AP Calculus AB · Full practice exam 2012

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

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Question Section I · 5

Multiple choice
Question Section I · 5 — 5. The graph of the function f is shown above. Which of the following statements is false? (A) ( ) 2 lim x f x Æ exists. (B) ( ) 3 lim x f x Æ exists. (C) ( ) 4 lim x f x Æ exists. (D) ( ) 5 lim x f x Æ exists. (E) The…

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

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Question Section I · 9

Multiple choice
Question Section I · 9 — ( ) ( )( ) 2 1 2 for 2 2 for 2 x x x f x x k x + - ÏÔ π = - Ì Ô = Ó 9. Let f be the function defined above. For what value of k is f continuous at 2 ? x = (A) 0 (B) 1 (C) 2 (D) 3 (E) 5

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

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Question Section I · 25

Multiple choice
Question Section I · 25 — 25. Which of the following is the solution to the differential equation 2sin dy x dx = with the initial condition ( ) 1 ? y p = (A) 2cos 3 y x = + (B) 2cos 1 y x = - (C) 2cos 3 y x = - + (D) 2cos 1 y x = - + (E) 2cos 1…

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

Question Section I · 77

Multiple choice
Question Section I · 77 — 77. Let f be a function that is continuous on the closed interval [ ] 2, 4 with ( ) 2 10 f = and ( ) 4 20. f = Which of the following is guaranteed by the Intermediate Value Theorem? (A) ( ) 13 f x = has at least one…

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

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