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

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

356 STEP 5. Build Your Test-Taking Confidence

Section II Part A

Number of Questions Time Use of Calculator

2 30 Minutes Yes

Directions:

Show all your 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 three places after the decimal point; and (c) the domain of a
functionf is the set of all real numbers.

0

y

x

1. As shown in the figure above,Sis the region
   enclosed by the graphs ofy= 2 x^4 − 5 x^3 and
   y= 4 x−x^2.
   (A) Find the area of the regionS.
   (B) Find the volume of the solid generated
   when the regionSis revolved about the
   liney=4.
   (C) If regionS is the base of a solid, the
   height of the solid for all points inSat
   a distancexfrom they-axis is given as
   h(x)= 0. 5 + 2 x.Find the volume of the
   solid.
   2. A particle is moving along thex-axis. For
   0 ≤t≤10, the acceleration of the particle is
   given bya(t)=
   sin(ln(x+ 1 ))
   x+ 1
   .Att=0, the

velocity of the particle isv(0)=− 1 .1.

(A) Find the velocity of the particle att=4.

(B) For 0≤t ≤10, at what time interval is

the speed of the particle increasing?

(C) For 0≤t≤10, what is the average

velocity of the particle?

(D) For 0≤t≤10, find the total distance

traveled by the particle.

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