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Wis driver license renewal. AP® Calculus AB 2008 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success. . 1998 AP Calculus AB and AP Calculus BC, Released Exams, The College Entrance Examination Board and Educational Testing Service, 1999. AP Calculus AB Free Response Questions, AP Calculus AB Free Response Items, Form B, AP Calculus AB Scoring Guidelines, AP Calculus AB Scoring Guidelines, Form B for the years 2004, 2005, 2006.

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## Annotated Solutions toPast Free-Response Questions

 This material is provided to you as a supplement to the book Be Prepared for the AP Calculus Exam. You are not authorized to publish or distribute it in any form without our permission. However, you may print out one copy of this chapter for personal use and for face-to-face teaching for each copy of the Be Prepared book that you own or receive from your school.

This chapter contains solutions and notes for the free-response questions from past AP Calculus exams. The free-response questions and scoring guidelines for these examsare posted on the College Board's apstudent web site and, for teachers, on AP Central:

For students:

For teachers:

## All solutions:

 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003

The best way to practice with the past exam questions is to first solve them on your own,then compare your solutions with our solutions and notes.

1971-1985 questions with solutions by Judith Broadwin and George Lenchner,and 1986-2000 questions with solutions by Judith Broadwin, George Lenchner, and Martin Rudolph,are available for purchase and free download (scanned-to-PDF) atmoems.org.

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Questions and Worked Solutions for AP Calculus BC Multiple Choice 2012.
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AP Calculus BC Multiple Choice 2012 Question 1
1. If y = sin3x, then dy/dx =
(A) cos3x (B) 3cos2x (C) 3sin2x (D) -3sin2xcos x (E) 3sin2x cosx
AP Calculus BC Multiple Choice 2012 Question 2
2. The position of a particle moving in the xy-plane is given by the parametric equations x(t) = t32 and y(t) = 12t - 3t2. At which of the following points (x,y), is the particle at rest?
(A) (-4, 12) (B) (-3, 6) (C) (-2, 9) (D) (0, 0) (E) (3,4)
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AP Calculus BC Multiple Choice 2012 Question 3
3. The graph of f is shown above for 0 ≤ x ≤ 4. What is the value of ? (A) -1 (B) 0 (C) 2 (D) 6 (E) 12
AP Calculus BC Multiple Choice 2012 Question 4
4. Which of the following integrals gives the length of the curve y = ln x from x = 1 to x = 2 ?
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AP Calculus BC Multiple Choice 2012 Question 5
5. The Maclaurin series for the function f is given by .What is the value of f(3) ?
(A) -3 (B) -3/7 (C) 4/7 (D) 13/16 (E) 4
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AP Calculus BC Multiple Choice 2012 Question 6
6. Using the substitution u = x2 -3, is equal to which of the following? AP Calculus BC Multiple Choice 2012 Question 7
7. If arcsin x = ln y = then dy/dx =
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AP Calculus BC Multiple Choice 2012 Question 8
8. A tank contains 50 liters of oil at time t = 4 hours. Oil is being pumped into the tank at a rate R(t), where R(t) is measured in liters per hour, and t is measured in hours. Selected values of R(t) are given in the table above. Using a right Riemann sum with three subintervals and data from the table, what is the approximation of the number of liters of oil that are in the tank at time t = 15 hours?
(A) 64.9 (B) 68.2 (C) 114.9 (D) 116.6 (E) 118.2
AP Calculus BC Multiple Choice 2012 Question 9
9. Which of the following series converge?
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AP Calculus BC Multiple Choice 2012 Question 10
AP Calculus BC Multiple Choice 2012 Question 11
11. Let f be the function defined by f(x) = √(x-2) for all x. Which of the following statements is true?
(A) f is continuous but not differentiable at x = 2.
(B) f is differentiable at x = 2.
(C) f is not continuous at x = 2.
(D) lim f(x) ≠ 0
(E) x = 2 is a vertical asymptote of the graph of f.
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AP Calculus BC Multiple Choice 2012 Question 12
12. The points (-1,-1) and (1,-5) are on the graph of a function y = f(x) that satisfies the differential equation dy/dx = x2 + y. Which of the following must be true?
(A) (1,-5) is a local maximum of f.
(B) (1,-5) is a point of inflection of the graph of f.
(C) (-1,-1) is a local maximum of f.
(D) (-1,-1) is a local minimum of f.
(E) (-1,-1) is a point of inflection of the graph of f.

AP Calculus BC Multiple Choice 2012 Question 13
13. What is the radius of convergence of the series AP Calculus BC Multiple Choice 2012 Question 14
14. Let k be a positive constant. Which of the following is a logistic differential equation?
AP Calculus BC Multiple Choice 2012 Question 15
15. The graph of a differentiable function f is shown above. If h(x) = , which of the following is true?
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AP Calculus BC Multiple Choice 2012 Question 16
16. Let y = f(x) be the solution to the differential equation dy/dx = x - y with initial condition f(1) = 3. What is the approximation for f(2) obtained by using Euler’s method with two steps of equal length starting at x = 1 ? AP Calculus BC Multiple Choice 2012 Question 17
17. For x > 0, the power series converges to which of the following?
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AP Calculus BC Multiple Choice 2012 Question 18
18. The graph of f', the derivative of a function f, consists of two line segments and a semicircle, as shown in the figure above. If f(2) = 1, then f(-5) =
(A) 2π - 2

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(B) 2π - 3
(C) 2π - 5
(D) 6 - 2π
(E) 4 - 2π AP Calculus BC Multiple Choice 2012 Question 19
19. The function f is defined by f(x) = x/(x+2). What points (x,y), on the graph of f have the property that the line tangent to f at (x,y), has slope 1/2?
(A) (0,0) only
(B) (1/2, 1/5) only
(C) (0,0) and (-4,2)
(D) (0,0) and (4,2/3)
(E) There are no such points.
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AP Calculus BC Multiple Choice 2012 Question 20

20. AP Calculus BC Multiple Choice 2012 Question 21

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21. The line y = 5 is a horizontal asymptote to the graph of which of the following functions?
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AP Calculus BC Multiple Choice 2012 Question 22
22. The power series converges at x = 5. Which of the following must be true? AP Calculus BC Multiple Choice 2012 Question 23
23. If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population?
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AP Calculus BC Multiple Choice 2012 Question 24
24. Let f be a differentiable function such that. Which of the following could be f(x) ? AP Calculus BC Multiple Choice 2012 Question 25
25.

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AP Calculus BC Multiple Choice 2012 Question 26
26. What is the slope of the line tangent to the polar curve r = 1 + 2sinθ at θ = 0? AP Calculus BC Multiple Choice 2012 Question 27
27. For what values of p will both series converge?