Free Printable AP Calc HW #84 (after 6.2)

1.

If the position of a particle is represented by s(t) = -t² + 1, what is its instantaneous velocity at t = 1?

a)

Velocity = 0

b)

Velocity = 1

c)

Velocity = -1

d)

Velocity = -2

2.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

3.

The position function x(t)=7t²-18t-7 is given. What is the velocity function?

a)

v(t)=14t-18

b)

v(t)=14t+18

c)

v(t)=18t-14

d)

v(t)=18t+14

4.

Given x(t)=t³-4t²+7, what is the initial position?

a)

11

b)

-10

c)

7

d)

0

5.

A particle's speed is decreasing if

a)

it's acceleration is positive

b)

it's velocity is positive

c)

it's velocity and acceleration have the same sign

d)

it's velocity and acceleration have different signs

6.

v(t)>0 means

a)

the particle is moving to the right

b)

the particle is moving to the left

c)

the particle has positive position

d)

the particle is at rest

7.

Which of the following can be used to determine when a particle is at rest?

a)

x(t)=0

b)

v(t)=0

c)

a(t)=0

8.

s(t) = t² - 20
Find the average velocity from t = 3 to t = 5.

a)

2

b)

4

c)

6

d)

8

9.

What is the total distance of the object represented in this motion graph?

a)

0 meters

b)

300 meters

c)

450 meters

d)

600 meters

10.

What is the total displacement of the object represented in this motion graph?

a)

0 meters

b)

300 meters

c)

450 meters

d)

600 meters

11.

A particle moves along an axis so that at any time t>0, its velocity is given by v(t)=4-6t². If the particle is at position p=7 at t=1, what is the position of the particle at t=2?

a)

-10

b)

-5

c)

-3

d)

3

12.

The function f is continuous on the closed interval [0,6] and has values given in the table above. The trapezoidal approximation found with 3 subintervals is 52. What is the value of k?

a)

2

b)

6

c)

7

d)

10

13.

a)

b)

c)

d)

14.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

15.

The image displays the ______

a)

Limit definition of the first derivative

b)

The bane of my existance

16.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

17.

If f'(x) = 0 what does that imply about the x value?

a)

It is a critical point, it is a possible max, min, or point of inflection.

b)

That the limit does not exist.

18.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

19.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

20.

a)

Intermediate Value Theorem

b)

Rolle's Theorem

c)

Average Rate of Change

d)

Average Value of f

21.

a)

Average Rate of Change

b)

Average Value of f

c)

Intermediate Value Theorem

d)

Rolle's Theorem

22.

a)

speed

b)

acceleration

c)

displacement

d)

total distance

23.

a)

A

b)

B

c)

C

d)

E

24.

a)

position

b)

acceleration

c)

total distance

d)

speed

25.

a)

position

b)

velocity

c)

acceleration

d)

total distance

26.

a)

position

b)

velocity

c)

acceleration

d)

total distance

27.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

28.

What is this expression equivalent to?

a)

f '(g'(x))

b)

f '(x)g'(x)

c)

f '(g(x))g'(x)

d)

f '(g(x)

29.

What is the slope of the line normal to the curve y = x² + x at x = 1?

a)

-1

b)

-1/2

c)

-1/3

d)

-1/4

30.

If f has an absolute minimum value at c, then $f'\left(x\right)=0$

a)

True

b)

False

31.

The gradient of the normal line to the function $f\left(x\right)=e^x-1$ at x =2 is

a)

$e^2$

b)

$-e^2$

c)

$\frac{1}{e^2}$

d)

$\frac{-1}{e^2}$

32.

a)

-ln |cosx| + C

b)

ln |cosx| + C

c)

ln |sinx| + C

d)

-ln |sinx| + C

33.

a)

(x¹¹⁄ 11) - 1

b)

(x¹⁰) - 1

c)

x¹⁰

d)

t¹¹ ∕ 11

34.

Differentiate $y=e^{7x}$ .

a)

$\frac{\text{d}y}{\text{d}x}=e^{7x}$

b)

$\frac{dy}{\text{d}x}=7e^x$

c)

$\frac{\text{d}y}{\text{d}x}=\frac{1}{7}e^x$

d)

$\frac{\text{d}y}{\text{d}x}=7e^{7x}$

35.

Determine the initial acceleration of a particle whose position is given by $s\left(t\right)=-e^{5t}+\sin t$ , where $s$ is the distance traveled in metres, $t$ seconds after it starts moving.

a)

$-e^5\ \frac{m}{s^2}$

b)

$-25\ \frac{m}{s^2}$

c)

$-5e^5+1\ \frac{m}{s^2}$

d)

$0\ \frac{m}{s^2}$

36.

Differentiate $y=\sqrt{e^x-\cos^2x+\tan5x}$

a)

$\frac{\text{d}y}{\text{d}x}=\frac{e^x+2\cos x\sin x+5\sec^2\left(5x\right)}{2\sqrt{e^x-\cos^2x+\tan5x}}$

b)

$\frac{\text{d}y}{\text{d}x}=\frac{1}{2}e^{\frac{x}{2}}+\sin x+\frac{5}{2}\sec^2\left(5x\right)$

c)

$\frac{\text{d}y}{\text{d}x}=\frac{1}{2\sqrt{e^x}}+\sin x+\frac{5}{2}\tan\left(5x\right)\sec^2\left(5x\right)$

d)

$\frac{\text{d}y}{\text{d}x}=\frac{\left(e^x+2\cos x\sin x+5\sec^2\left(5x\right)\right)^{-\frac{1}{2}}}{2}$

37.

$\int_{ }^{ }\left[5^x-\csc^2x\right]dx$

a)

$5^x-\cot x+C$

b)

$5^x+\cot x+C$

c)

$\frac{5^x}{\ln5}+\cot x+C$

d)

$\frac{5^x}{\ln x}-\cot x+C$

38.

What are the conditions that satisfy the mean value theorem, and what does it mean?

a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

b)

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

c)

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

d)

Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

39.

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x²+6x+3, is the speed of the particle increasing at x=4?

a)

No because both velocity and acceleration at x=4 is positive

b)

Yes because both velocity and acceleration at x=4 is positive

c)

No because both velocity and acceleration at x=4 is negative

d)

Yes because both velocity and acceleration at x=5 is positive

40.

The second derivative of a function f is given by f"(x)=sin(3x)-cos(x²). How many points of inflection does the graph of f have on the interval 0 < x < 3?

a)

One

b)

Three

c)

Four

d)

Five

AP Calc HW #84 (after 6.2)

Total questions: 40

Worksheet time: 1hrs 21mins

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