{"id":10706,"date":"2017-08-03t19:00:46","date_gmt":"2017-08-04t02:00:46","guid":{"rendered":"\/\/www.catharsisit.com\/hs\/?p=10706"},"modified":"2022-06-14t19:00:46","modified_gmt":"2022-06-15t02:00:46","slug":"ap-calculus-review-basic-formulas-properties","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-review-basic-formulas-properties\/","title":{"rendered":"ap calculus review: basic formulas &amp; properties"},"content":{"rendered":"<p>it&#8217;s important to know the basics.  you have to have a solid foundation in order to build a skyscraper, right?  in this short review, i&#8217;ll discuss the basic formulas and properties that you&#8217;ll need to master in order to success on the ap calculus exam.<\/p>\n<figure id=\"attachment_10728\" aria-describedby=\"caption-attachment-10728\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/07\/pexels-photo-316879-600x400.jpeg\" alt=\"sky scrapers. ap calculus review basic formulas\" width=\"600\" height=\"400\" class=\"size-large wp-image-10728\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/07\/pexels-photo-316879-600x400.jpeg 600w, \/\/www.catharsisit.com\/hs\/files\/2017\/07\/pexels-photo-316879-300x200.jpeg 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/07\/pexels-photo-316879-768x512.jpeg 768w, \/\/www.catharsisit.com\/hs\/files\/2017\/07\/pexels-photo-316879.jpeg 1280w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-10728\" class=\"wp-caption-text\">the tallest skyscrapers require a solid foundation in order to stand.<\/figcaption><\/figure>\n<h2>the basic formulas<\/h2>\n<p>first and foremost, you must be you must know arithmetic, algebra, and trigonometry inside-out.  for a quick review check out the following helpful articles.<\/p>\n<ul>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-exam-arithmetic-review\/\">arithmetic review<\/a><\/li>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/act\/act-algebra-everything-need-know\/\">algebra review (act)<\/a><\/li>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-review-trigonometric-identities\/\">trigonometric identities<\/a><\/li>\n<\/ul>\n<p>once you have mastered those fundamental topics of mathematics, you can then build your expertise in calculus.<\/p>\n<h2>calculus-specific formulas<\/h2>\n<p>there are a number of basic formulas from calculus that you need to memorize for the exam.  <\/p>\n<p>moreover, if you plan to take the calculus bc exam, then you will have to know every formula that could show up on the ab exam, plus a whole slew of additional formulas and concepts that are specific to the bc exam.<\/p>\n<p>it might help to look through the following &#8220;cram sheets&#8221; first.<\/p>\n<ul>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-ab-cram-sheet\/\">ap calculus ab cram sheet<\/a><\/li>\n<li><a href=\"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-bc-cram-sheet\/\">ap calculus bc cram sheet<\/a><\/li>\n<\/ul>\n<p>the formulas can be categorized into four <strong>big ideas<\/strong>.  <\/p>\n<ol>\n<li>limits and continuity <em>(ab and bc)<\/em><\/li>\n<li>derivatives and their applications <em>(ab and bc)<\/em><\/li>\n<li>integrals and their applications <em>(ab and bc)<\/em><\/li>\n<li>sequences and series <em>(bc only)<\/em><\/li>\n<\/ol>\n<h3>limits and continuity<\/h3>\n<p>there are not a lot of formulas for computing limits.  instead, each limit problem may require different algebraic or trigonometric &#8220;tricks.&#8221;  however, it helps to know <strong>l&#8217;hospital&#8217;s rule<\/strong>:<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/lhospitals_rule.jpg\" alt=\"l&#039;hospital&#039;s rule\" width=\"173\" height=\"51\" class=\"aligncenter size-full wp-image-8615\" \/><\/p>\n<p>a function <em>f<\/em> is <strong>continuous<\/strong> at a point <em>x<\/em> = <em>a<\/em> if: <\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/limit_def_continuity.jpg\" alt=\"the limit as x approaches a is equal to f(a)\" width=\"138\" height=\"33\" class=\"aligncenter size-full wp-image-8617\" \/><\/p>\n<p>the <strong>intermediate value theorem (ivt)<\/strong> states that if a function <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 must be a value <em>x<\/em> = <em>c<\/em> where <em>a<\/em> &lt; <em>c<\/em> &lt; <em>b<\/em>, such that <em>f<\/em>(<em>c<\/em>) = <em>l<\/em>.<\/p>\n<h3>average rate\/velocity<\/h3>\n<p>although this formula does not have to do with limits directly, it&#8217;s a useful concept and very important for developing the concepts of derivatives.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/06\/avg_velocity.gif\" alt=\"average velocity formula\" width=\"190\" height=\"39\" class=\"aligncenter size-full wp-image-10519\" \/><\/p>\n<h2>derivatives and their applications<\/h2>\n<p><strong>limit definition<\/strong> for the derivative:<\/p>\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<p>make sure you know <em>every<\/em> derivative rule.  <\/p>\n<h3>basic differentiation rules<\/h3>\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\" \/><\/p>\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\" \/><\/p>\n<h4>product and quotient rule<\/h4>\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<h4>chain rule<\/h4>\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<h4>inverse functions<\/h4>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/07\/inverse_function_derivative.gif\" alt=\"derivative formula for inverse function\" width=\"200\" height=\"42\" class=\"aligncenter size-full wp-image-10773\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/07\/inverse_trig_derivatives.gif\" alt=\"derivatives of inverse trig functions\" width=\"161\" height=\"175\" class=\"aligncenter size-full wp-image-10774\" \/><\/p>\n<h4>polar and parametric functions<\/h4>\n<p>the ap calculus bc exam also includes polar and parametric functions and their derivatives.<\/p>\n<p>the derivative of a <strong>polar function<\/strong>, <em>r<\/em> = <em>f<\/em>(<em>&theta;<\/em>):<\/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<p>the derivative of a <strong>parametric function<\/strong>, <em>x<\/em> = <em>f<\/em>(<em>t<\/em>) and <em>y<\/em> = <em>g<\/em>(<em>t<\/em>):<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/03\/parametric_derivative.gif\" alt=\"formula for derivative of a parametric function\" width=\"150\" height=\"51\" class=\"aligncenter size-full wp-image-9354\" \/><\/p>\n<h4>applications of derivatives &#8212; velocity<\/h4>\n<p>it&#8217;s important to know the relationship between position, velocity, and acceleration in terms of derivatives.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/05\/position_velocity_acceleration.gif\" alt=\"position, velocity, and acceleration\" width=\"331\" height=\"109\" class=\"aligncenter size-full wp-image-10074\" \/><\/p>\n<p>on the ap calculus bc test, the position may be a vector function.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/07\/vector_velocity_acceleration_speed.gif\" alt=\"velocity, acceleration, and speed for vector position function\" width=\"314\" height=\"103\" class=\"aligncenter size-full wp-image-10776\" \/> <\/p>\n<h4>mean value theorem and rolle&#8217;s theorem<\/h4>\n<p>there are two related theorems involving differentiable functions, the mean value theorem, and rolle&#8217;s theorem.<\/p>\n<p><strong>mean value theorem (mvt)<\/strong>: suppose <em>f<\/em> is a function that is continuous on [<em>a<\/em>, <em>b<\/em>] and differentiable on (<em>a<\/em>, <em>b<\/em>). then there is at least one value <em>x<\/em> = <em>c<\/em>, where <em>a<\/em> &lt; <em>c<\/em> &lt; <em>b<\/em>, such that<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/mean_value_theorem.gif\" alt=\"statement of the mean value theorem\" width=\"157\" height=\"39\" class=\"aligncenter size-full wp-image-9238\" \/><\/p>\n<p><strong>rolle&#8217;s theorem<\/strong>: suppose <em>f<\/em> is a function that is continuous on [<em>a<\/em>, <em>b<\/em>], differentiable on (<em>a<\/em>, <em>b<\/em>), and <em>f(<\/em><em>a<\/em>) = <em>f<\/em>(<em>b<\/em>). then there is at least one value <em>x<\/em> = <em>c<\/em>, where <em>a<\/em> &lt; <em>c<\/em> &lt; <em>b<\/em>, such that <em>f<\/em>&nbsp;&#039;(<em>c<\/em>) = 0.<\/p>\n<h3>integrals and their applications<\/h3>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/power_rule_integral.gif\" alt=\"power rule for integrals\" width=\"388\" height=\"44\" class=\"aligncenter size-full wp-image-8694\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/sum_diff_rule_integral.gif\" alt=\"sum and difference rule for integrals\" width=\"542\" height=\"41\" class=\"aligncenter size-full wp-image-8695\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/constant_mult_integral.gif\" alt=\"constant multiple rule for integrals\" width=\"419\" height=\"41\" class=\"aligncenter size-full wp-image-8693\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/constant_function_rule.gif\" alt=\"constant function rule\" width=\"350\" height=\"41\" class=\"aligncenter size-full wp-image-8739\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/rule_for_1_over_x.gif\" alt=\"rule for 1\/x\" width=\"273\" height=\"41\" class=\"aligncenter size-full wp-image-8741\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/exponential_antiderivatives.gif\" alt=\"exponential antiderivatives\" width=\"397\" height=\"88\" class=\"aligncenter size-full wp-image-8740\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/trig_antiderivatives.gif\" alt=\"trigonometric antiderivatives\" width=\"455\" height=\"274\" class=\"aligncenter size-full wp-image-8742\" \/><\/p>\n<p>on the bc test, you may have to find velocity and speed for a <strong>vector<\/strong> position function.<\/p>\n<h4>integration techniques<\/h4>\n<p>the following formulas are useful for working out integrals of more complicated functions.  think of each rule as a potential tool in your toolbox.  sometimes an integral will require multiple tools.<\/p>\n<ul>\n<li><strong><em>u<\/em>-substitution<\/strong><br \/>\n<img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/substitution_rule.gif\" alt=\"substitution rule\" width=\"547\" height=\"41\" class=\"aligncenter size-full wp-image-8746\" \/>\n<\/li>\n<li><strong>integration by parts<\/strong> (<em>bc only<\/em>)<br \/>\n<img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/integration_by_parts.gif\" alt=\"integration by parts formula\" width=\"179\" height=\"41\" class=\"aligncenter size-full wp-image-8747\" \/><\/li>\n<\/ul>\n<h4>the fundamental theorem of calculus (ftc)<\/h4>\n<p>the <strong>fundamental theorem of calculus<\/strong> comes in two versions.<\/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<p>if <em>f<\/em>(<em>x<\/em>) is any particular antiderivative for <em>f<\/em>(<em>x<\/em>), then<\/p>\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<h4>average value and mean value theorem for integrals<\/h4>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/06\/average_value.gif\" alt=\"average value formula\" width=\"372\" height=\"45\" class=\"aligncenter size-full wp-image-10520\" \/><\/p>\n<p><strong>mean value theorem for integrals (mvti)<\/strong>: suppose <em>f<\/em> is continuous on [<em>a<\/em>, <em>b<\/em>]. then there is at least one value <em>x<\/em> = <em>c<\/em>, where <em>a<\/em> &lt; <em>c<\/em> &lt; <em>b<\/em>, such that<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/07\/mvt_for_integrals.gif\" alt=\"mean value theorem for integrals\" width=\"195\" height=\"45\" class=\"aligncenter size-full wp-image-10775\" \/><\/p>\n<h4>applications of integrals<\/h4>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/acceleration_velocity_position_integrals.gif\" alt=\"acceleration to velocity and velocity to position formula\" width=\"372\" height=\"88\" class=\"aligncenter size-full wp-image-8705\" \/><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/length_of_curve.gif\" alt=\"length of curve formula\" width=\"339\" height=\"45\" class=\"aligncenter size-full wp-image-8706\" \/><\/p>\n<p>on the ap calculus bc exam, you may also have to find the length of a <strong>parametric curve<\/strong> defined by <em>x<\/em> = <em>f<\/em>(<em>t<\/em>) and <em>y<\/em> = <em>g<\/em>(<em>t<\/em>).<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/03\/length_of_parametric_curve.gif\" alt=\"formula for the length of a parametric curve\" width=\"271\" height=\"45\" class=\"aligncenter size-full wp-image-9359\" \/><\/p>\n<p>use the <strong>washer<\/strong> or <strong>shell method<\/strong> to find the volume of a <strong>solid of revolution<\/strong>.<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/01\/washer_shell_methods.gif\" alt=\"formulas for washer\/disk and shell methods\" width=\"426\" height=\"97\" class=\"aligncenter size-full wp-image-8707\" \/><\/p>\n<h3>sequences and series<\/h3>\n<p>one of the most important formulas involving series is the <strong>geometric series formula<\/strong>:<\/p>\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<h4>convergence tests<\/h4>\n<p>given a series,<\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/05\/series_notation.gif\" alt=\"series notation\" width=\"247\" height=\"51\" class=\"aligncenter size-full wp-image-9901\" \/>,<\/p>\n<p>the following tests can help to prove that the series converges or diverges.<\/p>\n<ul>\n<li><strong><em>p<\/em>-series test<\/strong>.  if the series has general term <em>a<sub>n<\/sub><\/em> = <em>1\/n<sup>p<\/sup><\/em>, then the series converges if <em>p<\/em> &gt; 1 and diverges if <em>p<\/em> &le; 1.\n<\/li>\n<li><strong>alternating series test<\/strong>.  if the series is <strong>alternating<\/strong> (i.e., the terms alternate in sign forever), then the series converges if and only if <em>a<sub>n<\/sub><\/em> &rarr; 0 as <em>n<\/em> &rarr; &infin;.  and in that case, the error bound for the <em>n<\/em>th partial sum is |<em>a<sub>n+1<\/sub><\/em>|.<\/li>\n<li><strong>ratio test<\/strong>.\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/07\/ratio_test.gif\" alt=\"ratio test\" width=\"449\" height=\"46\" class=\"aligncenter size-full wp-image-10777\" \/><br \/>\nhowever, if the limit is &gt; 1, then the series diverges.  no information if the limit equals 1.<\/p>\n<\/li>\n<li><strong>root test<\/strong>.\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/07\/root_test.gif\" alt=\"root test\" width=\"447\" height=\"28\" class=\"aligncenter size-full wp-image-10778\" \/><\/p>\n<p>just as in the ratio test, if the limit is &gt; 1, then the series diverges.  no information if the limit equals 1.<\/li>\n<\/ul>\n<h4>taylor and maclaurin series<\/h4>\n<p>if a function <em>f<\/em> is differentiable to all orders, then you can build its <strong>taylor series<\/strong> centered at <em>c<\/em> as follows.<\/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 taylor series centered at c = 0 is called a <strong>maclaurin series<\/strong>.  below are some common maclaurin series that are worth memorizing.<\/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<h2>get ready!<\/h2>\n<p>this list provides just the foundation for your study.  memorizing a list of formulas will not guarantee you a high score on the exam.  you must also understand <em>how<\/em> and <em>when<\/em> to use each formula.<\/p>\n<p>furthermore, there are tons of more specialized formulas that didn&#8217;t make it to this list.  master <em>all<\/em> of the ap topics and practice, practice, practice!<\/p>\n<figure id=\"attachment_9784\" aria-describedby=\"caption-attachment-9784\" style=\"width: 568px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/1np3oj.jpg\" alt=\"meme - one does not simply walk into the ap calculus exam unprepared and score a 5\" width=\"568\" height=\"335\" class=\"size-full wp-image-9784\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/04\/1np3oj.jpg 568w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/1np3oj-300x177.jpg 300w, \/\/www.catharsisit.com\/hs\/files\/2017\/04\/1np3oj-30x18.jpg 30w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><figcaption id=\"caption-attachment-9784\" class=\"wp-caption-text\">are you prepared?<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>it&#8217;s important to know the basics. click here for the basic formulas and properties that you&#8217;ll need to master in order to succeed on the ap calculus exam.<\/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-10706","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 review: basic formulas &amp; 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