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 1 357

Section II Part B

Number of Questions Time Use of Calculator

4 60 Minutes No

Directions:

The use of a calculator isnotpermitted in this part of the exam. 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 function f is the set of all real numbers. 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 may not use a calculator.

3. Given the differential equation
   dy
   dx
   − 2 x=xy.

• 10

1

2

1

y

x

(A) On the axes provided in the figure above,

sketch a slope field at the six indicated

points.

(B) Lety=f(x) be the particular solution to

the differential equation with the initial

conditionf(0)= 1 .Write an equation of

the tangent line to the solution curve at

the point (0, 1).

(C) Using the equation of the tangent line in

part (b), find the approximate value of

f(0.02).

(D) Findy= f(x) with f(0)=1.

4. Let fbe a continuous function on the interval
   [−2, 6], andf is twice differentiable with
   f′′(x)<0 on the open interval (−2, 6).
   Selected values off are shown below.

x − 2 − 1 0 2 6

f(x) 1 4 6 7 8

(A) Using trapezoidal approximation with

four trapezoids, find the approximate

value of

∫ 6

− 2

f(x)dx.

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

age value offon [−2, 6].

(C) Find the average rate of change offover

the interval [−2, 6].

(D) Examinef′(0) andf′(2), and determine

iff′(0) is greater than, less than, or equal

tof′(2). Explain.

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