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The problems cover function domains, volumes of solids of revolution, tangent line intercepts, parametric curves, derivatives and critical points, differentials, inequality conditions, average value, related rates with ladder geometry, inflection points, and volumes generated by rotation about an 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EXAMINATION  \nDirections:Solve each of the following problems,using the available space for scratchwork.After examining theform of the choices,decide which is the best of the choices given and filin the corresponding oval on the answersheet.No credit will be given for anything written in the test book.Do not spend too much time on any one problem.  \n   \nIn this test:Unless otherwise specified,the domain of a functionfis assumed to be the set of allreal numbers x forwhich f(x)is a real number.  \n   \n(E)  \n(C)  \n(D)  \n(B)y-e  \n(A)x-ey  \n2.The volume of the solid that results when the area between the curvey=e and the line y=0,from x=1 tox=2,is revolved around the x-axis is(E)2πe²(A)2π(e⁴-e²)(C)(D)2π(e²-e)(B)  \n(A)  \n(B)  \n(C)  \n(D)  \n(E)  \n(A)  \n(B)10tlnt+4t  \n(C)  \n(D)  \n(E)  \n(B)  \n(C)0  \n(A)  \n(D)-6  \n(E)6  \n6.The tangent line to the curve y=x³-4x+8at the point(2,8)has an x-intercept at  \n(A)(-1,0)  \n(B)(1,0)  \n(C)(0,-8)  \n(D)(0,8)  \n(E)(8,0)  \n7.The graph in the xy-plane represented byx=3sin(t)and y=2cos(t)is(A)a circle(C)a hyperbola (D)a parabola(E)a line(B)an ellipse  \n8.  \n9.  \n(A)  \n(B)  \n(C)  \n(D)  \n(E)  \n(A)0  \n(B)2  \n(C)4  \n(D)4π  \n(E)nonexistent  \n10.The position of a particle moving along the x-axis at time tis given by x(t)=ecos²0,0≤t≤π.For which of thefollowing values of t will x'(t)=0?  \nI.t=0II.III.t=π(A)I only(B)II only(C)I and II only (D)I and I only (E)I,II,and II  \n(E)√2  \n(A)-1  \n(B)0  \n(C)  \n(D)1  \n12.Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to  \n7.99 cm.(in cm³)(A)-19.2(B)-15.36(C)-1.92(D)-0.01(E)-0.0001  \n>0 is13.(A)(a-2)≤x≤(a+2)(B)(a-2)\u003Cx\u003C(a+2)(C)(-a-2)>x>(a-2)(D)(a-2)>x>(-a-2)(E)(a-2)≤x≤(-a-2)  \n14.  \n(A)0  \n(A)81x-60y=142  \n(B)81x+60y=182  \n(C)20x+27y=49  \n(D)20x+27y=31  \n(E)81x-60y=182  \n(B)  \n(C)  \n(D)  \n(E)  \n16.If c satisfies the conclusion of the Mean Value Theorem for derivatives forf(x)=2 sinx on the interval [0,π],then c could be  \n(A)0  \n(B)  \n(C)  \n(D)π  \n(E)There is no value of con [0,π]  \n17.The average value of f(x)=x Ilnx on the interval [1,e]is  \n(A)  \n(B)  \n(C)  \n(D)  \n(E)  \n18.A 17-foot ladder is sliding down a wall at a rate of-5 feet/sec.When the top of the ladder is 8 feet from theground,how fast is the foot of the ladder sliding away from the wall (in feet/sec)?  \n(D)-16  \n(E)  \n(A)  \n(B)  \n(C)  \n(A)8e3sinx  \n(B)8e³cosx  \n(C)8e³sinx+3  \n(D)  \n20.The length of the curve determined byx=3t andy=2t²fromt=0 tot=9 is  \n(A)  \n(B)  \n(C)  \n(D)  \n(E)  \n(E)  \n21.If a particle moves in the xyplane so that at timet>0 itsposition vector is (e²,e⁻³)then its velocity vectorat time t=3 is(A)(ln6,In(-27))(B)(ln9,ln(-27))(C)(e⁹,e-27)(D)(6e⁹,-27e-27)(E)(9e⁹,-27e-27)  \n22.The graph of f(x)=√11+x²has a point of inflection at  \n(A)(0,11)  \n(B)(-√11,0)  \n(C)(0,-√11)  \n(D)  \n(E)There is no point of inflection.  \n23.What is the volume of the solid generated by rotating about the y-axis the region enclosed byy=sinx and  \nthe x-axis,from x=0 to x=π?  \n(A)π²  \n(B)2π²  \n(C)4π²  \n(D)2  \n(E)4  \n24.  \n(A)1  \n(B)0  \n(C)-1  \n(E)Undefined  \n(D)2  \n25.A rectangle is to be inscribed between the parabolay=4-x²and the x-axis,with its base on the x-axis.Avalue of x that maximizes the area of the rectangle is  \n(A)0  \n(B)  \n(C)  \n(D)  \n(E)","cbCaiomVaBL8n2w2","https://ap.wps.com/l/cbCaiomVaBL8n2w2","pdf",8729150,12,"English","# Section I\n## Part A","[{\"question\":\"Is a calculator allowed for Part A of this exam?\",\"answer\":\"No. The document states that a calculator may not be used on this part of the examination.\"},{\"question\":\"How should answers be recorded for the multiple-choice questions?\",\"answer\":\"After choosing the best option, the examinee should fill in the corresponding oval on the answer sheet.\"},{\"question\":\"What topics do the questions mainly cover?\",\"answer\":\"The problems focus on calculus concepts such as derivatives, tangent lines, average value of functions, differentials, inflection points, and volumes generated by rotating regions about axes.\"}]","SECTIONI - Part A - Exam Practice Questions | PDF"]