5 Steps to a 5 AP Calculus BC 2019

AP Calculus BC Practice Exam 1 377

x

f

y

0–1

9. The graph offis shown above and
   f is twice differentiable. Which of the
   following has the smallest value?
   I. f(−1)
   II. f′(−1)
   III. f′′(−1)
   (A) I (B) II
   (C) III (D) II and III


10. A particle moves in thexy-plane so that its
    velocity vector at timetis
    v(t)=

〈

2 − 3 t^2 ,πsin(πt)

〉

and the particle's

position vector at timet=2is

〈

4, 3

〉

. What is
the position vector of the particle whent=3?
(A)

〈

−25, 0

〉

(B)

〈

−21, 1

〉

(C)

〈

−10, 0

〉

(D)

〈

−13, 5

〉

11. If
    dy
    dx
    = 3 e^2 x, and atx=0,y=

5

2

, a solution to

the differential equation is

(A) 3 e^2 x−

1

2

(B) 3 e^2 x+

1

2

(C)

3

2

e^2 x+ 1

(D)

3

2

e^2 x+ 2

40

20

–20

0 5101520

–40

t

(seconds)

v(t)

v(t)

meters/sec.

12. The graph of the velocity function of a moving
    particle is shown above. What is the total
    displacement of the particle during
    0 ≤t≤20?
    (A) 20 m (B) 50 m
    (C) 100 m (D) 500 m


13. Ifh′(x)=k(x) andkis a continuous function
    for all real values ofx, then

∫ 1

− 1

k(5x)dxis

(A) h(5)−h(−5)

(B) 5 h(5)− 5 h(−5)

(C)

1

5

h(5)+

1

5

h(−5)

(D)

1

5

h(5)−

1

5

h(−5)

14. The position function of a moving particle is
    s(t)=
    t^3
    6

−

t^2

2

+t−3 for 0≤t≤4. What is

the maximum velocity of the particle on

the interval 0≤t≤4?

(A)

1

2

(B) 1 (C)

14

16

(D) 5

15. Which of the following is an equation of the
    line tangent to the curve with parametric
    equationsx= 3 t^2 −2,y= 2 t^3 +2 at the point
    whent=1?
    (A) y= 3 x^2 + 7 x
    (B) y= 6 x− 2
    (C) y=x
    (D) y=x+ 3

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