\" \/><\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8695\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/sum_diff_rule_integral.gif\" alt=\"sum and difference rule for integrals\" width=\"542\" height=\"41\" \/><\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8693\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/constant_mult_integral.gif\" alt=\"constant multiple rule for integrals\" width=\"419\" height=\"41\" \/><\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8739\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/constant_function_rule.gif\" alt=\"constant function rule\" width=\"350\" height=\"41\" \/><\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8741\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/rule_for_1_over_x.gif\" alt=\"rule for 1\/x\" width=\"273\" height=\"41\" \/><\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8740\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/exponential_antiderivatives.gif\" alt=\"exponential antiderivatives\" width=\"397\" height=\"88\" \/><\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8742\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/trig_antiderivatives.gif\" alt=\"trigonometric antiderivatives\" width=\"455\" height=\"274\" \/>\n<\/li>\n<li>integration by <strong>substitution<\/strong>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8746\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/substitution_rule.gif\" alt=\"substitution rule\" width=\"547\" height=\"41\" \/><\/p>\n<\/li>\n<li>the fundamental theorem of calculus (both parts)\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/definite_integral.gif\" alt=\"definite integral of f(x) from x=a to x=b\" width=\"291\" height=\"45\" class=\"aligncenter size-full wp-image-8690\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/ftc2.jpg\" alt=\"second fundamental theorem of calculus\" width=\"171\" height=\"49\" class=\"aligncenter size-full wp-image-8717\" \/><\/p>\n<\/li>\n<li>area below a curve\n<p> <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/area_below_f.gif\" alt=\"area below f by definition integration\" width=\"124\" height=\"45\" class=\"aligncenter size-full wp-image-9642\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/area_below_f.gif 124w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/area_below_f-30x11.gif 30w\" sizes=\"(max-width: 124px) 100vw, 124px\" \/><\/li>\n<li>area between curves, with <em>f<\/em> on top and <em>g<\/em> on bottom\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/area_between_f_and_g.gif\" alt=\"area between f and g by definite integration\" width=\"193\" height=\"45\" class=\"aligncenter size-full wp-image-9643\" \/><\/li>\n<li>volumes of solids of revolution by washer method and shell method.\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/washer_method.gif\" alt=\"washer method\" width=\"374\" height=\"45\" class=\"alignnone size-full wp-image-9645\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/shell_method.gif\" alt=\"shell method\" width=\"357\" height=\"45\" class=\"alignnone size-full wp-image-9644\" \/><\/p>\n<\/li>\n<li><em>further topics and applications:<\/em>\n<ul>\n<li>estimating area or displacement by finite riemann sums or trapezoid rule\n<li>average value of a function over an interval<\/li>\n<li>models for exponential growth and decay<\/li>\n<\/ul>\n<\/ul>\n<p>note that you do not have to do <em>integration by parts (ibp)<\/em> or <em>partial fractions<\/em> on the ab test.  <\/p>\n<h2>final thoughts<\/h2>\n<p>you can use this calculus ab cram sheet as a checklist in order to ensure that you&#8217;ve done all of the necessary prep work.  if you are reading this with plenty of time to spare before the exam, then consider setting up a <a href=\"\/\/www.catharsisit.com\/hs\/ap\/3-month-ap-calculus-exam-study-guide\/\">3-month ap calculus exam study guide<\/a>.<\/p>\n<p><em>best of luck on test day!<\/em><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/success-479568_640-600x337.jpg\" alt=\"sign pointing toward success\" width=\"600\" height=\"337\" class=\"alignnone size-large wp-image-9646\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/success-479568_640-600x337.jpg 600w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/success-479568_640-300x168.jpg 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/success-479568_640-30x17.jpg 30w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/success-479568_640.jpg 640w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>are you prepared for the ap calculus ab exam? with this calculus ab cram sheet, you can check that you have the skills necessary to score a 5 on the test.<\/p>\n","protected":false},"author":223,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[240],"tags":[241],"ppma_author":[24932],"class_list":["post-9636","post","type-post","status-publish","format-standard","hentry","category-ap","tag-ap-calculus"],"acf":[],"yoast_head":"<!-- this site is optimized with the yoast seo premium plugin v21.7 (yoast seo v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>ap calculus ab cram sheet - magoosh blog | high school<\/title>\n<meta name=\"description\" content=\"are you prepared for the ap calculus ab exam? with this calculus ab cram sheet, you can check that you have the skills necessary to score a 5 on the test.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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