Question 1

$\text { Find the slope of the line } x + 3 y = 15 \text {. }$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $- \frac { 1 } { 15 }$ 
E)  $- \frac { 1 } { 3 }$ 
A)  $\frac { 1 } { 3 }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $- \frac { 1 } { 15 }$ 
E)  $- \frac { 1 } { 3 }$

Question 2

Find the coordinates of a second point on the graph of a function f if the given point $\left( - \frac { 6 } { 5 } , 8 \right)$ is on the graph and the function is even.

Accepted Answer

A)  $\left( 8 , - \frac { 6 } { 5 } \right)$ 
B)  $\left( - 8 , - \frac { 6 } { 5 } \right)$ 
C)  $\left( - \frac { 6 } { 5 } , - 8 \right)$ 
D)  $\left( \frac { 6 } { 5 } , - 8 \right)$ 
E)  $\left( \frac { 6 } { 5 } , 8 \right)$ 
A)  $\left( 8 , - \frac { 6 } { 5 } \right)$ 
B)  $\left( - 8 , - \frac { 6 } { 5 } \right)$ 
C)  $\left( - \frac { 6 } { 5 } , - 8 \right)$ 
D)  $\left( \frac { 6 } { 5 } , - 8 \right)$ 
E)  $\left( \frac { 6 } { 5 } , 8 \right)$

Question 3

Sketch the graph of the equation: $$x = y ^ { 3 } - 9 y$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E)  none of the above 
A) 
  
B) 
  
C) 
  
D) 
  
E)  none of the above

Question 4

Students in a lab measured the breaking strength S (in pounds) of wood 2 inches thick, $x$ inches high, and 12 inches long. The results are shown in the table below. Use the model $S = 180.89 x ^ { 2 } - 205.79 x + 284$ to approximate the breaking strength when $x = 2$. Round your answer to two decimal places.
$\begin{array}{|c|c|c|c|c|c|}
\hline x & 4 & 6 & 8 & 10 & 12 \
\hline S & 2382 & 5472 & 10,322 & 16,262 & 23,872 \
\hline
\end{array}$

Accepted Answer

A)  $595.98$ pounds 
B)  $390.19$ pounds 
C)  $957.76$ pounds 
D)  $801.77$ pounds 
E)  $751.97$ pounds 
A)  $595.98$ pounds 
B)  $390.19$ pounds 
C)  $957.76$ pounds 
D)  $801.77$ pounds 
E)  $751.97$ pounds

Question 5

Write the following expression in algebraic form. $$\cos \left( \arcsin \left( 2 x ^ { 2 } \right) \right)$$

Accepted Answer

A)  $\sqrt { 1 - 4 x ^ { 4 } }$ 
B)  $1 + 4 x ^ { 4 }$ 
C)  $\sqrt { 1 - 2 x ^ { 2 } }$ 
D)  $1 + 2 x ^ { 2 }$ 
E)  $1 + 2 x ^ { 4 }$ 
A)  $\sqrt { 1 - 4 x ^ { 4 } }$ 
B)  $1 + 4 x ^ { 4 }$ 
C)  $\sqrt { 1 - 2 x ^ { 2 } }$ 
D)  $1 + 2 x ^ { 2 }$ 
E)  $1 + 2 x ^ { 4 }$

Question 6

$\text { Find an equation of the line that passes through the points } \left( - \frac { 8 } { 11 } , - \frac { 70 } { 11 } \right) \text { and }$ $\left( \frac { 3 } { 2 } , - \frac { 21 } { 4 } \right) \text {. }$

Accepted Answer

A)  $y = \frac { 1 } { 2 } x$ 
B)  $y = \frac { 1 } { 2 } x + 6$ 
C)  $y = \frac { 1 } { 2 } x + 12$ 
D)  $y = \frac { 1 } { 2 } x - 12$ 
E)  $y = \frac { 1 } { 2 } x - 6$ 
A)  $y = \frac { 1 } { 2 } x$ 
B)  $y = \frac { 1 } { 2 } x + 6$ 
C)  $y = \frac { 1 } { 2 } x + 12$ 
D)  $y = \frac { 1 } { 2 } x - 12$ 
E)  $y = \frac { 1 } { 2 } x - 6$

Question 7

Write the following expression in algebraic form. $\sin ( \arccos ( 2 x ) )$

Accepted Answer

A)  $\sqrt { 1 - 4 x ^ { 2 } }$ 
B)  $1 - 2 x ^ { 2 }$ 
C)  $1 + 2 x ^ { 2 }$ 
D)  $1 + 4 x ^ { 2 }$ 
E)  $\sqrt { 1 - 2 x ^ { 2 } }$ 
A)  $\sqrt { 1 - 4 x ^ { 2 } }$ 
B)  $1 - 2 x ^ { 2 }$ 
C)  $1 + 2 x ^ { 2 }$ 
D)  $1 + 4 x ^ { 2 }$ 
E)  $\sqrt { 1 - 2 x ^ { 2 } }$

Question 8

$\text { Which of the following is the correct graph of } y = - \sqrt { 3 - x ^ { 2 } } \text { ? }$

Accepted Answer

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

Question 9

$\text { Find an equation of the line that passes through the point } ( 7,2 ) \text { and has the slope } m$ that is undefined.

Accepted Answer

A)  $y = 7$ 
B)  $x = 7$ 
C)  $y = 2$ 
D)  $x = 2$ 
E)  $y = 7 x$ 
A)  $y = 7$ 
B)  $x = 7$ 
C)  $y = 2$ 
D)  $x = 2$ 
E)  $y = 7 x$

Question 10

Write an equation of the line that passes through the given point and is perpendicular to the given line. $\begin{array}{cl}
\text { Point } & \text { Line } \
(-1,-7) & x=6
\end{array}$

Accepted Answer

A)  $y = 7$ 
B)  $y = - 7$ 
C)  $y = - 1$ 
D)  $x = - 1$ 
E)  $x = 1$ 
A)  $y = 7$ 
B)  $y = - 7$ 
C)  $y = - 1$ 
D)  $x = - 1$ 
E)  $x = 1$

Question 11

$\text { Sketch the line passing through the point } ( 3,4 ) \text { with the slope } - \frac { 3 } { 2 } \text {. }$

Accepted Answer

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

Question 12

$\text { The resistance } y \text { in ohms of } 1000 \text { feet of solid metal wire at } 77 \circ \mathrm {F} \text { can be approximated by the }$ model $y = \frac { 10,000 } { x ^ { 2 } } - 0.57,5 \leq x \leq 100$, where $x$ is the diameter of the wire in mils ( $0.001$ in). Use a graphing utility to graph the model $y = \frac { 10,000 } { x ^ { 2 } } - 0.57,5 \leq x \leq 100$.

Accepted Answer

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

Question 13

$$\text { Which of the following is the correct graph of } y = x - x ^ { 3 } \text { ? }$$

Accepted Answer

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

Question 14

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

Accepted Answer

A)  symmetric with respect to the origin 
B)  symmetric with respect to the $y$-axis 
C)  symmetric with respect to the $x$-axis 
D)  both $\mathrm { B }$ and $\mathrm { C }$ 
E)  no symmetry 
A)  symmetric with respect to the origin 
B)  symmetric with respect to the $y$-axis 
C)  symmetric with respect to the $x$-axis 
D)  both $\mathrm { B }$ and $\mathrm { C }$ 
E)  no symmetry

Question 15

$\text { Solve the following equation for } x \text {. }$ $\ln x ^ { - 10 } = 6$

Accepted Answer

A)  $x = \sqrt [ 10 ] { \ln ( 6 ) }$ 
B) $x = \frac { 6 } { \ln ( 10 ) }$ 
C)  $x = \sqrt [ 10 ] { e ^ { - 6 } }$ 
D)  $x = \sqrt [ 10 ] { e ^ { 6 } }$ 
E)  $x = \ln ( 10 ) \ln ( 6 )$ 
A)  $x = \sqrt [ 10 ] { \ln ( 6 ) }$ 
B) $x = \frac { 6 } { \ln ( 10 ) }$ 
C)  $x = \sqrt [ 10 ] { e ^ { - 6 } }$ 
D)  $x = \sqrt [ 10 ] { e ^ { 6 } }$ 
E)  $x = \ln ( 10 ) \ln ( 6 )$

Question 16

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 17

$\text { An open box of maximum volume is to be made from a square piece of material } 30$ centimeters on a side by cutting equal squares from the corners and turning up the sides(see figure). What is the domain of the function $V = x ( 30 - 2 x ) ^ { 2 }$.

Accepted Answer

A)  domain: $0 < x < \infty$ 
B)  domain: 30 
C)  domain: $0 < x < 15$ 
D)  domain: $0 < x < 30$ 
E)  domain: 15 
A)  domain: $0 < x < \infty$ 
B)  domain: 30 
C)  domain: $0 < x < 15$ 
D)  domain: $0 < x < 30$ 
E)  domain: 15

Question 18

an experiment, students measured the speed s (in meters per second) of a falling object $t$ seconds after it was released. The results are shown in the table below. Use the regression capabilities of a graphing utility to find a linear model for the data. Round all numerical values in your answer to one decimal place.
$\begin{array}{|c|c|c|c|c|c|}
\hline t & 0 & 1 & 2 & 3 & 4 \
\hline s & 0 & 40 & 48.4 & 58.2 & 68.4 \
\hline
\end{array}$

Accepted Answer

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

Question 19

$$\text { Evaluate (if possible) the function } f ( x ) = \sqrt { x - 5 } \text { at } x = 9 \text {. Simplify the result. }$$

Accepted Answer

A)  3 
B)  2 
C)  $- 2$ 
D)  4 
E)  undefined 
A)  3 
B)  2 
C)  $- 2$ 
D)  4 
E)  undefined

Question 20

Determine whether y is a function of x. $y - 5 x ^ { 2 } = 6$

Accepted Answer

A) True 
 B)False

$\text { Find the slope of the line } x + 3 y = 15 \text {. }$

Find the coordinates of a second point on the graph of a function f if the given point $\left( - \frac { 6 } { 5 } , 8 \right)$ is on the graph and the function is even.

Sketch the graph of the equation: $x = y ^ { 3 } - 9 y$

Write the following expression in algebraic form. $\cos \left( \arcsin \left( 2 x ^ { 2 } \right) \right)$

$\text { Find an equation of the line that passes through the points } \left( - \frac { 8 } { 11 } , - \frac { 70 } { 11 } \right) \text { and }$ $\left( \frac { 3 } { 2 } , - \frac { 21 } { 4 } \right) \text {. }$

Write the following expression in algebraic form. $\sin ( \arccos ( 2 x ) )$

$\text { Which of the following is the correct graph of } y = - \sqrt { 3 - x ^ { 2 } } \text { ? }$

$\text { Find an equation of the line that passes through the point } ( 7,2 ) \text { and has the slope } m$ that is undefined.

Write an equation of the line that passes through the given point and is perpendicular to the given line. Point Line (-1,-7) x=6

$\text { Sketch the line passing through the point } ( 3,4 ) \text { with the slope } - \frac { 3 } { 2 } \text {. }$

$\text { Which of the following is the correct graph of } y = x - x ^ { 3 } \text { ? }$

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

$\text { Solve the following equation for } x \text {. }$ $\ln x ^ { - 10 } = 6$

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

$\text { Evaluate (if possible) the function } f ( x ) = \sqrt { x - 5 } \text { at } x = 9 \text {. Simplify the result. }$

Determine whether y is a function of x. $y - 5 x ^ { 2 } = 6$

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

Find the slope of the line x+3y=15. \text { Find the slope of the line } x + 3 y = 15 \text {. } Find the slope of the line x+3y=15.

Find the coordinates of a second point on the graph of a function f if the given point (−65,8)\left( - \frac { 6 } { 5 } , 8 \right)(−56​,8) is on the graph and the function is even.

Sketch the graph of the equation: x=y3−9yx = y ^ { 3 } - 9 yx=y3−9y

Write the following expression in algebraic form. cos⁡(arcsin⁡(2x2))\cos \left( \arcsin \left( 2 x ^ { 2 } \right) \right)cos(arcsin(2x2))

Write the following expression in algebraic form. sin⁡(arccos⁡(2x))\sin ( \arccos ( 2 x ) )sin(arccos(2x))

Which of the following is the correct graph of y=−3−x2 ? \text { Which of the following is the correct graph of } y = - \sqrt { 3 - x ^ { 2 } } \text { ? } Which of the following is the correct graph of y=−3−x2​ ?

Find an equation of the line that passes through the point (7,2) and has the slope m\text { Find an equation of the line that passes through the point } ( 7,2 ) \text { and has the slope } m Find an equation of the line that passes through the point (7,2) and has the slope m that is undefined.

Write an equation of the line that passes through the given point and is perpendicular to the given line. Point Line (-1,-7) x=6

Sketch the line passing through the point (3,4) with the slope −32. \text { Sketch the line passing through the point } ( 3,4 ) \text { with the slope } - \frac { 3 } { 2 } \text {. } Sketch the line passing through the point (3,4) with the slope −23​.

Which of the following is the correct graph of y=x−x3 ? \text { Which of the following is the correct graph of } y = x - x ^ { 3 } \text { ? } Which of the following is the correct graph of y=x−x3 ?

for symmetry with respect to each axis and to the origin. y=x2+2xy = \frac { x ^ { 2 } + 2 } { x }y=xx2+2​

Solve the following equation for x. \text { Solve the following equation for } x \text {. } Solve the following equation for x. ln⁡x−10=6\ln x ^ { - 10 } = 6lnx−10=6

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

Evaluate (if possible) the function f(x)=x−5 at x=9. Simplify the result. \text { Evaluate (if possible) the function } f ( x ) = \sqrt { x - 5 } \text { at } x = 9 \text {. Simplify the result. } Evaluate (if possible) the function f(x)=x−5​ at x=9. Simplify the result.

Determine whether y is a function of x. y−5x2=6y - 5 x ^ { 2 } = 6y−5x2=6

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

$\text { Find the slope of the line } x + 3 y = 15 \text {. }$

Find the coordinates of a second point on the graph of a function f if the given point $\left( - \frac { 6 } { 5 } , 8 \right)$ is on the graph and the function is even.

Sketch the graph of the equation: $x = y ^ { 3 } - 9 y$

Write the following expression in algebraic form. $\cos \left( \arcsin \left( 2 x ^ { 2 } \right) \right)$

Write the following expression in algebraic form. $\sin ( \arccos ( 2 x ) )$

$\text { Which of the following is the correct graph of } y = - \sqrt { 3 - x ^ { 2 } } \text { ? }$

$\text { Find an equation of the line that passes through the point } ( 7,2 ) \text { and has the slope } m$ that is undefined.

$\text { Sketch the line passing through the point } ( 3,4 ) \text { with the slope } - \frac { 3 } { 2 } \text {. }$

$\text { Which of the following is the correct graph of } y = x - x ^ { 3 } \text { ? }$

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

$\text { Solve the following equation for } x \text {. }$ $\ln x ^ { - 10 } = 6$

$\text { Evaluate (if possible) the function } f ( x ) = \sqrt { x - 5 } \text { at } x = 9 \text {. Simplify the result. }$

Determine whether y is a function of x. $y - 5 x ^ { 2 } = 6$