Free Printable OPTIONAL EXTRA CREDIT- AP Calc Fall Final Review

1.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

2.

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

3.

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

a)

Position = 0

b)

Position = 1

c)

Position = 2

d)

Position = -1

4.

What is the derivative of sin(x)?

a)

-sin(x)

b)

-cos(x)

c)

cos(x)

d)

sin(x)

5.

What is the derivative of cos(x)?

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

6.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

7.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

8.

Given $f\left(x\right)=\frac{x^3}{1-x^2}$ , what is $f'\left(x\right)$ ?

a)

$\frac{x^2\left(3-5x^2\right)}{\left(1-x^2\right)^2}$

b)

$\frac{3x^2-x^4}{\left(1-x^2\right)}$

c)

$\frac{-3x^2+x^4}{\left(1-x^4\right)}$

d)

$\frac{x^2\left(3-x^2\right)}{\left(1-x^2\right)^2}$

9.

Find the slope of the line tangent to $f$ at $x=9$ given $f\left(x\right)=-x^2+5\sqrt{x}$

a)

$18+\frac{5}{6}$

b)

$-18+\frac{5}{6}$

c)

$-18-\frac{5}{6}$

d)

$18-\frac{5}{6}$

10.

$f$ be the function given by $f\left(x\right)=x^3.$ What are all values of $c$ that satisfy the conclusion of the Mean Value Theorem on the closed interval $\left[-1,2\right]$ ?

a)

$1$ only

b)

$\sqrt{3}$ only

c)

$-1$ and $1$

d)

$-\sqrt{3}$ and $\sqrt{3}$

11.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

12.

Select all statements that are TRUE.

a)

b)

c)

d)

e)

13.

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

a)

6 -x

b)

3x² +3y²

c)

−x²/y²

d)

0

14.

Find the limit as x approaches 1⁺

a)

1

b)

-1

c)

-3

d)

Infinity

e)

DNE

15.

Find the limit at infinity

a)

0

b)

infinity

c)

4/3

d)

-3/2

e)

DNE

16.

Find the limit of the function as x approaches 2.

a)

1

b)

-1

c)

5

d)

DNE

17.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

18.

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

a)

7

b)

0

c)

7x

d)

14

19.

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

a)

64 m/s/s

b)

60 m/s/s

c)

66 m/s/s

d)

70 m/s/s

20.

v (t) > 0 means

a)

the particle is moving to the right

b)

the particle is speeding up

c)

the particle has positive position

d)

the particle is at rest

21.

Which is true for the graph of velocity of an object?

a)

The object is speeding up for parts A, B, and C

b)

The object is speeding up in parts D and E

c)

The object is speeding up in parts A and D.

d)

The object is stopped or at rest in part B

22.

What is the total displacement of the object represented in this position/time graph?

a)

0 meters

b)

300 meters

c)

450 meters

d)

600 meters

23.

Differentiate means to:

a)

Find a differential equation

b)

Take the derivative

c)

Take the integral

d)

Write the equation of the tangent line

24.

Find the antiderivative means to :

a)

Take the integral

b)

Take the derivative

c)

Find the slope

d)

Use the fundamental theorem of calculus

25.

Find dy/dx

a)

A

b)

B

c)

C

d)

D

26.

If a function's FIRST derivative is negative at a certain point, what does that tell you?

a)

The function is increasing at that point

b)

The function is decreasing at that point

c)

The concavity of the function is up at that point

d)

The concavity of the function is down at that point

27.

If (a,b) is a local maximum, then what will be true about f''(a)?

a)

It's positive

b)

It's negative

c)

It's zero

d)

Cannot be determined

28.

The concavity of a function is described by its _______________.

a)

first derivative

b)

second derivative

c)

third derivative

d)

expression

29.

Evaluate the indefinite Integral

a)

-5/x⁵- 2/x³+ C

b)

-5/x³- 2/x⁴+ C

c)

5/x³- 2/x⁴+ C

d)

-5/x³- 2/x⁴

30.

a)

A

b)

B

c)

C

d)

D

31.

Given a continuous function on the interval [4,7]. Let's say that f(4) = 10 and f(7) = 20. Is there a value on the interval [4,7] where f(x) = 15?

a)

Yes - if the function is continuous, then there must be an x value on that interval that passes through 15 on its way from 10 to 20.

b)

No because there is no sign change on the interval [4,7].

c)

No because that would be just too good to be true.

d)

Yes - at x = 5.5.

32.

The Mean Value Theorem applies to f(x) = 3x - x² on the interval [2, 5]. Find the value of x where the slope of the tangent line is equal to the slope of the secant line

a)

2

b)

-4

c)

3.5

d)

-2

33.

Given the attached graph of the object's POSITION, identify intervals where the object is moving right.

a)

(0,1), (17,18)

b)

(7,9), (13,18)

c)

(6,8), (11,18)

d)

(4,7), (9,13)

34.

Determine the interval(s) where the object is moving to the left.

a)

(1,2)

b)

(0,1), (3, infinity)

c)

(1,3)

d)

(0,1), (2,3)

35.

Determine intervals where the object's acceleration is negative.

a)

(1,15)

b)

(8, infinity)

c)

(0,8)

d)

(0,1), (15, infinity)

OPTIONAL EXTRA CREDIT- AP Calc Fall Final Review

Total questions: 35

Worksheet time: 29mins

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