Question 1

Use the appropriate addition formula to find the exact value of the expression.
-$\sin \left( - \frac { 11 \pi } { 12 } \right)$

Accepted Answer

A)  $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$ 
B)  $- \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
C)  $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$ 
D)  $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
A)  $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$ 
B)  $- \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
C)  $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$ 
D)  $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$

Question 2

Consider the function y Can x be 0?
-For what values of $x$ is $\lfloor x \rfloor = 1$ ?

Accepted Answer

A)  $1 < x \leq 2$ 
B)  $1 \leq \mathrm { x } < 2$ 
C)  $0 \leq \mathrm { x } < 1$ 
D)  $0 < x \leq 1$ 
A)  $1 < x \leq 2$ 
B)  $1 \leq \mathrm { x } < 2$ 
C)  $0 \leq \mathrm { x } < 1$ 
D)  $0 < x \leq 1$

Question 3

Solve for the angle , where 0 2
-$\sin 2 \theta - \cos \theta = 0$

Accepted Answer

A)  $\frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
B)  $0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } , 2 \pi$ 
C)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
D)  $\theta = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$ 
A)  $\frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
B)  $0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } , 2 \pi$ 
C)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
D)  $\theta = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$

Question 4

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
-$y = \frac { 1 } { x ^ { 3 } }$

Accepted Answer

A)  Increasing $- \infty < x < \infty$
  
B)  Increasing $- \infty < x < 0$ and $0 < x < \infty$
  
C)  Decreasing $- \infty < x < 0$;
Increasing $0 < x < \infty$
  
D)  Decreasing $- \infty < x < 0$ and $0 < x < \infty$
  
A)  Increasing $- \infty < x < \infty$
  
B)  Increasing $- \infty < x < 0$ and $0 < x < \infty$
  
C)  Decreasing $- \infty < x < 0$;
Increasing $0 < x < \infty$
  
D)  Decreasing $- \infty < x < 0$ and $0 < x < \infty$

Question 5

Graph the function.
-$f(x)=4^{x}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Is the function graphed below one-to-one?
-

Accepted Answer

A) True 
 B)False

Question 7

Solve the problem.
-A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents time in years and y represents the amount of the isotope left then the equation for the situation is $$\mathrm { y } = \mathrm { y } 0 \mathrm { e } ^ { - 0.0002 \mathrm { t } }$$ In how many years will
There be 94% of the isotope left?

Accepted Answer

A)  300 yr 
B)  256 yr 
C)  600 yr 
D)  309 yr 
A)  300 yr 
B)  256 yr 
C)  600 yr 
D)  309 yr

Question 8

Find the formula for the function.
-Express the perimeter of a square as a function of the square's side length x.

Accepted Answer

A)  p = 4x 
B)   $p=\frac{3 x}{2}$ 
C)  $p=x^{3}$ 
D)  p = 6x 
A)  p = 4x 
B)   $p=\frac{3 x}{2}$ 
C)  $p=x^{3}$ 
D)  p = 6x

Question 9

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$$f ( x ) = 3 \cos 50 x$$

Accepted Answer

A)  $[ - 0.2,0.2 ]$ by $[ - 1,1 ]$ 
B)  $[ - 10,10 ]$ by $[ - 10,10 ]$ 
C)  $[ - 1,1 ]$ by $[ - 4,4 ]$ 
D)  $[ - 0.2,0.2 ]$ by $[ - 4,4 ]$ 
A)  $[ - 0.2,0.2 ]$ by $[ - 1,1 ]$ 
B)  $[ - 10,10 ]$ by $[ - 10,10 ]$ 
C)  $[ - 1,1 ]$ by $[ - 4,4 ]$ 
D)  $[ - 0.2,0.2 ]$ by $[ - 4,4 ]$

Question 10

Solve the problem.
-$$\text { If } f ( x ) = - 9 x - 3 \text { and } g ( x ) = 9 x ^ { 2 } - 8 x - 6 \text {, find } g ( f ( - 3 ) )$$

Accepted Answer

A)  -894 
B)  4986 
C)  18 
D)  78 
A)  -894 
B)  4986 
C)  18 
D)  78

Question 11

Solve the problem.
-$$\text { If } f ( x ) = - 4 x - 4 \text { and } g ( x ) = 2 x ^ { 2 } + 9 x - 3 \text {, find } g ( f ( 4 ) )$$

Accepted Answer

A)  -264 
B)  -223 
C)  -168 
D)  617 
A)  -264 
B)  -223 
C)  -168 
D)  617

Question 12

State the period of the function and graph.
-$\sin \left(x-\frac{\pi}{2}\right)$

Accepted Answer

A)  Period $2 \pi$
  
B) $\text { Period } 2 \pi$
  
C)  Period $2 \pi$
  
D)  Period $2 \pi$
  
A)  Period $2 \pi$
  
B) $\text { Period } 2 \pi$
  
C)  Period $2 \pi$
  
D)  Period $2 \pi$

Question 13

Use the laws of exponents to simplify. Do not use negative exponents in your answer.
-$$4 ^ { 4 } \cdot 4 ^ { 3 }$$

Accepted Answer

A)  $4 ^ { 7 }$ 
B)  $8 ^ { 7 }$ 
C)  $4 ^ { 12 }$ 
D)  $16 ^ { 12 }$ 
A)  $4 ^ { 7 }$ 
B)  $8 ^ { 7 }$ 
C)  $4 ^ { 12 }$ 
D)  $16 ^ { 12 }$

Use the appropriate addition formula to find the exact value of the expression. - $\sin \left( - \frac { 11 \pi } { 12 } \right)$

Consider the function y Can x be 0? -For what values of $x$ is $\lfloor x \rfloor = 1$ ?

Solve for the angle , where 0 2 - $\sin 2 \theta - \cos \theta = 0$

Graph the function. - $f(x)=4^{x}$ $Graph the function. - f(x)=4^{x}$

Is the function graphed below one-to-one? -

Find the formula for the function. -Express the perimeter of a square as a function of the square's side length x.

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - $f ( x ) = 3 \cos 50 x$

Solve the problem. - $\text { If } f ( x ) = - 9 x - 3 \text { and } g ( x ) = 9 x ^ { 2 } - 8 x - 6 \text {, find } g ( f ( - 3 ) )$

Solve the problem. - $\text { If } f ( x ) = - 4 x - 4 \text { and } g ( x ) = 2 x ^ { 2 } + 9 x - 3 \text {, find } g ( f ( 4 ) )$

State the period of the function and graph. - $\sin \left(x-\frac{\pi}{2}\right)$ $State the period of the function and graph. - \sin \left(x-\frac{\pi}{2}\right)$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $4 ^ { 4 } \cdot 4 ^ { 3 }$

Limits and Continuity

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Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

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Exam 2: Functions

Use the appropriate addition formula to find the exact value of the expression. - sin⁡(−11π12)\sin \left( - \frac { 11 \pi } { 12 } \right)sin(−1211π​)

Consider the function y Can x be 0? -For what values of xxx is ⌊x⌋=1\lfloor x \rfloor = 1⌊x⌋=1 ?

Solve for the angle , where 0 2 - sin⁡2θ−cos⁡θ=0\sin 2 \theta - \cos \theta = 0sin2θ−cosθ=0

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=1x3y = \frac { 1 } { x ^ { 3 } }y=x31​

Graph the function. - f(x)=4xf(x)=4^{x}f(x)=4x