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Workbook
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\n\"The\n\n
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\nCurated OER\n
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\nThe AP Calculus Problem Book\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nAre you always looking for extra problem resources to incorporate in your classes?  A set of problems for a full AP Calculus course may be all you need! Each unit has a full set of questions and a sample test.\n
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Worksheet
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\n\"Calculus\n\n
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\nCurated OER\n
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\nCalculus Worksheet\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nIn this calculus activity, students solve 10 different problems that include determining the first derivative in each. First, they apply properties of logarithmic functions to expand the right side of each equation. Then, students...\n
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AP Test Prep
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\n\"2004\n\n
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\nCollege Board\n
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\n2004 AP® Calculus AB Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nThe test is not all about skills. The six free-response questions contain two real-world application problems. Those items deal with populations and velocities. The other four questions ask pupils to show their knowledge of calculus...\n
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Instructional Video9:44
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\n\"Graphing\n\n
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\nCurated OER\n
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\nGraphing with Calculus\n

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\nIn a problem where you are not given the original function, but rather only three known points on the graph and a few additional pieces of information about when the first and second derivatives are positive or negative, Sal shows how...\n
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Instructional Video11:32
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\n\"Introduction\n\n
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\nKhan Academy\n
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\nIntroduction to Limits, Limits, Differential Calculus\n

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\nSal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...\n
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Instructional Video16:48
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\n\"Mean\n\n
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\nKhan Academy\n
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\nMean Value Theorem, Derivative Applications, Differential Calculus\n

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\nSal spends most of this video explaining the Mean Value Theorem in a very intuitive way. He follows this with a concrete example of finding the value of a function on a closed interval where the slope is the same as the average slope of...\n
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Instructional Video17:30
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\n\"Optimization\n\n
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\nCurated OER\n
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\nOptimization with Calculus 3\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nUsing what one learned about finding the minimum and maximum of functions, the optimization problem to find two numbers whose product is -16 and whose sum of squares is a minimum is solved. Sal starts by writing the equations and...\n
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AP Test Prep
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\n\"2013\n\n
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\nCollege Board\n
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\n2013 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nWhat is the important stuff? The free-response questions from the 2013 Calculus AB exam highlight the topics in calculus assessed that year. Items provide pupils the opportunity to experience questions similar to what they will see on...\n
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AP Test Prep
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\n\"2010\n\n
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\nCollege Board\n
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\n2010 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nIs this going to be on the test? The resource contains the AP Calculus AB free-response questions that were on the 2010 test. Pupils use the six questions to prepare for their tests. Teachers use the included response resources...\n
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\n\nGet Free Access\n\nSee Review\n
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AP Test Prep
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\n\"2007\n\n
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\nCollege Board\n
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\n2007 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nGrow your knowledge of Calculus AB. Items released from the 2007 AP® Calculus AB exam provide information to teachers about the importance of particular topics. Pupils use the questions to gain an understanding of ways the exam assesses...\n
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AP Test Prep
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\n\"2014\n\n
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\nCollege Board\n
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\n2014 AP® Calculus BC Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nHow much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...\n
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\n\nGet Free Access\n\nSee Review\n
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AP Test Prep
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\n\"2015\n\n
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\nCollege Board\n
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\n2015 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nHow will the topics be assessed? Using the six released items from the Calculus AB test, pupils see how the exam assesses content from the course. With the additional materials covering test taker's responses and scoring keys, teachers...\n
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AP Test Prep
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\n\"2014\n\n
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\nCollege Board\n
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\n2014 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nGive classes a sneak peek at an upcoming test. Scholars work released items from the AP Calculus AB test to prepare for their own exams. The resource consists of six items, two graphing calculator items, and four non-calculator items....\n
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AP Test Prep
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\n\"2012\n\n
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\nCollege Board\n
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\n2012 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nWhat's on the test? Released items provide insight into the AP Calculus test. The six items are split into two groups, two calculator items and four non-calculator items. Resources allow teachers to see what kinds of answers test takers...\n
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AP Test Prep
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\n\"2011\n\n
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\nCollege Board\n
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\n2011 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nSo this is the real test? The resource provides the free-response questions from the 2011 AP Calculus AB exam. The six questions are split into two sections, calculator and non-calculator items. Several resources give teachers...\n
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AP Test Prep
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\n\"2016\n\n
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\nCollege Board\n
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\n2016 AP® Calculus BC Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nThe split is 50-50. Released free-response questions from the 2016 AP Calculus BC show that half the questions are from the AB portion of the course and the others are from the BC portion. Teachers and pupils use the items to prepare and...\n
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AP Test Prep
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\n\"2009\n\n
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\nCollege Board\n
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\n2009 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nWhat was one of the big takeaways from 2009? By reviewing the released AP® Calculus free-response questions, pupils and teachers realize that performing mathematics is not all there is to doing well on the exam. Several items require...\n
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AP Test Prep
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\n\"2015\n\n
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\nCollege Board\n
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\n2015 AP® Calculus BC Free-Response Questions\n

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\nHow will the exam ask this question? The free-response questions from the 2015 AP Calculus BC exam demonstrate how questions appear on the test. Using the questions, pupils gain experience answering similar inquiries to what they see on...\n
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eBook
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\n\"Calculus\n\n
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\nRice University\n
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\nCalculus Volume 2\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nDelve into the middle of calculus. The resource is the second eBook of three that covers the complete calculus content. Seven chapters begin with integrals and different methods of integration before moving on to differential equations....\n
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AP Test Prep
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\n\"Calculus\n\n
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\nCalculus at the Battle of Trafalgar\n

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\n\nFor Teachers\n\n10th - 12th\n
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\nAll's fair in math and war. Scholars examine the Battle of Trafalgar using calculus. They set up and solve a system of differential equations to determine the number of ships remaining in each fleet over time. \n
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AP Test Prep
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\nAP Calculus: Slope Fields\n

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\n\nFor Teachers\n\n10th - 12th\n
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\nReady to field questions about slope fields? An article on AP® Calculus teaching methods describes how to teach about slope fields to solve differential equations. It gives some sample problems to consider with the class and how to...\n
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Instructional Video8:49
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\n\"Product\n\n
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\nKhan Academy\n
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\nProduct Rule, Taking Derivatives, Differential Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal defines the product rule and then shows two examples of its use. He then shows an example of finding the derivative using the chain and product rules together.\n
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Instructional Video9:02
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\n\"Calculus:\n\n
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\nCalculus: Derivative of x^(x^x)\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal starts by showing how to find dy/dx of y = x2 and then moves on to show the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x.\n
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Instructional Video15:43
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\n\"Calculus:\n\n
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\nCalculus: Derivatives 1 (New HD Version)\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal defines the term derivative by taking the listener on a well-organized tour of the slope. First, he reviews the concept of the slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining...\n
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