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

MA 3972-MA-Book April 11, 2018 16:20

AP Calculus AB Practice Exam 2 385

Section II Part A

Number of Questions Time Use of Calculator

2 30 Minutes Yes

Directions:

Show all work.You maynotreceive any credit for correct answers without supporting work. You may use an

approved calculator to help solve a problem. However, you must clearly indicate the setup of your solution using

mathematical notations andnotcalculator syntax. Calculators may be used to find the derivative of a function

at a point, compute the numerical value of a definite integral, or solve an equation. Unless otherwise indicated,

you may assume the following: (a) the numeric or algebraic answers need not be simplified; (b) your answer,

if expressed in approximation, should be correct to 3 places after the decimal point; and (c) the domain of a

functionf is the set of all real numbers.

1. LetRbe the region in the first quadrant
   enclosed by the graph ofy=2 cosx, thex-axis,
   and they-axis.

(A) Find the area of the regionR.

(B) If the linex=adivides the regionRinto

two regions of equal area, finda.

(C) Find the volume of the solid obtained by

revolving regionRabout thex-axis.

(D) IfRis the base of a solid whose cross

sections perpendicular to thex-axis are

semicircles, find the volume of the solid.

2. The temperature of a liquid at a chemical plant
   during a 20-minute period is given as
   g(t)= 90 −4 tan

(

t

20

)

, whereg(t) is measured

in degrees Fahrenheit, 0≤t≤20 andtis

measured in minutes.

(A) Sketch the graph ofgon the provided grid.

What is the temperature of the liquid to the

nearest hundredth of a degree Fahrenheit

whent=10? (See below.)

90

88

86

84

82

80

0 5 10 15 20

t(minutes)

degrees (Fahrenheit)

(B) What is the instantaneous rate of change of

the temperature of the liquid to the nearest

hundredth of a degree Fahrenheit att=10?

(C) At what values oftis the temperature of the

liquid below 86◦F?

(D) During the time within the 20-minute

period when the temperature is below

86 ◦F, what is the average temperature

to the nearest hundredth of a degree

Fahrenheit?

STOP. AP Calculus AB Practice Exam 2, Section II Part A.