5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 16:32

AP Calculus AB Practice Exam 1 353

Section I Part B

Number of Questions Time Use of Calculator

15 45 Minutes Yes

Directions:

Continue using the same answer sheet.Please note that the questions begin with number 76. This is not an error; it

was done to be consistent with the numbering system of the actual AP Calculus AB exam. All questions are given

equal weight. Points arenotdeducted for incorrect answers, and no points are given to unanswered questions.

Unless otherwise indicated, the domain of a functionfis the set of all real numbers. If the exact numerical value

does not appear among the given choices, select the best approximate value. The use of a calculator ispermitted

in this part of the exam.

76. Given thatf(x)=

{

x^3 +x+a for x≤ 1

2 bx− 1 for x> 1 ,

iff is differentiable atx=1, what is the value

ofa+ 2 b?

(A) 2 (B) 3

(C) 4 (D) 5

77. Ifg′(x)=cos

(

πx^2 + 1

)

andg( 1 )=

1

2

, then

g( 2 )=

(A) − 0. 681 (B) − 0. 319

(C) 0.181 (D) 0.681

78. The point(−2, 5)is on the graph of a
    differential functionf, andf′(−2)=3. What
    is the estimate forf(− 1 .9), using local linear
    approximation forfatx=−2?
    (A) − 16. 7 (B) − 6. 7
    (C) − 4. 7 (D) 5.3


79. If a functionf has its derivativef′(x) given as
    f′(x)=− 3 e−xcosx+2 for− 2 <x<2, on
    what interval(s) isf increasing?
    (A) (− 1 .0407, 0.345)
    (B) (0, 0.345)
    (C) (−2, 0)
    (D) (−2,− 1 .407) and (0.345, 2)
    80. A particle moving in a straight line has a
    velocity ofv(t)= 2 −tcos( 2 t)feet per minute.
    What is the total distance in feet traveled by
    the particle when 0≤t≤3 minutes?
    (A) 0.096 (B) 0.121
    (C) 0.732 (D) 0.813
    81. How many points of inflection does the graph
    ofy= 5 e(
    − 2 x)
    sin

(

3 x

2

)

have on the intervals

(0, 2π)?

(A) 0 (B) 1

(C) 2 (D) 3

82. The table below shows selected values of a
    continuous function fon the closed interval
    [1,16].

x 1 6 11 16

f(x) 1.1 2.1 2.6 2.9

Using three left endpoint rectangles of equal

length (LRAM), what is the approximate value

of

∫ 16

1

f(x)dx?

(A) 16.5 (B) 29

(C) 33.5 (D) 38

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