{"id":9671,"date":"2017-05-19t10:57:27","date_gmt":"2017-05-19t17:57:27","guid":{"rendered":"\/\/www.catharsisit.com\/hs\/?p=9671"},"modified":"2018-10-26t06:31:22","modified_gmt":"2018-10-26t13:31:22","slug":"ap-calculus-bc-cram-sheet","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-bc-cram-sheet\/","title":{"rendered":"ap calculus bc cram sheet"},"content":{"rendered":"<p>with the ap calculus bc exam right around the corner, now&#8217;s the time to gear up your preparations. hopefully you&#8217;ve started studying already.  and if not, then <em>what are you waiting for<\/em>?  either way, i hope this calculus bc cram sheet could be just the right way for you to review for the test.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2016\/03\/board-935455_640-600x399.jpg\" alt=\"prepare for the exam with this ap calculus bc cram sheet -magoosh\" width=\"600\" height=\"399\" class=\"aligncenter size-large wp-image-5996\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2016\/03\/board-935455_640-600x399.jpg 600w, \/\/www.catharsisit.com\/hs\/files\/2016\/03\/board-935455_640-300x200.jpg 300w, \/\/www.catharsisit.com\/hs\/files\/2016\/03\/board-935455_640.jpg 640w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<h2>about the test<\/h2>\n<p>the ap calculus bc exam is a standardized test lasting 3 hours and 15 minutes.  if you&#8217;re planning to take the bc test, then you have to put in a lot of time studying and prepping.<\/p>\n<p>a high score (4-5) may qualify you for college credit or equivalency for two full semesters of calculus.  <\/p>\n<h3>format of the exam<\/h3>\n<ul>\n<li>there are two main sections, <strong>multiple choice<\/strong> and <strong>free response<\/strong>.  you might find the following articles helpful as you prepare for each type of problem.\n<ul>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-bc-exam-multiple-choice-practice-problems\/\">ap calculus bc exam multiple choice practice problems<\/a><\/li>\n<li> <a href=\"\/\/www.catharsisit.com\/hs\/ap\/understanding-ap-calculus-free-response-questions\/\">understanding ap calculus free response questions<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/can-i-use-a-calculator-on-the-ap-calculus-exam\/\">can i use a calculator on the ap calculus exam?<\/a> well yes, but only on the parts of each section that all calculators.  for the <em>no calculator<\/em> sections, check out these <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-no-calculator-section-tips\/\">ap calculus no calculator section tips<\/a>.<\/li>\n<figure id=\"attachment_9729\" aria-describedby=\"caption-attachment-9729\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/4646471157_2a312f3518_b-600x449.jpg\" alt=\"the exam. photo by bitjingle\" width=\"600\" height=\"449\" class=\"size-large wp-image-9729\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/4646471157_2a312f3518_b-600x449.jpg 600w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/4646471157_2a312f3518_b-300x225.jpg 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/4646471157_2a312f3518_b-768x575.jpg 768w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/4646471157_2a312f3518_b.jpg 1024w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-9729\" class=\"wp-caption-text\">photo by <a href=\"http:\/\/www.bitjungle.com\" target=\"_blank\" rel=\"noopener noreferrer\">bitjungle<\/a><\/figcaption><\/figure>\n<h3>general tips<\/h3>\n<li>if you can&#8217;t come up with the right answer, then <strong>guessing<\/strong> doesn&#8217;t hurt your score.  but try to <em>eliminate<\/em> answers that you are sure can&#8217;t be correct.<\/li>\n<li><strong>pace yourself<\/strong> in the multiple choice section.  if you find yourself spending too much time on a question, skip it and move on.<\/li>\n<li>use a <strong>two-pass<\/strong> method.  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>in the free response section, spend enough time to clearly <strong>write out each step<\/strong>.  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<p>click here to learn more about the format of the exam: <a href=\"\/\/www.catharsisit.com\/hs\/ap\/format-ap-calculus-bc-test\/\">what is the format of the ap calculus bc test?<\/a>.<\/p>\n<h3>what&#8217;s on the exam?<\/h3>\n<p>there are four <strong>big ideas<\/strong> that comprise the material on the test.<\/p>\n<ol>\n<li>limits and continuity<\/li>\n<li>derivatives and their applications<\/li>\n<li>integrals and their applications<\/li>\n<li>sequences and series<\/li>\n<\/ol>\n<p>check out <a href=\"\/\/www.catharsisit.com\/hs\/ap\/topics-ap-calculus-bc-exam\/\">what topics are on the ap calculus bc exam?<\/a>.  <\/p>\n<p>basically, the ap calculus bc exam covers everything that the ab exam covers, <em>and then some<\/em>.  so it may be helpful to review this <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-ab-cram-sheet\/\">ap calculus ab cram sheet<\/a> first.<\/p>\n<p>in what follows, we will highlight a few of the definitions, properties, theorems, and formulas you&#8217;ll need for the test, focusing on those items that are specific to calculus bc.<\/p>\n<h2>ap calculus bc cram sheet<\/h2>\n<p>the best way to study for any ap exam is to review over a period of many weeks or months.  unfortunately, you probably won&#8217;t do well if your study plan consists of an all-night<br \/>\n<em>cram<\/em> session on the night before the test.<\/p>\n<figure id=\"attachment_9730\" aria-describedby=\"caption-attachment-9730\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/172914606_546132cbe9_o-600x400.jpg\" alt=\"student fell asleep studying. photo by dean+barb. \" width=\"600\" height=\"400\" class=\"size-large wp-image-9730\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/172914606_546132cbe9_o-600x400.jpg 600w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/172914606_546132cbe9_o-300x200.jpg 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/172914606_546132cbe9_o-768x512.jpg 768w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/172914606_546132cbe9_o-30x20.jpg 30w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/172914606_546132cbe9_o.jpg 800w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-9730\" class=\"wp-caption-text\">coffee won&#8217;t be enough to save you.  make sure your studying is spread out over at least a month. photo by dean+barb.<\/figcaption><\/figure>\n<p>so don&#8217;t think of this calculus bc cram sheet as a substitute for weeks and weeks of hard work.  instead, think of it as a concise summary to help you review.<\/p>\n<h3>big idea 1.  limits and continuity<\/h3>\n<p>the ab and bc tests both cover the same topics as far as <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-exam-review-limits-continuity\/\">limits and continuity<\/a>.  <\/p>\n<p>so because this calculus bc cram sheet is focusing on just the bc material, let&#8217;s move on to the other big ideas.<\/p>\n<figure id=\"attachment_8618\" aria-describedby=\"caption-attachment-8618\" style=\"width: 515px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/example_graph_discontinuous.jpg\" alt=\"graph with discontinuities\" width=\"515\" height=\"295\" class=\"size-full wp-image-8618\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/example_graph_discontinuous.jpg 515w, \/\/www.catharsisit.com\/hs\/files\/2017\/01\/example_graph_discontinuous-300x172.jpg 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><figcaption id=\"caption-attachment-8618\" class=\"wp-caption-text\">limits and continuity help in analyzing the behavior of graphs. this graph has discontinuities at <em>x<\/em> = -3.5, -1, and 3.<\/figcaption><\/figure>\n<h3>big idea 2.  derivatives and their applications<\/h3>\n<p>here again, the ab and bc tests cover a lot of the same ground.  however, the bc test does go beyond the ab in the inclusion of <em>vector-valued<\/em>, <em>parametric<\/em>, and <em>polar<\/em> functions and their derivatives as well as <em>euler&#8217;s method<\/em> for estimating solutions to differential equations.<\/p>\n<h4>vector-valued and parametric functions<\/h4>\n<p>on the ap calculus bc test, vector and parametric functions are essential the same thing.  they are both defined by a single input variable (or <strong>parameter<\/strong>) <em>t<\/em>, and multiple outputs, <em>x<\/em> and <em>y<\/em>.<\/p>\n<p>a vector function looks like this: <em>f<\/em>(<em>t<\/em>) = (<em>f<\/em>(<em>t<\/em>), <em>g<\/em>(<em>t<\/em>)).<\/p>\n<p>a parametric function looks like a list of two functions: <em>x<\/em> = <em>f<\/em>(<em>t<\/em>) and <em>y<\/em> = <em>g<\/em>(<em>t<\/em>).  another term for this is a set of parametric equations.<\/p>\n<p>in either case, the values of the function are pairs (<em>x<\/em>, <em>y<\/em>) defined by plugging in <em>t<\/em>-values to <em>f<\/em>(<em>t<\/em>) and <em>g<\/em>(<em>t<\/em>).<\/p>\n<p>for example, the parametric equations defining a circle of radius 4 centered at the origin are <em>x<\/em> = 4cos <em>t<\/em> and <em>y<\/em> = 4sin <em>t<\/em>, for 0 &le; <em>t<\/em> &le; 2&pi;.<\/p>\n<figure id=\"attachment_9732\" aria-describedby=\"caption-attachment-9732\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/circle.png\" alt=\"circle of radius 4\" width=\"300\" height=\"300\" class=\"size-full wp-image-9732\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/circle.png 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/circle-150x150.png 150w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-9732\" class=\"wp-caption-text\">circle of radius 4. parametric function: <em>x<\/em> = 4cos <em>t<\/em> and <em>y<\/em> = 4sin <em>t<\/em>, for 0 &le; <em>t<\/em> &le; 2&pi;.<\/figcaption><\/figure>\n<p>vector and parametric functions are both examples of multivariable functions.  check out this <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-review-mutlivariables\/\">ap calculus review: multivariables<\/a> for more information.<\/p>\n<p>you should know how to find the first and second derivatives and what their interpretations are.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/derivatives_vector_function.gif\" alt=\"derivative and second derivative of a vector function\" width=\"336\" height=\"45\" class=\"aligncenter size-full wp-image-9733\" \/><\/p>\n<p>recall, the speed of a particle is found by taking the length, or <strong>magnitude<\/strong>, of the velocity.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/speed_of_vector_function.gif\" alt=\"speed of a vector function\" width=\"240\" height=\"86\" class=\"aligncenter size-full wp-image-9734\" \/><\/p>\n<p>the slope of a parametric curve is given by:<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/param_derivative.gif\" alt=\"derivative of a parametric function\" width=\"128\" height=\"50\" class=\"aligncenter size-full wp-image-9740\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/param_derivative.gif 128w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/param_derivative-30x12.gif 30w\" sizes=\"(max-width: 128px) 100vw, 128px\" \/><\/p>\n<h4>polar functions<\/h4>\n<p>a <strong>polar<\/strong> function <em>r<\/em> = <em>f<\/em>(<em>&theta;<\/em>) defines a curve by how far away from the origin (<em>r<\/em>) each point is at any given angle (<em>&theta;<\/em>).<\/p>\n<figure id=\"attachment_9735\" aria-describedby=\"caption-attachment-9735\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/trefoil_graph.png\" alt=\"graph of a polar function\" width=\"300\" height=\"300\" class=\"size-full wp-image-9735\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/trefoil_graph.png 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/trefoil_graph-150x150.png 150w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-9735\" class=\"wp-caption-text\">the graph of <em>r<\/em> = 5cos(3<em>&theta;<\/em>) is called a three-leaf rose.<\/figcaption><\/figure>\n<p>there are conversion formulas that may help to transform an equation written in terms of <em>x<\/em> and <em>y<\/em> (<em>cartesian<\/em> coordinates) into a polar equation, and vice versa.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/polar_conversion_formulas.gif\" alt=\"polar conversion formulas\" width=\"209\" height=\"46\" class=\"aligncenter size-full wp-image-9736\" \/><\/p>\n<p>if you need to know the slope of a polar curve <em>r<\/em> = <em>f<\/em>(<em>&theta;<\/em>), then use the following <strong>polar derivative<\/strong> formula.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/polar_derivative.gif\" alt=\"polar derivative\" width=\"182\" height=\"43\" class=\"aligncenter size-full wp-image-9737\" \/><\/p>\n<h4>euler&#8217;s method<\/h4>\n<p>suppose you have an initial value problem of the following form.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/diff_eq_for_eulermethod.gif\" alt=\"initial value problem\" width=\"188\" height=\"18\" class=\"aligncenter size-full wp-image-9738\" \/><\/p>\n<p>then, with any chosen small step size <em>h<\/em>, you may approximate the solution using the following procedure algorithm:<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/eulermethod.gif\" alt=\"euler&#039;s method\" width=\"185\" height=\"43\" class=\"aligncenter size-full wp-image-9739\" \/><\/p>\n<h3>big idea 3.  integrals and their applications<\/h3>\n<p>on the ap calculus bc exam, you will be expected to know additional techniques of integration, including <em>integration by parts<\/em> and <em>partial fractions<\/em>.  here&#8217;s a summary of all of the antidifferentiation techniques you&#8217;ll need for the test: <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-exam-review-antidifferentiation\/\">ap calculus exam review: antidifferentiation<\/a><\/p>\n<p>you&#8217;ll also need to understand <a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-review-improper-integrals\/\">improper integrals<\/a>.  <\/p>\n<p>certain applications of integration not typically found on the ab exam will also show up, including:<\/p>\n<ul>\n<li>particle moving along a vector-valued or parametric curve.\n<\/li>\n<li>arc length for polar and parametric functions<\/li>\n<li>area bounded by polar curves<\/li>\n<li>logistic growth<\/li>\n<\/ul>\n<h4>particle motion<\/h4>\n<p>if a vector function <em>v<\/em>(t) represents the velocity of a particle, then its indefinite integral provides the <strong>position<\/strong> function.<\/p>\n<p>the <strong>total distance<\/strong> covered by a particle whose vector function is (<em>x<\/em>(<em>t<\/em>), <em>y<\/em>(<em>t<\/em>)) is exactly the same as the arc length, which we&#8217;ll talk about next.<\/p>\n<h4>arc length integrals<\/h4>\n<p>arc length measures the distance along the curve between two specified points.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/arc_length_integrals.gif\" alt=\"arc length integrals\" width=\"458\" height=\"168\" class=\"aligncenter size-full wp-image-9741\" \/><\/p>\n<p>note that the formula for the arc length of a parametric function is exactly the same as the formula for the vector function.<\/p>\n<h4>area in polar coordinates<\/h4>\n<p>to find the area enclosed by a polar function <em>r<\/em> = <em>f<\/em>(<em>&theta;<\/em>) between two specified angles, use the following formula.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/polar_area.gif\" alt=\"polar area integral\" width=\"165\" height=\"49\" class=\"aligncenter size-full wp-image-9742\" \/><\/p>\n<h4>logistic growth model<\/h4>\n<p>the logistic growth model is defined by a certain differential equation,<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/logistics_equation.gif\" alt=\"logistics equation\" width=\"118\" height=\"38\" class=\"aligncenter size-full wp-image-9743\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/logistics_equation.gif 118w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/logistics_equation-30x10.gif 30w\" sizes=\"(max-width: 118px) 100vw, 118px\" \/><\/p>\n<p>here, <em>k<\/em> and <em>a<\/em> are supposed to be constants.  you can find a nice description of the logistics equation as well as information about how to work with it <a href=\"https:\/\/teachingcalculus.com\/2017\/01\/31\/the-logistic-equation\/\" target=\"_blank\" rel=\"noopener noreferrer\">here<\/a>.<\/p>\n<h3>big idea 4.  sequences and series<\/h3>\n<p>last but not least, the ap calculus bc exam includes topics on sequences and series.  in this calculus bc cram sheet, i&#8217;ll provide just a few concepts and formulas that you should be aware of.<\/p>\n<h4>sequence and series concepts<\/h4>\n<ul>\n<li>a <strong>sequence<\/strong> is just a list of numbers, (<em>a<\/em><sub>1<\/sub>, <em>a<\/em><sub>2<\/sub>, <em>a<\/em><sub>3<\/sub>, &#8230;).<\/li>\n<li>a <strong>series<\/strong> is the sum of a sequence, which typically involves infinitely many terms.<\/li>\n<li>the <em>n<\/em>th <strong>partial sum<\/strong> of a series is the sum of the first <em>n<\/em> terms:<br \/>\n<img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/partial_sum.gif\" alt=\"partial sum\" width=\"293\" height=\"52\" class=\"aligncenter size-full wp-image-9744\" \/>\n<\/li>\n<li>a series <strong>converges<\/strong> if and only if the sequence of its partial sums converges.<\/li>\n<li>there are many different tests for convergence of series.  most of these tests only work on specific kinds of series.\n<ul>\n<li><em>p<\/em>-series test (convergent if <em>p<\/em> &gt; 1)<\/li>\n<li>geometric series test (convergent if |<em>r<\/em>| &lt; 1)<\/li>\n<li>comparison test and limit comparison<\/li>\n<li>integral test<\/li>\n<li>root and ratio tests<\/li>\n<li>alternating series test<\/li>\n<\/ul>\n<li>the sum of a geometric series formula:\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/geometric_series.gif\" alt=\"formula for the sum of a geometric series\" width=\"220\" height=\"50\" class=\"aligncenter size-full wp-image-9745\" \/><\/p>\n<\/li>\n<h4>taylor and maclaurin series<\/h4>\n<p>a function may be represented by a <strong>taylor series<\/strong> centered at <em>x<\/em> = <em>c<\/em>.  <\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/taylor_series-600x91.gif\" alt=\"taylor series for a function f\" width=\"600\" height=\"91\" class=\"aligncenter size-large wp-image-9746\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/taylor_series-600x91.gif 600w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/taylor_series-300x46.gif 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/taylor_series-30x5.gif 30w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>a <strong>maclaurin series<\/strong> is simply a taylor series centered at <em>x<\/em> = 0.<\/p>\n<p>it&#8217;s very useful to have memorized the maclaurin series for some common functions.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/common_power_series.gif\" alt=\"common maclaurin series\" width=\"220\" height=\"226\" class=\"aligncenter size-full wp-image-9747\" \/><\/p>\n<\/ul>\n<h3>power series and convergence<\/h3>\n<p>the taylor and maclaurin series are examples of <strong>power series<\/strong>.<\/p>\n<p>make sure you know how to find the <strong>radius<\/strong> and <strong>interval of convergence<\/strong> for a given power series.  often, the easiest method to use is the root or ratio test.<\/p>\n<p>the <strong>lagrange error bound<\/strong> is useful for quantifying how accurately a taylor polynomial approximates the function.  check out this <a href=\"https:\/\/calcworkshop.com\/sequences-series\/lagrange-error-bound\/\" target=\"_blank\" rel=\"noopener noreferrer\">video<\/a> for more details.<\/p>\n<figure id=\"attachment_9750\" aria-describedby=\"caption-attachment-9750\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/taylor_approximations.png\" alt=\"taylor approximations for sin x\" width=\"500\" height=\"300\" class=\"size-full wp-image-9750\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/taylor_approximations.png 500w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/taylor_approximations-300x180.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-9750\" class=\"wp-caption-text\">the maclaurin series for sin <em>x<\/em> approximates the function better and better as more terms are included.<\/figcaption><\/figure>\n<h2>final thoughts<\/h2>\n<p>keep in mind, this calculus bc cram sheet should only serve as a review checklist for you, not as a primary studying resource.<\/p>\n<p>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>.  or, if you&#8217;ve been putting things off, maybe this <a href=\"\/\/www.catharsisit.com\/hs\/ap\/1-month-ap-calculus-exam-study-guide\/\">1-month ap calculus exam study guide<\/a> is more up your alley.<\/p>\n<figure id=\"attachment_9731\" aria-describedby=\"caption-attachment-9731\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/snail-306356_640-600x361.png\" alt=\"snail with glasses.  (license: public domain cc0)\" width=\"600\" height=\"361\" class=\"size-large wp-image-9731\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/snail-306356_640-600x361.png 600w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/snail-306356_640-300x180.png 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/snail-306356_640.png 640w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-9731\" class=\"wp-caption-text\">this is steve.  steve is a snail.  steve is ready for the ap calculus bc exam because he paced his studying over a few months.  be like steve!<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>with the ap calculus bc exam right around the corner, now&#8217;s the time to gear up your preparations. hopefully you&#8217;ve started studying already. and if not, then what are you waiting for? either way, i hope this calculus bc cram sheet could be just the right way for you to review for the test. about [&hellip;]<\/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],"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 bc cram sheet - magoosh blog | high school<\/title>\n<meta name=\"description\" content=\"with the ap calculus bc exam right around the corner, now&#039;s the time to gear up your preparations - check out this calculus bc cram sheet!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-bc-cram-sheet\/\" \/>\n<meta property=\"og:locale\" content=\"en_us\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ap calculus bc cram sheet\" \/>\n<meta property=\"og:description\" content=\"with the ap calculus bc exam right around the corner, now&#039;s the time to gear up your preparations - check out this calculus bc cram sheet!\" \/>\n<meta property=\"og:url\" content=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-bc-cram-sheet\/\" \/>\n<meta property=\"og:site_name\" content=\"magoosh blog | high school\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/magooshsat\/\" \/>\n<meta property=\"article:published_time\" content=\"2017-05-19t17:57:27+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-10-26t13:31:22+00:00\" \/>\n<meta property=\"og:image\" content=\"\/\/www.catharsisit.com\/hs\/files\/2016\/03\/board-935455_640-600x399.jpg\" \/>\n<meta name=\"author\" content=\"shaun ault\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@shaunaultmath\" 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