Question 1

$\text { Evaluate the expression } \arcsin \left( \frac { 1 } { 2 } \right) \text { without using a calculator. }$

Accepted Answer

A)  0 
B)  $\frac { 3 \pi } { 2 }$ 
C)  $\frac { 7 \pi } { 2 }$ 
D)  $\frac { \pi } { 6 }$ 
E)  $\frac { 4 \pi } { 5 }$ 
A)  0 
B)  $\frac { 3 \pi } { 2 }$ 
C)  $\frac { 7 \pi } { 2 }$ 
D)  $\frac { \pi } { 6 }$ 
E)  $\frac { 4 \pi } { 5 }$ D

Question 2

$\text { Solve the following equation for } x \text {. }$ $\arccos ( 10 x - \pi ) = \frac { 1 } { 2 }$

Accepted Answer

A)  $x = \frac { \sin \left( \pi + \frac { 1 } { 2 } \right) } { 10 }$ 
B)  $x = \frac { \pi + \sec \left( \frac { 1 } { 2 } \right) } { 10 }$ 
C)  $x = \frac { \sec \left( \pi + \frac { 1 } { 2 } \right) } { 10 }$ 
D)  $x = \frac { \cos \left( \pi + \frac { 1 } { 2 } \right) } { 10 }$ 
E)  $x = \frac { \pi + \cos \left( \frac { 1 } { 2 } \right) } { 10 }$ 
A)  $x = \frac { \sin \left( \pi + \frac { 1 } { 2 } \right) } { 10 }$ 
B)  $x = \frac { \pi + \sec \left( \frac { 1 } { 2 } \right) } { 10 }$ 
C)  $x = \frac { \sec \left( \pi + \frac { 1 } { 2 } \right) } { 10 }$ 
D)  $x = \frac { \cos \left( \pi + \frac { 1 } { 2 } \right) } { 10 }$ 
E)  $x = \frac { \pi + \cos \left( \frac { 1 } { 2 } \right) } { 10 }$ E

Question 3

horsepower H required to overcome wind drag on a certain automobile is approximated by $H ( x ) = 0.002 x ^ { 2 } + 0.005 x - 0.027,10 \leq x \leq 100$ where $x$ is the speed of the car in miles per hour. Find $H \left( \frac { x } { 1.1 } \right)$. Round the numerical values in your answer to five decimal places.

Accepted Answer

A)  $H \left( \frac { x } { 1.1 } \right) = 0.00150 x ^ { 2 } + 0.00455 x - 0.02700$ 
B)  $H \left( \frac { x } { 1.1 } \right) = 0.00150 x ^ { 2 } + 0.00165 x - 0.00455$ 
C)  $H \left( \frac { x } { 1.1 } \right) = 0.00165 x ^ { 2 } + 0.00150 x - 0.02700$ 
D)  $H \left( \frac { x } { 1.1 } \right) = 0.00165 x ^ { 2 } + 0.00455 x - 0.02700$ 
E)  $H \left( \frac { x } { 1.1 } \right) = 0.00455 x ^ { 2 } + 0.00165 x - 0.02700$ 
A)  $H \left( \frac { x } { 1.1 } \right) = 0.00150 x ^ { 2 } + 0.00455 x - 0.02700$ 
B)  $H \left( \frac { x } { 1.1 } \right) = 0.00150 x ^ { 2 } + 0.00165 x - 0.00455$ 
C)  $H \left( \frac { x } { 1.1 } \right) = 0.00165 x ^ { 2 } + 0.00150 x - 0.02700$ 
D)  $H \left( \frac { x } { 1.1 } \right) = 0.00165 x ^ { 2 } + 0.00455 x - 0.02700$ 
E)  $H \left( \frac { x } { 1.1 } \right) = 0.00455 x ^ { 2 } + 0.00165 x - 0.02700$ D

Question 4

$\text { Find an equation of the line that passes through the point } ( - 11 , - 9 ) \text { and has the slope }$ $m = \frac { 9 } { 2 } .$

Accepted Answer

A)  $y = \frac { 9 } { 2 } x - \frac { 81 } { 2 }$ 
B)  $y = \frac { 9 } { 2 } x + \frac { 81 } { 2 }$ 
C)  $y = \frac { 9 } { 2 } x + 162$ 
D)  $y = \frac { 9 } { 2 } x$ 
E)  $y = - \frac { 9 } { 2 } x$ 
A)  $y = \frac { 9 } { 2 } x - \frac { 81 } { 2 }$ 
B)  $y = \frac { 9 } { 2 } x + \frac { 81 } { 2 }$ 
C)  $y = \frac { 9 } { 2 } x + 162$ 
D)  $y = \frac { 9 } { 2 } x$ 
E)  $y = - \frac { 9 } { 2 } x$

Question 5

Estimate the slope of the line from the graph.

Accepted Answer

A)  $- \frac { 1 } { 5 }$ 
B)  5 
C)  2 
D)  $- \frac { 1 } { 2 }$ 
E)  $\frac { 1 } { 5 }$ 
A)  $- \frac { 1 } { 5 }$ 
B)  5 
C)  2 
D)  $- \frac { 1 } { 2 }$ 
E)  $\frac { 1 } { 5 }$

Question 6

$\text { If a line has slope } m = - 4 \text { and passes through the point } ( 4,8 ) \text {, through which of the }$ following points does the line also pass?

Accepted Answer

A)  $( 1,20 )$ 
B)  $( 1,12 )$ 
C)  $( 1,0 )$ 
D)  $( 8 , - 16 )$ 
E)  $( 8 , - 24 )$ 
A)  $( 1,20 )$ 
B)  $( 1,12 )$ 
C)  $( 1,0 )$ 
D)  $( 8 , - 16 )$ 
E)  $( 8 , - 24 )$

Question 7

Determine which type of function would be most appropriate to fit the given data.

Accepted Answer

A)  exponential 
B)  linear 
C)  quadratic 
D)  no relationship 
E)  trigonometric 
A)  exponential 
B)  linear 
C)  quadratic 
D)  no relationship 
E)  trigonometric

Question 8

The following ordered pairs represent temperatures in degrees Fahrenheit taken each hour from $1 : 00 \mathrm { pm }$ until 5:00 pm. Let $T$ be temperature, and let $t$ be time, where $t = 1$ corresponds to $1 : 00 \mathrm { pm } , t = 2$ corresponds to $2 : 00 \mathrm { pm }$, and so on. Plot the data. Visually find a linear model for the data and find its equation. From the visual linear model that you created, determine which of the models that follow appears to best approximate the data.
$$\left( 1 : 00 \mathrm { pm } , 67.4 ^ { \circ } \right) , \left( 2 : 00 \mathrm { pm } , 71.6 ^ { \circ } \right) , \left( 3 : 00 \mathrm { pm } , 73.4 ^ { \circ } \right) , \left( 4 : 00 \mathrm { pm } , 77.6 ^ { \circ } \right) , \left( 5 : 00 \mathrm { pm } , 79.4 ^ { \circ } \right)$$

Accepted Answer

A)  $T = 2 t + 60$ 
B)  $T = - 2 t + 70$ 
C)  $T = - 4 t + 60$ 
D)  $T = 4 t + 70$ 
E)  $T = 3 t + 65$ 
A)  $T = 2 t + 60$ 
B)  $T = - 2 t + 70$ 
C)  $T = - 4 t + 60$ 
D)  $T = 4 t + 70$ 
E)  $T = 3 t + 65$

Question 9

Write the following expression in algebraic form. $\tan \left( \operatorname { arcsec } \left( \frac { x } { 8 } \right) \right)$

Accepted Answer

A)  $x ^ { 2 } - 64$ 
B)  $\frac { \sqrt { x ^ { 2 } - 64 } } { 8 }$ 
C)  $1 + 64 x ^ { 2 }$ 
D)  $\sqrt { x ^ { 2 } - 8 }$ 
E)  $1 + 8 x ^ { 2 }$ 
A)  $x ^ { 2 } - 64$ 
B)  $\frac { \sqrt { x ^ { 2 } - 64 } } { 8 }$ 
C)  $1 + 64 x ^ { 2 }$ 
D)  $\sqrt { x ^ { 2 } - 8 }$ 
E)  $1 + 8 x ^ { 2 }$

Question 10

Match the graph of the function given below with the graph of its inverse function.

Accepted Answer

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

Question 11

$\text { Use the result, "the line with intercepts } ( a , 0 ) \text { and } ( 0 , b ) \text { has the equation }$ $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ", to write an equation of the line with $x$-intercept: $( 8,0 )$ and $y$ intercept: $( 0,7 )$.

Accepted Answer

A)  $8 x - 7 y - 8 = 0$ 
B)  $7 x - 8 y + 7 = 0$ 
C)  $8 x + 7 y + 8 = 0$ 
D)  $7 x + 8 y + 56 = 0$ 
E)  $7 x + 8 y - 56 = 0$ 
A)  $8 x - 7 y - 8 = 0$ 
B)  $7 x - 8 y + 7 = 0$ 
C)  $8 x + 7 y + 8 = 0$ 
D)  $7 x + 8 y + 56 = 0$ 
E)  $7 x + 8 y - 56 = 0$

Question 12

Each ordered pair gives the exposure index x of a carcinogenic substance and the cancer mortality $y$ per 100,000 people in the population. Use the model $y = 9.2 x + 108.4$ to approximate $y$ if $x = 7$. Round your answer to one decimal place.
$$\begin{array} { l } 
( 3.50,150.1 ) , ( 3.58,133.1 ) , ( 4.42,132.9 ) , ( 2.26,116.7 ) , ( 2.36,140.7 ) , ( 4.85,165.5 ) \
( 12.65,210.7 ) , ( 7.42,181.0 ) , ( 9.35,213.4 )
\end{array}$$

Accepted Answer

A)  $168.2$ 
B)  $163.6$ 
C)  $182.0$ 
D)  $172.8$ 
E)  $177.4$ 
A)  $168.2$ 
B)  $163.6$ 
C)  $182.0$ 
D)  $172.8$ 
E)  $177.4$

Question 13

all intercepts: $$y = x ^ { 2 } - x - 12$$

Accepted Answer

A)  $x$-intercepts: $( 4,0 ) , ( - 3,0 ) ; y$-intercepts: $( 0,4 ) , ( 0,3 )$ 
B)  $x$-intercept: $( 12,0 ) ; y$-intercepts: $( 0,4 ) , ( 0,3 )$ 
C)  $x$-intercepts: $( 4,0 ) , ( - 3,0 ) ; y$-intercept: $( 0 , - 12 )$ 
D)  $x$-intercepts: $( 4,0 ) , ( - 3,0 ) ; y$-intercepts: $( 0 , - 12 ) , ( 0,12 )$ 
E)  $x$-intercept: $( - 3,0 ) ; y$-intercept: $( 0 , - 12 )$ 
A)  $x$-intercepts: $( 4,0 ) , ( - 3,0 ) ; y$-intercepts: $( 0,4 ) , ( 0,3 )$ 
B)  $x$-intercept: $( 12,0 ) ; y$-intercepts: $( 0,4 ) , ( 0,3 )$ 
C)  $x$-intercepts: $( 4,0 ) , ( - 3,0 ) ; y$-intercept: $( 0 , - 12 )$ 
D)  $x$-intercepts: $( 4,0 ) , ( - 3,0 ) ; y$-intercepts: $( 0 , - 12 ) , ( 0,12 )$ 
E)  $x$-intercept: $( - 3,0 ) ; y$-intercept: $( 0 , - 12 )$

Question 14

Fine the slope of the line passing through the pair of points. $$( - 3 , - 6 ) , ( 0 , - 11 )$$

Accepted Answer

A)  $\frac { 3 } { 5 }$ 
B)  $- \frac { 5 } { 3 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  0 
E)  $- \frac { 3 } { 5 }$ 
A)  $\frac { 3 } { 5 }$ 
B)  $- \frac { 5 } { 3 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  0 
E)  $- \frac { 3 } { 5 }$

Question 15

for symmetry with respect to each axis and to the origin. $$x ^ { 2 } y ^ { 2 } = 8$$

Accepted Answer

A)  symmetric with respect to the origin 
B)  symmetric with respect to the $x$-axis 
C)  symmetric with respect to the $y$-axis 
D)  no symmetry 
E)  $A , B$, and $C$ 
A)  symmetric with respect to the origin 
B)  symmetric with respect to the $x$-axis 
C)  symmetric with respect to the $y$-axis 
D)  no symmetry 
E)  $A , B$, and $C$

Question 16

$\text { Write an equation of the line that passes through the point } \left( \frac { 5 } { 4 } , \frac { 5 } { 8 } \right) \text { and is parallel to }$ the line $7 x - 3 y = 0$.

Accepted Answer

A)  $56 x - 24 y - 55 = 0$ 
B)  $56 x + 12 y - 55 = 0$ 
C)  $56 x - 8 y + 55 = 0$ 
D)  $56 x + 6 y + 55 = 0$ 
E)  $56 x + 4 y - 55 = 0$ 
A)  $56 x - 24 y - 55 = 0$ 
B)  $56 x + 12 y - 55 = 0$ 
C)  $56 x - 8 y + 55 = 0$ 
D)  $56 x + 6 y + 55 = 0$ 
E)  $56 x + 4 y - 55 = 0$

Question 17

$\text { Evaluate the expression } \cos \left( \arcsin \frac { 3 } { 5 } \right) \text { without using a calculator. }$

Accepted Answer

A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 4 } { 5 }$ 
C)  3 
D)  5 
E)  4 
A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 4 } { 5 }$ 
C)  3 
D)  5 
E)  4

Question 18

$\text { Find an equation of the line that passes through the points } ( 18 , - 7 ) \text { and } ( - 18,23 ) \text {. }$

Accepted Answer

A)  $y = - \frac { 5 } { 6 } x - 8$ 
B)  $y = \frac { 5 } { 6 } x - 8$ 
C)  $y = \frac { 5 } { 6 } x + 8$ 
D)  $y = - \frac { 5 } { 6 } x + 8$ 
E)  $y = - \frac { 5 } { 6 } x$ 
A)  $y = - \frac { 5 } { 6 } x - 8$ 
B)  $y = \frac { 5 } { 6 } x - 8$ 
C)  $y = \frac { 5 } { 6 } x + 8$ 
D)  $y = - \frac { 5 } { 6 } x + 8$ 
E)  $y = - \frac { 5 } { 6 } x$

Question 19

Write an equation of the line that passes through the given point and is parallel to the given line. $\begin{array}{cc}
\text { Point } & \text { Line } \
(3,-4) & -2 x-5 y=9
\end{array}$

Accepted Answer

A)  $- 2 x - 5 y = 14$ 
B)  $- 2 x - 5 y = 23$ 
C)  $2 x - 5 y = 14$ 
D)  $- 2 x + 5 y = - 26$ 
E)  $2 x - 5 y = 23$ 
A)  $- 2 x - 5 y = 14$ 
B)  $- 2 x - 5 y = 23$ 
C)  $2 x - 5 y = 14$ 
D)  $- 2 x + 5 y = - 26$ 
E)  $2 x - 5 y = 23$

Question 20

Use the Horizontal Line Test to determine whether the following statement is true or false. The function $f ( x ) = \frac { 3 } { 19 } x + 3$ is one-to-one on its entire domain and therefore has an inverse function.

Accepted Answer

A) True 
 B)False

$\text { Evaluate the expression } \arcsin \left( \frac { 1 } { 2 } \right) \text { without using a calculator. }$

$\text { Solve the following equation for } x \text {. }$ $\arccos ( 10 x - \pi ) = \frac { 1 } { 2 }$

$\text { Find an equation of the line that passes through the point } ( - 11 , - 9 ) \text { and has the slope }$ $m = \frac { 9 } { 2 } .$

Estimate the slope of the line from the graph.

$\text { If a line has slope } m = - 4 \text { and passes through the point } ( 4,8 ) \text {, through which of the }$ following points does the line also pass?

Determine which type of function would be most appropriate to fit the given data.

Write the following expression in algebraic form. $\tan \left( \operatorname { arcsec } \left( \frac { x } { 8 } \right) \right)$

Match the graph of the function given below with the graph of its inverse function.

$\text { Use the result, "the line with intercepts } ( a , 0 ) \text { and } ( 0 , b ) \text { has the equation }$ $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ", to write an equation of the line with $x$ -intercept: $( 8,0 )$ and $y$ intercept: $( 0,7 )$ .

all intercepts: $y = x ^ { 2 } - x - 12$

Fine the slope of the line passing through the pair of points. $( - 3 , - 6 ) , ( 0 , - 11 )$

for symmetry with respect to each axis and to the origin. $x ^ { 2 } y ^ { 2 } = 8$

$\text { Write an equation of the line that passes through the point } \left( \frac { 5 } { 4 } , \frac { 5 } { 8 } \right) \text { and is parallel to }$ the line $7 x - 3 y = 0$ .

$\text { Evaluate the expression } \cos \left( \arcsin \frac { 3 } { 5 } \right) \text { without using a calculator. }$

$\text { Find an equation of the line that passes through the points } ( 18 , - 7 ) \text { and } ( - 18,23 ) \text {. }$

Write an equation of the line that passes through the given point and is parallel to the given line. Point Line (3,-4) -2x-5y=9

Use the Horizontal Line Test to determine whether the following statement is true or false. The function $f ( x ) = \frac { 3 } { 19 } x + 3$ is one-to-one on its entire domain and therefore has an inverse function.

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Exam 1: Graphs and Models

Evaluate the expression arcsin⁡(12) without using a calculator. \text { Evaluate the expression } \arcsin \left( \frac { 1 } { 2 } \right) \text { without using a calculator. } Evaluate the expression arcsin(21​) without using a calculator.

Solve the following equation for x. \text { Solve the following equation for } x \text {. } Solve the following equation for x. arccos⁡(10x−π)=12\arccos ( 10 x - \pi ) = \frac { 1 } { 2 }arccos(10x−π)=21​

Estimate the slope of the line from the graph.

Determine which type of function would be most appropriate to fit the given data.

Write the following expression in algebraic form. tan⁡(arcsec⁡(x8))\tan \left( \operatorname { arcsec } \left( \frac { x } { 8 } \right) \right)tan(arcsec(8x​))

Match the graph of the function given below with the graph of its inverse function.

all intercepts: y=x2−x−12y = x ^ { 2 } - x - 12y=x2−x−12

Fine the slope of the line passing through the pair of points. (−3,−6),(0,−11)( - 3 , - 6 ) , ( 0 , - 11 )(−3,−6),(0,−11)

for symmetry with respect to each axis and to the origin. x2y2=8x ^ { 2 } y ^ { 2 } = 8x2y2=8

Evaluate the expression cos⁡(arcsin⁡35) without using a calculator. \text { Evaluate the expression } \cos \left( \arcsin \frac { 3 } { 5 } \right) \text { without using a calculator. } Evaluate the expression cos(arcsin53​) without using a calculator.

Find an equation of the line that passes through the points (18,−7) and (−18,23). \text { Find an equation of the line that passes through the points } ( 18 , - 7 ) \text { and } ( - 18,23 ) \text {. } Find an equation of the line that passes through the points (18,−7) and (−18,23).

Write an equation of the line that passes through the given point and is parallel to the given line. Point Line (3,-4) -2x-5y=9

Use the Horizontal Line Test to determine whether the following statement is true or false. The function f(x)=319x+3f ( x ) = \frac { 3 } { 19 } x + 3f(x)=193​x+3 is one-to-one on its entire domain and therefore has an inverse function.

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

$\text { Evaluate the expression } \arcsin \left( \frac { 1 } { 2 } \right) \text { without using a calculator. }$

$\text { Solve the following equation for } x \text {. }$ $\arccos ( 10 x - \pi ) = \frac { 1 } { 2 }$

Write the following expression in algebraic form. $\tan \left( \operatorname { arcsec } \left( \frac { x } { 8 } \right) \right)$

all intercepts: $y = x ^ { 2 } - x - 12$

Fine the slope of the line passing through the pair of points. $( - 3 , - 6 ) , ( 0 , - 11 )$

for symmetry with respect to each axis and to the origin. $x ^ { 2 } y ^ { 2 } = 8$

$\text { Evaluate the expression } \cos \left( \arcsin \frac { 3 } { 5 } \right) \text { without using a calculator. }$

$\text { Find an equation of the line that passes through the points } ( 18 , - 7 ) \text { and } ( - 18,23 ) \text {. }$

Use the Horizontal Line Test to determine whether the following statement is true or false. The function $f ( x ) = \frac { 3 } { 19 } x + 3$ is one-to-one on its entire domain and therefore has an inverse function.