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Lesson Plan
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\n\"Definite\n\n
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\nCurated OER\n
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\nDefinite Integral\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nLearners investigate the intervals represented by a function in this calculus lesson. They decide what interval of the function will be positive, negative or zero. They are then given graphs of functions and asked to analyze it.\n
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AP Test Prep
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\n\"2003\n\n
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\nCollege Board\n
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\n2003 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nTake a free look. Released free-response questions from the 2003 AP® Calculus AB exam show how questions cover different topics. Pupils and teachers review the topics of bounded regions, particle movement, rates, relationships between...\n
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AP Test Prep
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\n\"2001\n\n
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\nCollege Board\n
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\n2001 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nTake a closer look at the exam. Released items from the 2001 Calculus AB exam allow teachers and pupils to view how the exam presents questions. Scholars use the questions to prepare for the test and compare their responses to the...\n
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AP Test Prep
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\n\"2009\n\n
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\n2009 AP® Calculus BC Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nLet them eat cake. The free-response questions from an AP® Calculus BC exam cover several topics that include finding the area under a curve within the context of creating a birthday cake. Calculus concepts include finding rates of...\n
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AP Test Prep
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\n\"2002\n\n
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\nCollege Board\n
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\n2002 AP® Calculus BC Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nThough the items may be older, they still provide information. Released free-response items from the 2002 AP® Calculus BC exam provide teachers and pupils with information about how topics appear on the exam. Questions come from the AB...\n
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AP Test Prep
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\n\"1999\n\n
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\nCollege Board\n
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\n1999 AP® Calculus BC Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nGet a 20/20 view of the exam. Free-response questions from the 1999 Calculus BC exam provide an insight to the exams. Pupils review the questions to see how topics show up on the test. Topics range from particle motion along a function,...\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 BC Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nKeep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...\n
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AP Test Prep17:14
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\n\"Calculus\n\n
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\nCalculus AB/BC - Integrating Functions Using Long Division and Completing the Square\n

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\n\nFor Students\n\n10th - 12th\n
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\nWith just a little work, integrals can become much easier. The 11th of 16 installments in Unit 6 - Integration has viewers watch a video to learn different ways to rewrite an integrand before determining the integral. They use polynomial...\n
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AP Test Prep17:00
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1
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\n\"Calculus\n\n
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\nCalculus AB/BC - Integrating Using Substitution\n

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\n\nFor Students\n\n10th - 12th\n
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\nU is for u-substitution. Viewers of an instructional video learn how to apply u-substitution to determine integrals for more complex functions. They first find indefinite integrals, then move on to definite integrals. \n
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AP Test Prep15:39
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\n\"Calculus\n\n
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\nCalculus AB/BC - Applying Properties of Definite Integral\n

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\n\nFor Students\n\n10th - 12th\n
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\nProperly apply the properties of integrals. By watching a video, scholars learn about the properties of definite integrals. They see how to use the area under a curve and the properties to determine the value of a given definite integral. \n
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AP Test Prep9:02
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1
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\n\"Calculus\n\n
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\nCalculus AB/BC - Interpreting the Behavior of Accumulation Functions Involving Area\n

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\n\nFor Students\n\n10th - 12th\n
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\nAccumulation functions should behave like other functions. Using content from Unit 5, pupils analyze the first and second derivative to determine the behavior of an accumulation function. Learners find out how to calculate the relative...\n
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AP Test Prep11:30
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1
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\n\"Calculus\n\n
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\nCalculus AB/BC - Particular Solutions using Initial Conditions and Separation of Variables\n

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\n\nFor Students\n\n10th - 12th\n
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\nTake the next step in separating. Pupils pick up from the previous lesson to now find the particular solution of a differential equation at a given point. Scholars watch three examples of finding the particular solution and hear the...\n
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Instructional Video3:23
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\n\"Volumes:\n\n
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\nVolumes: Solids That are Not Solid of Revolution\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nViewers learn how to calculate the volume when the cross section is not a circle by using the same principle as if it was a circle. The video goes through an example of finding the volume of a figure where the cross sections are squares...\n
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Worksheet
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\n\"Functions\n\n
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\nCurated OER\n
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\nFunctions\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nFor this functions worksheet, students solve and complete 5 different sets of problems that include determining functions on intervals. First, they define a definite integral and the Fundamental Theorem of Calculus. Then, students draw a...\n
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Worksheet
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\n\"Definite\n\n
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\nDefinite Integrals\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn this calculus worksheet, students calculate the definite integral given different functions. They evaluate the functions for given values. There are 20 questions.\n
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Worksheet
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\nAP Calculus Practice Exam\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn this practice exam learning exercise, students solve 17 multiple choice problems. Students find derivatives, points of continuity, maximums, minimums, integrals, and area of enclosed regions.\n
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Worksheet
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\n\"Calculus\n\n
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\nCalculus Test\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this calculus instructional activity, students integrate various functions, find the sum of a series, and solve differential equations. There are 16 questions including multiple choice and free response.\n
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Worksheet
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\n\"The\n\n
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\nThe Integration of Exponential Functions\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn this calculus activity, students solve problems using integration. They solve exponential functions using differentiation formulas. There are 12 problems with an answer key.\n
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Interactive
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\nThe Method of Integration by Parts\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn this calculus instructional activity, students perform integration by parts. They solve differential equations as they use integration by part to solve unlike terms. There are 23 problems with an answer key.\n
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\nThe Method of Integration by Partial Fractions\n

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\n\nFor Students\n\n9th - 10th\n
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\nFor this calculus worksheet, students solve problems using integration by partial fractions. They add fractions to get a common denominator, then take the derivative. There are 20 questions with an answer key.\n
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\nThe Limit Definition of a Definite Integral\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn this calculus worksheet, students calculate the derivative and integral of different functions. They use interval to mark the beginning and end of their calculations. There are 15 questions with an answer key.\n
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\n\"Proof\n\n
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\nProof That One Equals Zero (Using Calculus)\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn this proofs worksheet, students evaluate the integral of 1 function. Students use uv-substitution to prove 0=1.\n
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Worksheet
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\nAP Calculus Practice Exam AB Version-Section1-Part 1\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this calculus practice exam, students select the best answer to 28 multiple choice questions. Questions cover information from the entire year of calculus. A suggested time limit of 55 minutes is included.\n
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Lesson Plan
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\n\"Integration\n\n
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\nIntegration By Substitution\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nYoung scholars calculate the solution using integrals in this calculus instructional activity. They use the TI to create a visual of how to compute integrals. Learners also use substitution by integration and all its properties.\n
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