Question 1

Graph the equation.
-$x ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$

Accepted Answer

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

Question 2

Graph the inequality.
-$y \leq-x^{2}-6 x-4$

Accepted Answer

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

Question 3

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { circle } & \text { ellipse } & \text { hyperbola } \
\text { conic sections } & \text { vertex } & \text { diameter } \
\text { center } & \text { radius } & \text { nonlinear system of equations }
\end{array}$$
-A(n) --------is the set of all points in a plane that are the same distance from a fixed point, called the .

Accepted Answer

A)  hyperbola; center 
B)  circle; center 
C)  ellipse; center 
D)  circle; radius 
A)  hyperbola; center 
B)  circle; center 
C)  ellipse; center 
D)  circle; radius

Question 4

Graph the equation.
-$\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 49 } = 1$

Accepted Answer

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

Question 5

Write an equation of the circle with the given center and radius.
-$( - 3,6 ) ; 12$

Accepted Answer

A)  $( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 12$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 144$ 
C)  $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 144$ 
D)  $( x - 6 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 12$ 
A)  $( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 12$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 144$ 
C)  $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 144$ 
D)  $( x - 6 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 12$

Question 6

Sketch the graph of the equation.
-$x^{2}-y^{2}=25$

Accepted Answer

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

Question 7

Graph the inequality.
-$\frac{x^{2}}{4}-\frac{y^{2}}{25} \leq 1$

Accepted Answer

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

Question 8

Solve the system.
-$\left\{ \begin{aligned}
x ^ { 2 } - 5 y ^ { 2 } & = - 32 \
y & = x
\end{aligned} \right.$

Accepted Answer

A)  $( 2 \sqrt { 2 } , - 2 \sqrt { 2 } )$ 
B)  $( 2 \sqrt { 2 } , - 2 \sqrt { 2 } ) , ( - 2 \sqrt { 2 } , 2 \sqrt { 2 } )$ 
C)  $( 2 \sqrt { 2 } , 2 \sqrt { 2 } )$ 
D)  $( 2 \sqrt { 2 } , 2 \sqrt { 2 } ) , ( - 2 \sqrt { 2 } , - 2 \sqrt { 2 } )$ 
A)  $( 2 \sqrt { 2 } , - 2 \sqrt { 2 } )$ 
B)  $( 2 \sqrt { 2 } , - 2 \sqrt { 2 } ) , ( - 2 \sqrt { 2 } , 2 \sqrt { 2 } )$ 
C)  $( 2 \sqrt { 2 } , 2 \sqrt { 2 } )$ 
D)  $( 2 \sqrt { 2 } , 2 \sqrt { 2 } ) , ( - 2 \sqrt { 2 } , - 2 \sqrt { 2 } )$

Question 9

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and
radius.
-$x = y ^ { 2 } + 3$

Accepted Answer

A)  vertex $( 0 , - 3 )$
  
B)  vertex $( 3,0 )$
  
C)  vertex $( - 3,0 )$
  
D)  vertex $( 0,3 )$
  
A)  vertex $( 0 , - 3 )$
  
B)  vertex $( 3,0 )$
  
C)  vertex $( - 3,0 )$
  
D)  vertex $( 0,3 )$

Question 10

Find the center and the radius of the circle.
-$14 x ^ { 2 } + 14 y ^ { 2 } = 196$

Accepted Answer

A)  center $( 0,0 )$, radius $= \sqrt { 14 }$ 
B)  center $( 0,0 )$, radius $= 196$ 
C)  center $( 0,0 )$, radius $= 14$ 
D)  center $( 14,14 )$, radius $= \sqrt { 14 }$ 
A)  center $( 0,0 )$, radius $= \sqrt { 14 }$ 
B)  center $( 0,0 )$, radius $= 196$ 
C)  center $( 0,0 )$, radius $= 14$ 
D)  center $( 14,14 )$, radius $= \sqrt { 14 }$

Question 11

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph.
-$x ^ { 2 } - 5 y ^ { 2 } = 7$

Accepted Answer

A)  hyperbola 
B)  ellipse 
A)  hyperbola 
B)  ellipse

Question 12

Solve.
-A rectangular holding pen for sheep is to be designed so that its perimeter is 22 meters and its area is 24 square meters. Find the dimensions of the holding pen.

Accepted Answer

A)  $3 \mathrm {~m}$ by $8 \mathrm {~m}$ 
B)  $4 \mathrm {~m}$ by $7 \mathrm {~m}$ 
C)  $2 \mathrm {~m}$ by $9 \mathrm {~m}$ 
D)  $2 \mathrm {~m}$ by $7 \mathrm {~m}$ 
A)  $3 \mathrm {~m}$ by $8 \mathrm {~m}$ 
B)  $4 \mathrm {~m}$ by $7 \mathrm {~m}$ 
C)  $2 \mathrm {~m}$ by $9 \mathrm {~m}$ 
D)  $2 \mathrm {~m}$ by $7 \mathrm {~m}$

Question 13

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola.
-$( x + 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 9$

Accepted Answer

A)  circle 
B)  parabola 
C)  hyperbola 
D)  ellipse 
A)  circle 
B)  parabola 
C)  hyperbola 
D)  ellipse

Question 14

Write an equation of the circle with the given center and radius.
-$( 6,0 ) ; 8$

Accepted Answer

A)  $( x + 6 ) ^ { 2 } + y ^ { 2 } = 64$ 
B)  $( x - 6 ) ^ { 2 } + y ^ { 2 } = 64$ 
C)  $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
D)  $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$ 
A)  $( x + 6 ) ^ { 2 } + y ^ { 2 } = 64$ 
B)  $( x - 6 ) ^ { 2 } + y ^ { 2 } = 64$ 
C)  $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
D)  $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$

Question 15

Write an equation of the circle with the given center and radius.
-$( 0 , - 2 ) ; 10$

Accepted Answer

A)  $( x - 2 ) ^ { 2 } + y ^ { 2 } = 100$ 
B)  $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 10$ 
C)  $( x + 2 ) ^ { 2 } + y ^ { 2 } = 100$ 
D)  $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 100$ 
A)  $( x - 2 ) ^ { 2 } + y ^ { 2 } = 100$ 
B)  $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 10$ 
C)  $( x + 2 ) ^ { 2 } + y ^ { 2 } = 100$ 
D)  $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 100$

Question 16

Solve.
-A bridge has an arch in the shape of half an ellipse. If the equation of the ellipse, measured in feet, is $225 x ^ { 2 } + 289 y ^ { 2 } = 65,025$, find the height of the arch from the road and the width of the arch.

Accepted Answer

A)  height: $30 \mathrm { ft }$; width: $34 \mathrm { ft }$ 
B)  height: $17 \mathrm { ft }$; width: $30 \mathrm { ft }$ 
C)  height: $15 \mathrm { ft }$; width: $34 \mathrm { ft }$ 
D)  height: $15 \mathrm { ft }$; width: $17 \mathrm { ft }$ 
A)  height: $30 \mathrm { ft }$; width: $34 \mathrm { ft }$ 
B)  height: $17 \mathrm { ft }$; width: $30 \mathrm { ft }$ 
C)  height: $15 \mathrm { ft }$; width: $34 \mathrm { ft }$ 
D)  height: $15 \mathrm { ft }$; width: $17 \mathrm { ft }$

Question 17

Graph the inequality.
-$y>-x^{2}$

Accepted Answer

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

Question 18

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and
radius.
-$x^{2}+y^{2}+12 x+12 y+56=0$

Accepted Answer

A)  center $( 6,6 )$; radius $= 4$
  
B)  center $( - 6 , - 6 )$; radius $= 4$
  
C)  center $( - 6,6 )$; radius $= 4$
  
D)  center $( 6 , - 6 )$; radius $= 4$
  
A)  center $( 6,6 )$; radius $= 4$
  
B)  center $( - 6 , - 6 )$; radius $= 4$
  
C)  center $( - 6,6 )$; radius $= 4$
  
D)  center $( 6 , - 6 )$; radius $= 4$

Question 19

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and
radius.
-$(x+3)^{2}+(y+2)^{2}=4$

Accepted Answer

A)  center $( - 3 , - 2 )$; radius $= 2$
  
B)  center $( 3,2 )$; radius $= 2$
  
C)  center $( 3 , - 2 )$; radius $= 2$
  
D)  center $( - 3,2 )$; radius $= 2$
  
A)  center $( - 3 , - 2 )$; radius $= 2$
  
B)  center $( 3,2 )$; radius $= 2$
  
C)  center $( 3 , - 2 )$; radius $= 2$
  
D)  center $( - 3,2 )$; radius $= 2$

Question 20

Solve the system.
-$\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 34 \ 3 x + 5 y = 0 \end{array} \right.$

Accepted Answer

A)  $( 5 , - 3 ) , ( - 5,3 )$ 
B)  $( 5 , - 3 ) , ( - 5 , - 3 )$ 
C)  $( 5 , - 3 )$ 
D)  $( 5,3 ) , ( - 5 , - 3 )$ 
A)  $( 5 , - 3 ) , ( - 5,3 )$ 
B)  $( 5 , - 3 ) , ( - 5 , - 3 )$ 
C)  $( 5 , - 3 )$ 
D)  $( 5,3 ) , ( - 5 , - 3 )$

Graph the equation. - $x ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$ $Graph the equation. - x ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$

Graph the inequality. - $y \leq-x^{2}-6 x-4$ $Graph the inequality. - y \leq-x^{2}-6 x-4$

Fill in the blank with one of the words or phrases listed below. circle ellipse hyperbola conic sections vertex diameter center radius nonlinear system of equations -A(n) --------is the set of all points in a plane that are the same distance from a fixed point, called the .

Graph the equation. - $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 49 } = 1$ $Graph the equation. - \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 49 } = 1$

Write an equation of the circle with the given center and radius. - $( - 3,6 ) ; 12$

Sketch the graph of the equation. - $x^{2}-y^{2}=25$ $Sketch the graph of the equation. - x^{2}-y^{2}=25$

Graph the inequality. - $\frac{x^{2}}{4}-\frac{y^{2}}{25} \leq 1$ $Graph the inequality. - \frac{x^{2}}{4}-\frac{y^{2}}{25} \leq 1$

Solve the system. - $\left\{ \begin{aligned}x ^ { 2 } - 5 y ^ { 2 } & = - 32 \\y & = x\end{aligned} \right.$

Find the center and the radius of the circle. - $14 x ^ { 2 } + 14 y ^ { 2 } = 196$

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - $x ^ { 2 } - 5 y ^ { 2 } = 7$

Solve. -A rectangular holding pen for sheep is to be designed so that its perimeter is 22 meters and its area is 24 square meters. Find the dimensions of the holding pen.

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $( x + 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 9$

Write an equation of the circle with the given center and radius. - $( 6,0 ) ; 8$

Write an equation of the circle with the given center and radius. - $( 0 , - 2 ) ; 10$

Graph the inequality. - $y>-x^{2}$ $Graph the inequality. - y>-x^{2}$

Solve the system. - $\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 34 \\ 3 x + 5 y = 0 \end{array} \right.$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Sequences, Series, and the Binomial Theorem

Filters

Exam 13: Conic Sections

Graph the equation. - x2+y264=1x ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1x2+64y2​=1

Graph the inequality. - y≤−x2−6x−4y \leq-x^{2}-6 x-4y≤−x2−6x−4

Fill in the blank with one of the words or phrases listed below. circle ellipse hyperbola conic sections vertex diameter center radius nonlinear system of equations -A(n) --------is the set of all points in a plane that are the same distance from a fixed point, called the .

Graph the equation. - y29−x249=1\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 49 } = 19y2​−49x2​=1

Write an equation of the circle with the given center and radius. - (−3,6);12( - 3,6 ) ; 12(−3,6);12

Sketch the graph of the equation. - x2−y2=25x^{2}-y^{2}=25x2−y2=25

Graph the inequality. - x24−y225≤1\frac{x^{2}}{4}-\frac{y^{2}}{25} \leq 14x2​−25y2​≤1

Solve the system. - {x2−5y2=−32y=x\left\{ \begin{aligned}x ^ { 2 } - 5 y ^ { 2 } & = - 32 \\y & = x\end{aligned} \right.{x2−5y2y​=−32=x​

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x=y2+3x = y ^ { 2 } + 3x=y2+3

Find the center and the radius of the circle. - 14x2+14y2=19614 x ^ { 2 } + 14 y ^ { 2 } = 19614x2+14y2=196

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - x2−5y2=7x ^ { 2 } - 5 y ^ { 2 } = 7x2−5y2=7

Solve. -A rectangular holding pen for sheep is to be designed so that its perimeter is 22 meters and its area is 24 square meters. Find the dimensions of the holding pen.

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - (x+1)2+(y+3)2=9( x + 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 9(x+1)2+(y+3)2=9

Write an equation of the circle with the given center and radius. - (6,0);8( 6,0 ) ; 8(6,0);8

Write an equation of the circle with the given center and radius. - (0,−2);10( 0 , - 2 ) ; 10(0,−2);10

Solve. -A bridge has an arch in the shape of half an ellipse. If the equation of the ellipse, measured in feet, is 225x2+289y2=65,025225 x ^ { 2 } + 289 y ^ { 2 } = 65,025225x2+289y2=65,025 , find the height of the arch from the road and the width of the arch.

Graph the inequality. - y>−x2y>-x^{2}y>−x2

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x2+y2+12x+12y+56=0x^{2}+y^{2}+12 x+12 y+56=0x2+y2+12x+12y+56=0

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - (x+3)2+(y+2)2=4(x+3)^{2}+(y+2)^{2}=4(x+3)2+(y+2)2=4

Solve the system. - {x2+y2=343x+5y=0\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 34 \\ 3 x + 5 y = 0 \end{array} \right.{x2+y2=343x+5y=0​

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Sequences, Series, and the Binomial Theorem

Filters

Graph the equation. - $x ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$ $Graph the equation. - x ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$

Graph the inequality. - $y \leq-x^{2}-6 x-4$ $Graph the inequality. - y \leq-x^{2}-6 x-4$

Graph the equation. - $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 49 } = 1$ $Graph the equation. - \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 49 } = 1$

Write an equation of the circle with the given center and radius. - $( - 3,6 ) ; 12$

Sketch the graph of the equation. - $x^{2}-y^{2}=25$ $Sketch the graph of the equation. - x^{2}-y^{2}=25$

Graph the inequality. - $\frac{x^{2}}{4}-\frac{y^{2}}{25} \leq 1$ $Graph the inequality. - \frac{x^{2}}{4}-\frac{y^{2}}{25} \leq 1$

Solve the system. - $\left\{ \begin{aligned}x ^ { 2 } - 5 y ^ { 2 } & = - 32 \\y & = x\end{aligned} \right.$

Find the center and the radius of the circle. - $14 x ^ { 2 } + 14 y ^ { 2 } = 196$

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - $x ^ { 2 } - 5 y ^ { 2 } = 7$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $( x + 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 9$

Write an equation of the circle with the given center and radius. - $( 6,0 ) ; 8$

Write an equation of the circle with the given center and radius. - $( 0 , - 2 ) ; 10$

Graph the inequality. - $y>-x^{2}$ $Graph the inequality. - y>-x^{2}$

Solve the system. - $\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 34 \\ 3 x + 5 y = 0 \end{array} \right.$