5 Steps to a 5 AP Calculus BC 2019

386 STEP 5. Build Your Test-Taking Confidence

Section II---Part B

Number of Questions Time Use of Calculator

4 60 Minutes No

Directions:

The use of a calculator is not permitted in this part of the exam. When you have finished this part of the exam,
you may return to the problems in Part A of Section II and continue to work on them. However, you maynot
use a calculator. You shouldshow all work. You maynotreceive any credit for correct answers without supporting
work. Unless otherwise indicated, the numeric or algebraic answers need not be simplified, and the domain of a
functionf is the set of all real numbers.

3. A particle is moving on a straight line. The
   velocity of the particle for 0≤t≤30 is shown
   in the table below for selected values oft.

t(sec) 0 3 6 9 12 15 18 21 24 27 30

v(t) (m/sec) 0 7.510.1 12 13 13.5 14.1 14 13.9 13 12

(A) Using MRAM (Midpoint Rectangular

Approximation Method) with five

rectangles, find the approximate value of∫

30

0

v(t)dt.

(B) Using the result in part (A), find the

average velocity over the interval

0 ≤t≤30.

(C) Find the average acceleration over the

interval 0≤t≤30.

(D) Find the approximate acceleration att=6.

(E) During what intervals of time is the

acceleration negative?

4. LetRbe the region enclosed by the graph of
   y=x^3 , thex-axis, and the linex=2.
   (A) Find the area of regionR.
   (B) Find the volume of the solid obtained by
   revolving regionRabout thex-axis.
   (C) The linex=adivides regionRinto two
   regions such that when the regions are
   revolved about thex-axis, the resulting
   solids have equal volume. Finda.

(D) If regionRis the base of a solid whose

cross sections perpendicular to thex-axis

are squares, find the volume of the solid.

5. Let fbe a function that has derivatives of all
   orders for all real numbers. Assumef(0)=1,
   f′(0)=6,f′′(0)=−4, and f′′′(0)=30.
   (A) Write the third-degree Taylor polynomial
   forfaboutx=0 and use it to
   approximate f(0.1).
   (B) Write the sixth-degree Taylor polynomial
   forg, whereg(x)=f

(

x^2

)

, aboutx=0.

(C) Write the seventh-degree Taylor

polynomial forh, whereh(x)=

∫x

0

g(t)dt,

about

x=0.

6. Given the parametric equationsx=2(θ−sinθ)
   andy=2(1−cosθ),

(A) find

dy

dx

in terms ofθ.

(B) find an equation of the line tangent to the

graph atθ=π.

(C) find an equation of the line tangent to the

graph atθ= 2 π.

(D) set up but do not evaluate an integral

representing the length of the curve over

the interval 0≤θ≤ 2 π.

STOP. AP Calculus BC Practice Exam 1 Section II Part B