U of I MATH 070 - 2003 BC Multiple Choice (20 pages)

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2003 BC Multiple Choice



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2003 BC Multiple Choice

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Pages:
20
School:
University of Illinois
Course:
Math 070 - Elementary Mathematics
Elementary Mathematics Documents
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Name Period AP Calculus BC 2003 Calculus BC Multiple Choice Exam Part A 1 If y sin 3 x then dy dx A 3cos 3 x B cos 3 x 1 3 D cos 3x C cos 3x E 3cos 3 x e x cos x 2 x 2 lim is x 0 x2 2 x A 1 2 B 0 1 2 D 1 C E nonexistent 3 3x 1 dx 5 3 x 1 6 A C 18 3 x 1 6 B C 6 3 x 1 6 C C 2 3x 2 x 6 D 2 C 2 3x 2 E x 5 C 2 PDF Created with deskPDF PDF Writer Trial http www docudesk com 4 For 0 t 13 an object travels along an elliptical path given by the parametric equations x 3cos t and y 4sin t At the point where t 13 the object leaves the path and travels along the line tangent to the path at that point What is the slope of the line on which the object travels 4 3 3 B 4 4 tan13 C 3 4 D 3 tan13 3 E 4 tan13 A dy x y with dx the initial condition f 1 2 What is the approximation for f 2 if Euler s method is used starting at x 1 with a step size of 0 5 A 3 B 5 C 6 D 10 E 12 5 Let y f x be the solution to the differential equation 6 What are all values of p for which 1 1 dx converges x2 p A p 1 B p 0 1 2 D p 1 C p E There are no values of p for which this integral converges PDF Created with deskPDF PDF Writer Trial http www docudesk com 7 The position of a particle moving in the xy plane is given by the parametric equations x t 3 3t 2 and y 2t 3 3t 2 12t For what values of t is the particle at rest A 1 only B 0 only C 2 only D 1 and 2 only E 1 0 and 2 8 x 2 cos x dx 3 A sin x 3 C 1 3 B sin x 3 C 1 3 C x3 sin x3 C 3 x3 D sin x3 C 3 x4 x3 E sin C 3 4 9 If f x ln x 4 e 3 x then f 0 is A 2 5 1 5 1 C 4 2 D 5 E nonexistent B PDF Created with deskPDF PDF Writer Trial http www docudesk com 10 What is the value of 2n 1 n n 1 3 A 1 B 2 C 4 D 6 E The series diverges 11 The Maclaurin series for power series expansion for 1 is 1 x xn n 0 Which of the following is a x2 1 x2 A 1 x 2 x 4 x 6 x8 B x 2 x 3 x 4 x5 C x 2 2 x3 3x 4 4 x 5 D x 2 x 4 x 6 x8 E x 2 x 4 x 6 x8 12 The rate of change of the volume V of water in a tank with respect to time t is directly proportional to the square root of the volume Which of the following is a differential equation that describes this relationship A V t k t B V t k V C dV k t dt D dV k dt V E dV k V dt PDF Created with deskPDF PDF Writer Trial http www docudesk com y O a c b x e d 13 The graph of a function f is shown above At which value of x is f continuous but not differentiable A a B b C c D d E e y y 3 3 x x 3 3 3 3 3 3 14 Shown above is a slope field for which of the following differential equations A dy x dx y dy x 2 dx y 2 dy x3 C dx y B D dy x 2 dx y E dy x 3 dx y 2 PDF Created with deskPDF PDF Writer Trial http www docudesk com 15 The length of a curve from x 1 to x 4 is given by 4 1 1 9 x 4 dx If the curve contains the point 1 6 which of the following could be an equation for this curve A y 3 3 x 2 B y 5 x 3 C y 6 x 3 D y 6 x3 E y 16 9 x x5 5 5 16 If the line tangent to the graph of the function f at the point 1 7 passes through the point 2 2 then f 1 is A 5 B 1 C 3 D 7 E undefined A curve C is defined by the parametric equations x t 2 4t 1 and y t 3 Which of the following is an equation of the line tangent to the graph of C at the point 3 8 A x 3 B x 2 C y 8 17 27 x 3 8 10 E y 12 x 3 8 D y PDF Created with deskPDF PDF Writer Trial http www docudesk com y 7 6 5 4 3 2 1 x 1 2 3 4 5 6 7 1 2 3 Graph of f 18 The graph of the function f shown in the figure above has horizontal tangents at x 3 and x 6 If g x 2x 0 f t dt what is the value of g 3 A 0 B 1 C 2 D 3 E 6 PDF Created with deskPDF PDF Writer Trial http www docudesk com 19 A curve has slope 2 x 3 at each point x y on the curve Which of the following is an equation for this curve if it passes through the point 1 2 A y 5 x 3 B y x 2 1 C y x 2 3x D y x 2 3x 2 E y 2 x 2 3x 3 20 x 4 x5 x6 x n 3 A function f has Maclaurin series given by 2 3 4 n 1 Which of the following is an expression for f x A 3 x sin x 3 x 2 B cos x2 1 C x 2 cos x x 2 D x 2e x x3 x 2 E e x x 2 1 2 21 The number of moose in a national park is modeled by the function M that satisfies the logistic differential equation dM M 0 6M 1 where dt 200 M t t is the time in years and M 0 50 What is lim t A 50 B 200 C 500 D 1000 E 2000 PDF Created with deskPDF PDF Writer Trial http www docudesk com 22 What are all values of p for which the infinite series n p n 1 n 1 converges A p 0 B p 1 C p 1 D p 2 E p …


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