{"id":9636,"date":"2017-05-11T12:52:34","date_gmt":"2017-05-11T19:52:34","guid":{"rendered":"https:\/\/magoosh.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":"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/files\/2016\/06\/SAT-Note-taking-600x400.jpg 600w, https:\/\/magoosh.com\/hs\/files\/2016\/06\/SAT-Note-taking-300x200.jpg 300w, https:\/\/magoosh.com\/hs\/files\/2016\/06\/SAT-Note-taking-768x512.jpg 768w, https:\/\/magoosh.com\/hs\/files\/2016\/06\/SAT-Note-taking-1536x1023.jpg 1536w, https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/files\/2016\/02\/SAT_testtaking-600x274.jpg 600w, https:\/\/magoosh.com\/hs\/files\/2016\/02\/SAT_testtaking-300x137.jpg 300w, https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/ap\/find-horizontal-asymptotes\/\">horizontal asymptotes<\/a>\n<\/li>\n<li><a href=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/ap\/derivatives-ap-calculus-ab-bc-exams\/\">derivative<\/a>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/ap\/ap-calculus-review-product-rule\/\">Product Rule<\/a> and <a href=\"https:\/\/magoosh.com\/hs\/ap\/ap-calculus-review-quotient-rule\/\">Quotient Rule<\/a>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/ap\/mastering-chain-rule\/\">Chain Rule<\/a>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/ap\/ap-calculus-exam-review-antidifferentiation\/\">Antidifferentiation<\/a>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-8694\" src=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/files\/2017\/04\/Area_below_f.gif 124w, https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.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=\"https:\/\/magoosh.com\/hs\/files\/2017\/04\/success-479568_640-600x337.jpg 600w, https:\/\/magoosh.com\/hs\/files\/2017\/04\/success-479568_640-300x168.jpg 300w, https:\/\/magoosh.com\/hs\/files\/2017\/04\/success-479568_640-30x17.jpg 30w, https:\/\/magoosh.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? 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