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

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

350 STEP 5. Build Your Test-Taking Confidence

6.

∫

x(3x^2 −^4 )dx=

(A)

3 x^2 −^4

2ln3

+c (B)

ln 3(3x^2 −^4 )

2

+c

(C)

3 x^2 −^3

2

+c (D) 3x^2 −^3 +c

y

x

D

C

B

A

7. In the figure above, which of the four given
   points on the graph is
   dy
   dx

   
   

   0 and
   d^2 y
   dx^2

   
   

   
   

<0?

(A) A (B) B

(C) C (D) D

x h(x) k(x) h′(x) k′(x)

4 6 4 1 3

8 12 8 2 5

8. The table above shows the values of the
   functionshandkand their derivatives atx= 4
   andx=8. What is the value of
   d
   dx
   h(k(x))

∣∣

∣∣

x= 4

?

(A) 3 (B) 4

(C) 12 (D) 24

9. Iff(x)=

∫ 1

x^2

1

2 +t^2

dt, thenf′(2)=

(A) −

2

9

(B)

1

18

(C)

1

6

(D)

2

9

• 4 – 20 2 4

y

x

10. The figure above shows the graph of a
    continuous function ffor− 4 ≤x≤4. On
    what intervals isf′(x)>0 for all values ofx?
    (A) (−4, 2) only
    (B) (−4,−2) and (0, 2)
    (C) (−2, 0) only
    (D) (0, 4)


11. Ifs(t)=
    t^3
    3
    − 2 t^2 + 3 t+4 fort≥0 is the
    position of a moving particle on a straight line,
    at which of the following intervals oftis the
    speed of the particle decreasing?
    (A) (1, 2) only
    (B) (3,∞) only
    (C) (0, 1) and (2, 3)
    (D) (1, 2) and (3,∞)

12.xlim→−∞

√

4 x^2 + 3

2 x− 1

is

(A) − 2 (B) − 1

(C) 1 (D) nonexistent

13.

∫ 1

− 1

2

1 +x^2

dx=

(A) −π (B) 0

(C)

π

2

(D) π

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