AP Calculus BC · Full practice exam 2012

51 questions, each with its course unit and the official scoring guidelines.

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Question Section I · 13

Multiple choice
Question Section I · 13 — 13. What is the radius of convergence of the series ( ) 0 4 ? 3n n x = - Â (A) 2 3 (B) 3 (C) 3 (D) 3 2 (E) 0

Source: College Board — AP Calculus BC, Full practice exam, 2012

Question Section I · 14

Multiple choice
Question Section I · 14 — 14. Let k be a positive constant. Which of the following is a logistic differential equation? (A) = dy kt dt (B) = dy ky dt (C) ( ) 1 = - dy kt t dt (D) ( ) 1 = - dy ky t dt (E) ( ) 1 = - dy ky y dt

Source: College Board — AP Calculus BC, Full practice exam, 2012

Question Section I · 16

Multiple choice
Question Section I · 16 — 16. Let ( ) = y f x be the solution to the differential equation = - dy x y dx with initial condition ( )1 3. = f What is the approximation for ( ) 2 f obtained by using Euler’s method with two steps of equal length…

Source: College Board — AP Calculus BC, Full practice exam, 2012

Question Section I · 17

Multiple choice
Question Section I · 17 — 17. For 0, x > the power series ( ) ( ) 2 4 6 2 1 1 3! 5! 7! 2 1 ! n n x x x x n - + - + + - + + " " converges to which of the following? (A) cos x (B) sin x (C) sin x x (D) 2 x x e e - (E) 2 1 x x e e + -

Source: College Board — AP Calculus BC, Full practice exam, 2012

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Question Section I · 21

Multiple choice
Question Section I · 21 — 21. The line 5 = y is a horizontal asymptote to the graph of which of the following functions? (A) ( ) sin 5 = x y x (B) 5 = y x (C) 1 5 = - y x (D) 5 1 = - x y x (E) 2 2 20 1 4 - = + x x y x

Source: College Board — AP Calculus BC, Full practice exam, 2012

Question Section I · 22

Multiple choice
Question Section I · 22 — 22. The power series ( ) 0 3 n n n a x = - Â converges at 5. x = Which of the following must be true? (A) The series diverges at 0. x = (B) The series diverges at 1. x = (C) The series converges at 1. x = (D) The series…

Source: College Board — AP Calculus BC, Full practice exam, 2012

Question Section I · 23

Multiple choice
Question Section I · 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? (A) 200 = dP dt (B) 200 = dP t dt (C) 2 100 = dP t dt (D) 200 =…

Source: College Board — AP Calculus BC, Full practice exam, 2012

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Question Section I · 27

Multiple choice
Question Section I · 27 — 27. For what values of p will both series 2 1 1 p n n =Â and 1 2 n p = Ê ˆ Ë ¯ Â converge? (A) 2 2 p - < < only (B) 1 1 2 2 p - < < only (C) 1 2 2 p < < only (D) 1 2 p < and 2 p > (E) There are no such values of p.

Source: College Board — AP Calculus BC, Full practice exam, 2012

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Question Section I · 79

Multiple choice
Question Section I · 79 — 79. Let f be a function having derivatives of all orders for 0 x > such that ( ) 3 2, f = ( ) 3 1, f = - ¢ ( ) 3 6, f = ¢¢ and ( ) 3 12. f = ¢¢¢ Which of the following is the third-degree Taylor polynomial for f about 3…

Source: College Board — AP Calculus BC, Full practice exam, 2012

Question Section I · 83

Multiple choice
Question Section I · 83 — 83. If the function f is continuous at 3, x = which of the following must be true? (A) ( ) ( ) 3 3 lim x f f x Æ < (B) ( ) ( ) 3 3 lim lim x x f x f x - + Æ Æ π (C) ( ) ( ) ( ) 3 3 3 lim lim x x f f x f x - + Æ Æ = =…

Source: College Board — AP Calculus BC, Full practice exam, 2012

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Question Section I · 90

Multiple choice
Question Section I · 90 — 90. If the series 1 n n a =Â converges and 0 n a > for all n, which of the following must be true? (A) 1 lim 0 n n n a a + Æ• = (B) 1 n a < for all n (C) 1 0 n n a = • = Â (D) 1 n n na = • Â diverges. (E) 1 n n a n = •…

Source: College Board — AP Calculus BC, Full practice exam, 2012

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Question Section II · 5

Open answer
Question Section II · 5 — 5. The rate at which a baby bird gains weight is proportional to the difference between its adult weight and its current weight. At time 0, t = when the bird is first weighed, its weight is 20 grams. If ( ) B t is the…

Source: College Board — AP Calculus BC, Full practice exam, 2012

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