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

MA 3972-MA-Book April 11, 2018 12:11

22 STEP 2. Determine Your Test Readiness

19. The graphs off′,g′, p′, andq′are shown
    below. Which of the functionsf, g, p,orq
    have a point of inflection on (a,b)?

a 0 b

y

y

x

aa 00 bbxx

ab 0

y

y

x

Chapter 9

20. When the area of a square is increasing four
    times as fast as the diagonals, what is the
    length of a side of the square?


21. Ifg(x)=|x^2 − 4 x− 12 |, which of the
    following statements aboutgis/are true?

I. g has a relative maximum atx=2.

II. g is differentiable atx=6.

III. g has a point of inflection at

x=−2.

Chapter 10

22. Given the equationy=

√

x−1, what is an

equation of the normal line to the graph at

x=5?

23. What is the slope of the tangent to the curve
    y=cos(xy)atx=0?


24. The velocity function of a moving particle
    on thex-axis is given asv(t)=t^2 −t,t≥0.
    For what values oftis the particle’s speed
    decreasing?
    25. The velocity function of a moving particle is
    v(t)=
    t^3
    3

− 2 t^2 +5 for 0≤t≤ 6 .What is the

maximum acceleration of the particle on the

interval 0≤t≤6?

26. Write an equation of the normal line to the
    graph of f(x)=x^3 forx≥0 at the point
    where f′(x)=12.


27. At what value(s) ofxdo the graphs of
    f(x)=
    lnx
    x
    andy=−x^2 have perpendicular
    tangent lines?


28. Given a differentiable functionf with
    f

(

π

2

)

=3 and f′

(

π

2

)

=−1. Using a

tangent line to the graph atx=

π

2

, find an

approximate value off

(

π

2

+

π

180

)

.

Chapter 11

29. Evaluate

∫

1 −x^2

x^2

dx.

30. If f(x) is an antiderivative of
    ex
    ex+ 1
    and
    f(0)=ln (2), findf(ln 2).


31. Find the volume of the solid generated by
    revolving about thex-axis the region bounded
    by the graph ofy=sin 2xfor
    0 ≤x≤πand the liney=

1

2

.

Chapter 12

32. Evaluate

∫ 4

1

1

√

x

dx.

33. If

∫k

− 1

(2x−3)dx=6, findk.

34. Ifh(x)=

∫x

π/ 2

√

sintdt, findh′(π).