5 Steps to a 5 AP Calculus BC 2019

AP Calculus BC Practice Exam 2 411

Section I---Part B

Number of Questions Time Use of Calculator

15 45 Minutes Yes

Directions:

Use the same answer sheet for Part A.Please note that the questions begin with number 76.This is not an error. It

is done to be consistent with the numbering system of the actual AP Calculus BC 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. Find the values ofaandbthat assure that

f(x)=

{

ln(3−x)ifx< 2

a−bx ifx≥ 2

is differentiable atx=2.

(A) a=3,b= 1

(B) a=1,b= 2

(C) a=2,b= 1

(D) a=−2,b=− 1

77. The table shows some of the values of
    differentiable functionsfandgand their
    derivatives. Ifh(x)=f(g(x)), thenh′(2) equals

x f(x) g(x) f′(x) g′(x)

1 0 − 1 − 2 5

2 4 3 5 1

3 2 3 − 1 0

(A) − 2

(B) − 1

(C) 0

(D) 1

78. Linelis tangent to the graph of a functionf at
    the point (0, 1). Iffis twice differentiable
    withf′( 0 )=2 and f′′( 0 )=3, what is the
    approximate value off( 0. 1 )using linel?
    (A) 0.1
    (B) 0.2
    (C) 1.2
    (D) 2.1
    79. Let f(x) be a differentiable function on the
    closed interval [1, 3]. The average value of
    f′(x) on [1, 3] is
    (A) 2(f′(3)− f′(1))
    (B)

1

2

(f′(3)−f′(1))

(C) f(3)−f(1)

(D)

1

2

(f(3)− f(1))

80. The position of a particle moving in the
    xy-plane at any timetis given as
    x(t)=2 cos( 4 t)andy(t)=

1

2

t^2. What is the

speed of the particle att=1?

(A) .807

(B) 2.656

(C) 6.136

(D) 7.054

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