Question 1

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

Accepted Answer

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

Question 2

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola.
-$x ^ { 2 } = 49 y ^ { 2 } + 49$

Accepted Answer

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

Question 3

Graph the inequality.
-$x^{2}+y^{2}>16$

Accepted Answer

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

Question 4

Find the center and the radius of the circle.
-$x ^ { 2 } + y ^ { 2 } + 10 x - 2 y + 18 = 0$

Accepted Answer

A)  center $( 5 , - 1 )$, radius $= 2 \sqrt { 2 }$ 
B)  center $( 5 , - 1 )$, radius $= 8$ 
C)  center $( - 5,1 )$, radius $= 8$ 
D)  center $( - 5,1 )$, radius $= 2 \sqrt { 2 }$ 
A)  center $( 5 , - 1 )$, radius $= 2 \sqrt { 2 }$ 
B)  center $( 5 , - 1 )$, radius $= 8$ 
C)  center $( - 5,1 )$, radius $= 8$ 
D)  center $( - 5,1 )$, radius $= 2 \sqrt { 2 }$

Question 5

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 20 \
x ^ { 2 } - y ^ { 2 } = 12
\end{array} \right.$

Accepted Answer

A)  $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$ 
B)  $( - 4 , - 2 ) , ( - 2 , - 4 )$ 
C)  $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$ 
D)  $( 4 , - 2 ) , ( 4,2 )$ 
A)  $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$ 
B)  $( - 4 , - 2 ) , ( - 2 , - 4 )$ 
C)  $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$ 
D)  $( 4 , - 2 ) , ( 4,2 )$

Question 6

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { r } 
x ^ { 2 } + y ^ { 2 } = 1 \
x ^ { 2 } + ( y - 2 ) ^ { 2 } = 9
\end{array} \right.$

Accepted Answer

A)  $( 0,1 )$ 
B)  $( - 1,0 )$ 
C)  $( 0 , - 1 )$ 
D)  $( 1,0 )$ 
A)  $( 0,1 )$ 
B)  $( - 1,0 )$ 
C)  $( 0 , - 1 )$ 
D)  $( 1,0 )$

Question 7

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{aligned}
y & = x ^ { 2 } - - 2 \
9 x - y & = 6
\end{aligned} \right.$

Accepted Answer

A)  $( 8,62 ) , ( 1 , - 1 )$ 
B)  $( - 8,66 ) , ( 1,3 )$ 
C)  $( - 8,66 ) , ( - 1,3 )$ 
D)  $( 8,66 ) , ( 1,3 )$ 
A)  $( 8,62 ) , ( 1 , - 1 )$ 
B)  $( - 8,66 ) , ( 1,3 )$ 
C)  $( - 8,66 ) , ( - 1,3 )$ 
D)  $( 8,66 ) , ( 1,3 )$

Question 8

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
y = x ^ { 2 } + 2 \
y = - x ^ { 2 } + 4
\end{array} \right.$

Accepted Answer

A)  $( 1,3 ) , ( - 1,3 )$ 
B)  $( 1,3 ) , ( 1 , - 3 ) , ( - 1,3 ) , ( - 1 , - 3 )$ 
C)  $\varnothing$ 
D)  $( 3,1 ) , ( 3 , - 1 )$ 
A)  $( 1,3 ) , ( - 1,3 )$ 
B)  $( 1,3 ) , ( 1 , - 3 ) , ( - 1,3 ) , ( - 1 , - 3 )$ 
C)  $\varnothing$ 
D)  $( 3,1 ) , ( 3 , - 1 )$

Question 9

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { circle } & \text { ellipse } & \text { hyperbola } \
\text { conic sections } & \text { vertex } & \text { diameter } \
\text { center } & \text { radius } & \text { nonlinear system of equations }
\end{array}$$
-For a parabola that opens upward, the lowest point is the ------

Accepted Answer

A)  vertex 
B)  radius 
C)  center 
D)  diameter 
A)  vertex 
B)  radius 
C)  center 
D)  diameter

Question 10

Graph the system.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \leq 81 \
9 x + 5 y \leq 45
\end{array} \right.$

Accepted Answer

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

Question 11

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola.
-$x ^ { 2 } + y ^ { 2 } = 81$

Accepted Answer

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

Question 12

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 points in a plane such that the sum of the distances of those points from two fixed points is a constant.

Accepted Answer

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

Question 13

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 15 \
x ^ { 2 } + y ^ { 2 } = 21
\end{array} \right.$

Accepted Answer

A)  $\varnothing$ 
B)  $( - 3 \sqrt { 2 } , - \sqrt { 3 } )$ 
C)  $( 3 \sqrt { 2 } , \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , \sqrt { 3 } )$ 
D)  $( 3 \sqrt { 2 } , \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , \sqrt { 3 } ) , ( 3 \sqrt { 2 } , - \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , - \sqrt { 3 } )$ 
A)  $\varnothing$ 
B)  $( - 3 \sqrt { 2 } , - \sqrt { 3 } )$ 
C)  $( 3 \sqrt { 2 } , \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , \sqrt { 3 } )$ 
D)  $( 3 \sqrt { 2 } , \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , \sqrt { 3 } ) , ( 3 \sqrt { 2 } , - \sqrt { 3 } ) , ( - 3 \sqrt { 2 } , - \sqrt { 3 } )$

Question 14

Graph the inequality.
-$y>(x-1)^{2}-4$

Accepted Answer

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

Question 15

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.
-$(x-5)^{2}+y^{2}=9$

Accepted Answer

A)  center $( - 5,0 )$; radius $= 3$
  
B)  center $( 0,5 )$; radius $= 3$
  
C)  center $( 5,0 )$; radius $= 3$
  
D)  center $( 0 , - 5 )$; radius $= 3$
  
A)  center $( - 5,0 )$; radius $= 3$
  
B)  center $( 0,5 )$; radius $= 3$
  
C)  center $( 5,0 )$; radius $= 3$
  
D)  center $( 0 , - 5 )$; radius $= 3$

Question 16

Graph the system.
-$\left\{ \begin{array} { c } 
x ^ { 2 } - y ^ { 2 } \geq 9 \
\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } \leq 1
\end{array} \right.$

Accepted Answer

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

Question 17

Graph the equation.
-$x^{2}-16 y^{2}=16$

Accepted Answer

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

Question 18

Write an equation of the circle with the given center and radius.
-$( 0,0 ) ; 14$

Accepted Answer

A)  $x ^ { 2 } - y ^ { 2 } = 14$ 
B)  $x ^ { 2 } + y ^ { 2 } = 14$ 
C)  $x ^ { 2 } + y ^ { 2 } = 196$ 
D)  $x ^ { 2 } + y ^ { 2 } = 28$ 
A)  $x ^ { 2 } - y ^ { 2 } = 14$ 
B)  $x ^ { 2 } + y ^ { 2 } = 14$ 
C)  $x ^ { 2 } + y ^ { 2 } = 196$ 
D)  $x ^ { 2 } + y ^ { 2 } = 28$

Question 19

Graph the system.
-$\left\{\begin{array}{l}
x^{2}+y^{2} \leq 36 \
x^{2}+y^{2} \geq 25
\end{array}\right.$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)  no solution
  
A) 
  
B) 
  
C) 
  
D)  no solution

Question 20

Write an equation of the circle with the given center and radius.
-$( 0 , - 9 ) ; \sqrt { 19 }$

Accepted Answer

A)  $( x - 9 ) ^ { 2 } + y ^ { 2 } = 361$ 
B)  $x ^ { 2 } + ( y + 9 ) ^ { 2 } = 19$ 
C)  $( x + 9 ) ^ { 2 } + y ^ { 2 } = 361$ 
D)  $x ^ { 2 } + ( y - 9 ) ^ { 2 } = 19$ 
A)  $( x - 9 ) ^ { 2 } + y ^ { 2 } = 361$ 
B)  $x ^ { 2 } + ( y + 9 ) ^ { 2 } = 19$ 
C)  $( x + 9 ) ^ { 2 } + y ^ { 2 } = 361$ 
D)  $x ^ { 2 } + ( y - 9 ) ^ { 2 } = 19$

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

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } = 49 y ^ { 2 } + 49$

Graph the inequality. - $x^{2}+y^{2}>16$ $Graph the inequality. - x^{2}+y^{2}>16$

Find the center and the radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 10 x - 2 y + 18 = 0$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 20 \\x ^ { 2 } - y ^ { 2 } = 12\end{array} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 1 \\x ^ { 2 } + ( y - 2 ) ^ { 2 } = 9\end{array} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}y & = x ^ { 2 } - - 2 \\9 x - y & = 6\end{aligned} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } y = x ^ { 2 } + 2 \\y = - x ^ { 2 } + 4\end{array} \right.$

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 -For a parabola that opens upward, the lowest point is the ------

Graph the system. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 81 \\9 x + 5 y \leq 45\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 81 \\ 9 x + 5 y \leq 45 \end{array} \right.$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } + y ^ { 2 } = 81$

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 points in a plane such that the sum of the distances of those points from two fixed points is a constant.

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 15 \\x ^ { 2 } + y ^ { 2 } = 21\end{array} \right.$

Graph the inequality. - $y>(x-1)^{2}-4$ $Graph the inequality. - y>(x-1)^{2}-4$

Graph the equation. - $x^{2}-16 y^{2}=16$ $Graph the equation. - x^{2}-16 y^{2}=16$

Write an equation of the circle with the given center and radius. - $( 0,0 ) ; 14$

Graph the system. - $\left\{\begin{array}{l}x^{2}+y^{2} \leq 36 \\x^{2}+y^{2} \geq 25\end{array}\right.$ $Graph the system. - \left\{\begin{array}{l} x^{2}+y^{2} \leq 36 \\ x^{2}+y^{2} \geq 25 \end{array}\right.$

Write an equation of the circle with the given center and radius. - $( 0 , - 9 ) ; \sqrt { 19 }$

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+64y2=64x^{2}+64 y^{2}=64x2+64y2=64

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - x2=49y2+49x ^ { 2 } = 49 y ^ { 2 } + 49x2=49y2+49

Graph the inequality. - x2+y2>16x^{2}+y^{2}>16x2+y2>16

Find the center and the radius of the circle. - x2+y2+10x−2y+18=0x ^ { 2 } + y ^ { 2 } + 10 x - 2 y + 18 = 0x2+y2+10x−2y+18=0

Solve the nonlinear system of equations for real solutions. - {x2+y2=20x2−y2=12\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 20 \\x ^ { 2 } - y ^ { 2 } = 12\end{array} \right.{x2+y2=20x2−y2=12​

Solve the nonlinear system of equations for real solutions. - {x2+y2=1x2+(y−2)2=9\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 1 \\x ^ { 2 } + ( y - 2 ) ^ { 2 } = 9\end{array} \right.{x2+y2=1x2+(y−2)2=9​

Solve the nonlinear system of equations for real solutions. - {y=x2−−29x−y=6\left\{ \begin{aligned}y & = x ^ { 2 } - - 2 \\9 x - y & = 6\end{aligned} \right.{y9x−y​=x2−−2=6​

Solve the nonlinear system of equations for real solutions. - {y=x2+2y=−x2+4\left\{ \begin{array} { l } y = x ^ { 2 } + 2 \\y = - x ^ { 2 } + 4\end{array} \right.{y=x2+2y=−x2+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 -For a parabola that opens upward, the lowest point is the ------

Graph the system. - {x2+y2≤819x+5y≤45\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 81 \\9 x + 5 y \leq 45\end{array} \right.{x2+y2≤819x+5y≤45​

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - x2+y2=81x ^ { 2 } + y ^ { 2 } = 81x2+y2=81

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 points in a plane such that the sum of the distances of those points from two fixed points is a constant.

Solve the nonlinear system of equations for real solutions. - {x2−y2=15x2+y2=21\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 15 \\x ^ { 2 } + y ^ { 2 } = 21\end{array} \right.{x2−y2=15x2+y2=21​

Graph the inequality. - y>(x−1)2−4y>(x-1)^{2}-4y>(x−1)2−4

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−5)2+y2=9(x-5)^{2}+y^{2}=9(x−5)2+y2=9

Graph the system. - {x2−y2≥9x216+y29≤1\left\{ \begin{array} { c } x ^ { 2 } - y ^ { 2 } \geq 9 \\\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } \leq 1\end{array} \right.{x2−y2≥916x2​+9y2​≤1​

Graph the equation. - x2−16y2=16x^{2}-16 y^{2}=16x2−16y2=16

Write an equation of the circle with the given center and radius. - (0,0);14( 0,0 ) ; 14(0,0);14

Graph the system. - {x2+y2≤36x2+y2≥25\left\{\begin{array}{l}x^{2}+y^{2} \leq 36 \\x^{2}+y^{2} \geq 25\end{array}\right.{x2+y2≤36x2+y2≥25​

Write an equation of the circle with the given center and radius. - (0,−9);19( 0 , - 9 ) ; \sqrt { 19 }(0,−9);19​

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

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } = 49 y ^ { 2 } + 49$

Graph the inequality. - $x^{2}+y^{2}>16$ $Graph the inequality. - x^{2}+y^{2}>16$

Find the center and the radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 10 x - 2 y + 18 = 0$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 20 \\x ^ { 2 } - y ^ { 2 } = 12\end{array} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 1 \\x ^ { 2 } + ( y - 2 ) ^ { 2 } = 9\end{array} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}y & = x ^ { 2 } - - 2 \\9 x - y & = 6\end{aligned} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } y = x ^ { 2 } + 2 \\y = - x ^ { 2 } + 4\end{array} \right.$

Graph the system. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 81 \\9 x + 5 y \leq 45\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 81 \\ 9 x + 5 y \leq 45 \end{array} \right.$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } + y ^ { 2 } = 81$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 15 \\x ^ { 2 } + y ^ { 2 } = 21\end{array} \right.$

Graph the inequality. - $y>(x-1)^{2}-4$ $Graph the inequality. - y>(x-1)^{2}-4$

Graph the equation. - $x^{2}-16 y^{2}=16$ $Graph the equation. - x^{2}-16 y^{2}=16$

Write an equation of the circle with the given center and radius. - $( 0,0 ) ; 14$

Graph the system. - $\left\{\begin{array}{l}x^{2}+y^{2} \leq 36 \\x^{2}+y^{2} \geq 25\end{array}\right.$ $Graph the system. - \left\{\begin{array}{l} x^{2}+y^{2} \leq 36 \\ x^{2}+y^{2} \geq 25 \end{array}\right.$

Write an equation of the circle with the given center and radius. - $( 0 , - 9 ) ; \sqrt { 19 }$