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Topics include parametric derivatives, solutions to differential equations using Euler’s method, antiderivatives and integration techniques, definite integrals applied to area, volume, and arc length, logistic growth modeling, and convergence tests for series. 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A curve is defined by the parametric equations  and  ~~ ~~  What is   in terms oft ?  \n(A) ~~ ~~  \n(B) ~~ ~~  \n(C) ~~ ~~  \n(D) ~~ ~~~~ ~~  \n| Learning Objective | Essential Knowledge | Mathematical Practice for AP Calculus |\n| --- | --- | --- |\n| LO 2. 1C: Calculate derivatives. | \u003Cbr>EK 2. 1C7: (BC) Methods for calculating derivatives of real-valued functions can be extended to vector-valued functions, parametric functions, and functions in polar coordinates. | MPAC 3: Implementing algebraic/ computational processes\u003Cbr>MPAC 2: Connecting concepts |\n\nReturn to  \nAP Calculus AB/BC Course and Exam Description Table of Contents 75  \n© 2015 The College Board  \nSample Exam Questions  \nAP CALCULUS BC SAMPLE EXAM QUESTIONS  \n2.  \n\n| | |\n| --- | --- |\n| | |\n| | |\n\nConsider the differential equation ~~ ~~  where A is a constant.  \nLet  be the particular solution to the differential equation with the initial condition  Euler’s method, starting at  with a step size of 2, is used to approximate  Steps from this approximation are shown in the table above. What is the value of A ?  \n(A) ~~ ~~  \n(B) 2 (C) 5 (D) ~~ ~~  \n| Learning Objective | Essential Knowledge | Mathematical Practice for AP Calculus |\n| --- | --- | --- |\n| LO 2.3F: Estimate solutions to differential equations. | \u003Cbr>EK 2.3F2: (BC) For differential equations, Euler’s method provides a procedure for approximating a solution or a point on a solution curve. | MPAC 4:\u003Cbr>Connecting multiple representations MPAC 3: Implementing algebraic/ computational processes |\n\nReturn to  \n76 AP Calculus AB/BC Course and Exam Description Table of Contents © 2015 The College Board  \nSample Exam Questions  \n| Learning Objective | Essential Knowledge | Mathematical Practice for AP Calculus |\n| --- | --- | --- |\n| LO 3.3B(a): Calculate antiderivatives. | EK 3.3B5:Techniques for finding antiderivatives include algebraic manipulation such as long division and completing the square, substitution of variables,(BC) integration by parts, and  nonrepeating linear partial fractions. | MPAC 3: Implementing algebraic/ computational processes\u003Cbr>MPAC 5: Building notational fluency |\n\nAP CALCULUS BC SAMPLE EXAM QUESTIONS  \nReturn to  \nAP Calculus AB/BC Course and Exam Description Table of Contents 77  \n© 2015 The College Board  \nSample Exam Questions  \nAP CALCULUS BC SAMPLE EXAM QUESTIONS  \n4. The shaded region in the figure above is bounded by the graphs of  ~~ ~~  and  \n~~ ~~ ~~ ~~  for ~~ ~~ ~~ ~~ Which of the following expressions gives the perimeter of the  \n| Learning Objective | Essential Knowledge | Mathematical Practice for AP Calculus |\n| --- | --- | --- |\n| LO 3.4D: Apply definite integrals to problems involving area, volume,(BC) and  length of a curve. | \u003Cbr>EK 3.4D3: (BC)The length of a planar curve defined by a function or by aparametrically defined curve can be calculated using a definite integral. | MPAC 2: Connecting concepts\u003Cbr>MPAC 4: Connecting multiple representations |\n\nReturn to  \n78 AP Calculus AB/BC Course and Exam Description Table of Contents © 2015 The College Board  \nSample Exam Questions  \n5. The number of fish in a lake is modeled by the function P that satisfies the differential equation  \n~~ ~~ ~~ ~~  where t is the time in years. Which of the following could be the graph of   \n(A)  \n(B)  \n(C)  \n(D)  \n| Learning Objective | Essential Knowledge | Mathematical Practice for AP Calculus |\n| --- | --- | --- |\n| LO 3.5B: Interpret, create and solve differential equations from problems in context. | \u003Cbr>EK 3.5B2: (BC)The model for logistic growth that arises from the statement “The rate of change of a quantity is jointly proportional to the size of the quantity and the difference between the quantity and the carrying capacity” is  ~~ ~~ \u003Cbr>| MPAC 2: Connecting concepts\u003Cbr>MPAC 4:\u003Cbr>Connecting multiple represent","cbCaigz1QsoVZWS9","https://ap.wps.com/l/cbCaigz1QsoVZWS9","pdf",659898,"English","# Sample Exam Questions\n## Section I, Part A\n## Multiple Choice Questions","[{\"question\":\"What calculator rule applies to Section I, Part A?\",\"answer\":\"A calculator may not be used on questions on this part of the exam.\"},{\"question\":\"Which method is referenced for approximating solutions to a differential equation?\",\"answer\":\"Euler’s method is used to approximate a solution, with steps shown in a provided table.\"},{\"question\":\"What topics beyond derivatives appear in these sample questions?\",\"answer\":\"The set includes integration and definite integrals (area/volume/length of a curve), logistic growth differential equations, and series convergence tests.\"}]","AP Calculus BC Sample Exam Questions - Section I - Part A | PDF"]