AP Calculus AB ’19-20 Name Anti-Derivative Practice Test Score 1. Which of the following statements are true? I. II.

III.

a) I only b) II only c) III only d) I and II e) II and III only 2. (A) (B) (C) (D) (E)

x5 sin x6( )⌠

⌡⎮ dx = − 1

6 cos x6 + c tan x dx∫ = sec2 x+ c

x3 + x( ) x4 + 2x2 − 54( )⌠

⌡⎮⎮ dx = 1

5 x4 + 2x2 − 5( )5 4 + c

sin2 x dx =∫

12 1+ cos2x( ) + c

12 x + sin2x( ) + c

12 1− cos2x( ) + c

12 x + 1

2 sin2x( ) + c 12 x − 1

2 sin2x( ) + c

3. Which of the following differential equations corresponds to this slope field?

(A) (B) (C)

(D) (E)

4. Which of the following equations might be the solution to the slope field shown in the figure below?

(A) (B) (C) (D) (E)

dydx

= x

dydx

= xy

dydx

= y − x

dydx

= x + y

dydx

= x − y

y = −x y = −x2 y = ex

y = x3 y = x

5. The solution curve to the differential equation through the point

is: (A) (B) (C)

(D) (E)

6. =

a) b) c)

d) e.)

dydx

= y

−2,−1( )

y = −ex+2 y = ex+2

y = −ex + e−2

y = −1

x +1 y = − −1

x +1

5x4 dx∫

4 5x4 +C

4ln5

5x4 +C

5x4

ln5+C

5x4 +C

5x4

4ln5+C

7. a)

b)

c)

d)

e)

8. Identify the first mistake (if any) in this process:

Step 1:

Step 2:

Step 3: Step 4: a) Step 1 b) Step 2 c) Step 3 d) Step 4 e) No Mistake

csc 5θ( )dθ =∫

−csc 5θ( )cot 5θ( ) + c

1

10csc2 5θ( ) + c

ln csc 5θ( )− cot 5θ( ) + c

− 1

5csc 5θ( )cot 5θ( ) + c

15

ln csc 5θ( )− cot 5θ( ) + c

dydx

= 2xcos2 y

sec2 y( )dy = 2xdx

sec2 y( )∫ dy = 2x dx∫ tan2 y = x2 + c

y = tan−2 x2 + c( )

9.

(A) (B) (C)

(D) (E)

10.

11.

ln 3x( )x

dx =⌠⌡⎮

ln2 3x( )2

+ c

ln2 3x( )x2 + c

ln2 3x( )6

+ c

3ln2 3x( )2

+ c

1− ln 3x( )x2 + c

5x3 − 2x− 6x+ x76 + 1

x9

⎛

⎝⎜

⎞

⎠⎟

⌠

⌡

⎮⎮⎮

dx

4y2dyy3 +5

⌠

⌡⎮⎮

12. A particle’s acceleration is given by meters per second squared. At time , the particle’s velocity is 4 meters per second and its position is 0 meters. Find the particle’s position at time .

13.

a(t) = 3t2 +1 t = 1

t = 2

1(1− x)2

+ x1+ x2

+ 11+ x2

⎛⎝⎜

⎞⎠⎟

⌠

⌡⎮ dx

14. Given the differential equation,

a. On the axis system provided, sketch the slope field for the at all points

plotted on the graph.

b. If the solution curve passes through the point (0, 1), sketch the solution curve on the same set of axes as your slope field.

dydx

=x y −1( )

y

dydx

15. Find the particular solution that passes through if

w = f t( ) 0, 34⎛

⎝⎜

⎞

⎠⎟

dwdt

= t3 1− 4w2