Question 1

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + 2 y ^ { 2 } = - 7 \
x - y = - 9
\end{array} \right.$

Accepted Answer

A) 
$\left( \frac { 9 + \sqrt { 345 } } { 3 } , \frac { - 18 + \sqrt { 345 } } { 3 } \right) , \left( \frac { 9 + \sqrt { 345 } } { 3 } , \frac { - 18 - \sqrt { 345 } } { 3 } \right) , \left( \frac { 9 - \sqrt { 345 } } { 3 } , \frac { - 18 + \sqrt { 345 } } { 3 } \right)$, $\left\{ \frac { 9 - \sqrt { 345 } } { 3 } , \frac { - 18 - \sqrt { 345 } } { 3 } \right\}$ 
B) 
$\left\{ \frac { - 18 + \sqrt { 345 } } { 3 } , \frac { 9 + \sqrt { 345 } } { 3 } \right) , \left( \frac { - 18 + \sqrt { 345 } } { 3 } , \frac { 9 - \sqrt { 345 } } { 3 } \right) , \left( \frac { - 18 - \sqrt { 345 } } { 3 } , \frac { 9 + \sqrt { 345 } } { 3 } \right)$,
$- 18$ $\varnothing$ 
C)  $\varnothing$
 
D)  $( 0,0 )$ 
A) 
$\left( \frac { 9 + \sqrt { 345 } } { 3 } , \frac { - 18 + \sqrt { 345 } } { 3 } \right) , \left( \frac { 9 + \sqrt { 345 } } { 3 } , \frac { - 18 - \sqrt { 345 } } { 3 } \right) , \left( \frac { 9 - \sqrt { 345 } } { 3 } , \frac { - 18 + \sqrt { 345 } } { 3 } \right)$, $\left\{ \frac { 9 - \sqrt { 345 } } { 3 } , \frac { - 18 - \sqrt { 345 } } { 3 } \right\}$ 
B) 
$\left\{ \frac { - 18 + \sqrt { 345 } } { 3 } , \frac { 9 + \sqrt { 345 } } { 3 } \right) , \left( \frac { - 18 + \sqrt { 345 } } { 3 } , \frac { 9 - \sqrt { 345 } } { 3 } \right) , \left( \frac { - 18 - \sqrt { 345 } } { 3 } , \frac { 9 + \sqrt { 345 } } { 3 } \right)$,
$- 18$ $\varnothing$ 
C)  $\varnothing$
 
D)  $( 0,0 )$

Question 2

Graph the system.
-$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \leq 36 \
\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } \geq 1
\end{array} \right.$

Accepted Answer

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

Question 3

Solve.
-How many real solutions are possible for a system of equations whose graphs are a parabola and a hyperbola?

Accepted Answer

A)  $0,1,2,3$, or 4 real solutions 
B)  $1,2,3$, or 4 real solutions 
C)  $0,1,2$, or 3 real solutions 
D)  1,2 , or 3 real solutions 
A)  $0,1,2,3$, or 4 real solutions 
B)  $1,2,3$, or 4 real solutions 
C)  $0,1,2$, or 3 real solutions 
D)  1,2 , or 3 real solutions

Question 4

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the
right. Do not graph.
-$x = 2 y ^ { 2 } - 5 y - 3$

Accepted Answer

A)  upward 
B)  downward 
C)  to the right 
D)  to the left 
A)  upward 
B)  downward 
C)  to the right 
D)  to the left

Question 5

Solve.
-An amusement park has a Ferris wheel with a height of 97 meters and a diameter of 94 meters. Using the drawing, write the equation of the wheel.

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 47 ^ { 2 }$ 
B)  $x ^ { 2 } + ( y - 50 ) ^ { 2 } = 47 ^ { 2 }$ 
C)  $x ^ { 2 } + ( y - 50 ) ^ { 2 } = 94 ^ { 2 }$ 
D)  $x ^ { 2 } + ( y + 50 ) ^ { 2 } = 47 ^ { 2 }$ 
A)  $x ^ { 2 } + y ^ { 2 } = 47 ^ { 2 }$ 
B)  $x ^ { 2 } + ( y - 50 ) ^ { 2 } = 47 ^ { 2 }$ 
C)  $x ^ { 2 } + ( y - 50 ) ^ { 2 } = 94 ^ { 2 }$ 
D)  $x ^ { 2 } + ( y + 50 ) ^ { 2 } = 47 ^ { 2 }$

Question 6

Graph the system.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } > 1 \
\frac { x ^ { 2 } } { 4 } - y ^ { 2 } \geq 1
\end{array} \right.$

Accepted Answer

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

Question 7

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola.
-$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph.
-$- x ^ { 2 } + 3 y ^ { 2 } = 8$

Accepted Answer

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

Question 10

Find the center and the radius of the circle.
-$x ^ { 2 } + ( y - 7 ) ^ { 2 } = 6$

Accepted Answer

A)  center $( 0,7 )$; radius $= 6$ 
B)  center $( 0,7 )$; radius $= \sqrt { 6 }$ 
C)  center $( 0,7 )$; radius $= 36$ 
D)  center $( 7,0 )$; radius $= \sqrt { 6 }$ 
A)  center $( 0,7 )$; radius $= 6$ 
B)  center $( 0,7 )$; radius $= \sqrt { 6 }$ 
C)  center $( 0,7 )$; radius $= 36$ 
D)  center $( 7,0 )$; radius $= \sqrt { 6 }$

Question 11

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{aligned}
10 x ^ { 2 } - 5 y ^ { 2 } & = 15 \
- x ^ { 2 } + y ^ { 2 } & = 1
\end{aligned} \right.$

Accepted Answer

A)  $( 2 , \sqrt { 5 } ) , ( - 2 , - \sqrt { 5 } )$ 
B)  $( \sqrt { 5 } , 2 ) , ( \sqrt { 5 } , - 2 ) , ( - \sqrt { 5 } , 2 ) , ( - \sqrt { 5 } , - 2 )$ 
C)  $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } ) , ( - 2 , \sqrt { 5 } ) , ( - 2 , - \sqrt { 5 } )$ 
D)  $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } )$ 
A)  $( 2 , \sqrt { 5 } ) , ( - 2 , - \sqrt { 5 } )$ 
B)  $( \sqrt { 5 } , 2 ) , ( \sqrt { 5 } , - 2 ) , ( - \sqrt { 5 } , 2 ) , ( - \sqrt { 5 } , - 2 )$ 
C)  $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } ) , ( - 2 , \sqrt { 5 } ) , ( - 2 , - \sqrt { 5 } )$ 
D)  $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } )$

Question 12

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.
-$2 x ^ { 2 } + 2 y ^ { 2 } = 4$

Accepted Answer

A)  center $( 2,2 )$; radius $= 2$
  
B)  center $( 2,2 )$; radius $= \sqrt { 2 }$
  
C)  center $( 0,0 )$; radius $= \sqrt { 2 }$
  
D)  center $( 0,0 )$; radius $= 2$
  
A)  center $( 2,2 )$; radius $= 2$
  
B)  center $( 2,2 )$; radius $= \sqrt { 2 }$
  
C)  center $( 0,0 )$; radius $= \sqrt { 2 }$
  
D)  center $( 0,0 )$; radius $= 2$

Question 13

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola.
-$x = y ^ { 2 } + 12 y + 34$

Accepted Answer

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

Question 14

Graph the equation.
-$\frac { x ^ { 2 } } { 25 } + y ^ { 2 } = 1$

Accepted Answer

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

Question 15

Graph the equation.
-$\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$

Accepted Answer

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

Question 16

Find the center and the radius of the circle.
-$( x + 1 ) ^ { 2 } + y ^ { 2 } = 16$

Accepted Answer

A)  center $( 0 , - 1 )$; radius $= 4$ 
B)  center $( - 1,0 )$; radius $= 4$ 
C)  center $( - 1,0 )$; radius $= 16$ 
D)  center $( 1,0 )$; radius $= 4$ 
A)  center $( 0 , - 1 )$; radius $= 4$ 
B)  center $( - 1,0 )$; radius $= 4$ 
C)  center $( - 1,0 )$; radius $= 16$ 
D)  center $( 1,0 )$; radius $= 4$

Question 17

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.
-$y=x^{2}-4$

Accepted Answer

A)  vertex $( 0,4 )$
  
B)  vertex $( 4,0 )$
  
C)  vertex $( - 4,0 )$
  
D)  vertex $( 0 , - 4 )$
  
A)  vertex $( 0,4 )$
  
B)  vertex $( 4,0 )$
  
C)  vertex $( - 4,0 )$
  
D)  vertex $( 0 , - 4 )$

Question 18

Graph the equation.
-$\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$

Accepted Answer

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

Question 19

Graph the system.
-$\left\{\begin{array}{r}
y>x^{2} \
4 x+5 y \leq 20
\end{array}\right.$

Accepted Answer

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

Question 20

Graph the equation.
-$9 x^{2}+25 y^{2}=225$

Accepted Answer

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

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + 2 y ^ { 2 } = - 7 \\x - y = - 9\end{array} \right.$

Solve. -How many real solutions are possible for a system of equations whose graphs are a parabola and a hyperbola?

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $x = 2 y ^ { 2 } - 5 y - 3$

Solve. -An amusement park has a Ferris wheel with a height of 97 meters and a diameter of 94 meters. Using the drawing, write the equation of the wheel.

Graph the system. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } > 1 \\\frac { x ^ { 2 } } { 4 } - y ^ { 2 } \geq 1\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } > 1 \\ \frac { x ^ { 2 } } { 4 } - y ^ { 2 } \geq 1 \end{array} \right.$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$

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

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - $- x ^ { 2 } + 3 y ^ { 2 } = 8$

Find the center and the radius of the circle. - $x ^ { 2 } + ( y - 7 ) ^ { 2 } = 6$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}10 x ^ { 2 } - 5 y ^ { 2 } & = 15 \\- x ^ { 2 } + y ^ { 2 } & = 1\end{aligned} \right.$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $x = y ^ { 2 } + 12 y + 34$

Graph the equation. - $\frac { x ^ { 2 } } { 25 } + y ^ { 2 } = 1$ $Graph the equation. - \frac { x ^ { 2 } } { 25 } + y ^ { 2 } = 1$

Graph the equation. - $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$

Find the center and the radius of the circle. - $( x + 1 ) ^ { 2 } + y ^ { 2 } = 16$

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

Graph the equation. - $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$

Graph the system. - $\left\{\begin{array}{r}y>x^{2} \\4 x+5 y \leq 20\end{array}\right.$ $Graph the system. - \left\{\begin{array}{r} y>x^{2} \\ 4 x+5 y \leq 20 \end{array}\right.$

Graph the equation. - $9 x^{2}+25 y^{2}=225$ $Graph the equation. - 9 x^{2}+25 y^{2}=225$

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

Solve the nonlinear system of equations for real solutions. - {x2+2y2=−7x−y=−9\left\{ \begin{array} { l } x ^ { 2 } + 2 y ^ { 2 } = - 7 \\x - y = - 9\end{array} \right.{x2+2y2=−7x−y=−9​

Graph the system. - {x2+y2≤36x225+y264≥1\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } \leq 36 \\\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } \geq 1\end{array} \right.{x2+y2≤3625x2​+64y2​≥1​

Solve. -How many real solutions are possible for a system of equations whose graphs are a parabola and a hyperbola?

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - x=2y2−5y−3x = 2 y ^ { 2 } - 5 y - 3x=2y2−5y−3

Solve. -An amusement park has a Ferris wheel with a height of 97 meters and a diameter of 94 meters. Using the drawing, write the equation of the wheel.

Graph the system. - {x2+y2>1x24−y2≥1\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } > 1 \\\frac { x ^ { 2 } } { 4 } - y ^ { 2 } \geq 1\end{array} \right.{x2+y2>14x2​−y2≥1​

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - y24−x225=1\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 14y2​−25x2​=1

Graph the inequality. - x2+y2≤4x^{2}+y^{2} \leq 4x2+y2≤4

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - −x2+3y2=8- x ^ { 2 } + 3 y ^ { 2 } = 8−x2+3y2=8

Find the center and the radius of the circle. - x2+(y−7)2=6x ^ { 2 } + ( y - 7 ) ^ { 2 } = 6x2+(y−7)2=6

Solve the nonlinear system of equations for real solutions. - {10x2−5y2=15−x2+y2=1\left\{ \begin{aligned}10 x ^ { 2 } - 5 y ^ { 2 } & = 15 \\- x ^ { 2 } + y ^ { 2 } & = 1\end{aligned} \right.{10x2−5y2−x2+y2​=15=1​

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. - 2x2+2y2=42 x ^ { 2 } + 2 y ^ { 2 } = 42x2+2y2=4

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - x=y2+12y+34x = y ^ { 2 } + 12 y + 34x=y2+12y+34

Graph the equation. - x225+y2=1\frac { x ^ { 2 } } { 25 } + y ^ { 2 } = 125x2​+y2=1

Graph the equation. - (x−2)216+(y−1)29=1\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 9 } = 116(x−2)2​+9(y−1)2​=1

Find the center and the radius of the circle. - (x+1)2+y2=16( x + 1 ) ^ { 2 } + y ^ { 2 } = 16(x+1)2+y2=16

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. - y=x2−4y=x^{2}-4y=x2−4

Graph the equation. - (x−2)24+(y+2)29=1\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 14(x−2)2​+9(y+2)2​=1

Graph the system. - {y>x24x+5y≤20\left\{\begin{array}{r}y>x^{2} \\4 x+5 y \leq 20\end{array}\right.{y>x24x+5y≤20​

Graph the equation. - 9x2+25y2=2259 x^{2}+25 y^{2}=2259x2+25y2=225

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

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + 2 y ^ { 2 } = - 7 \\x - y = - 9\end{array} \right.$

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $x = 2 y ^ { 2 } - 5 y - 3$

Graph the system. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } > 1 \\\frac { x ^ { 2 } } { 4 } - y ^ { 2 } \geq 1\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } > 1 \\ \frac { x ^ { 2 } } { 4 } - y ^ { 2 } \geq 1 \end{array} \right.$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$

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

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - $- x ^ { 2 } + 3 y ^ { 2 } = 8$

Find the center and the radius of the circle. - $x ^ { 2 } + ( y - 7 ) ^ { 2 } = 6$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}10 x ^ { 2 } - 5 y ^ { 2 } & = 15 \\- x ^ { 2 } + y ^ { 2 } & = 1\end{aligned} \right.$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $x = y ^ { 2 } + 12 y + 34$

Graph the equation. - $\frac { x ^ { 2 } } { 25 } + y ^ { 2 } = 1$ $Graph the equation. - \frac { x ^ { 2 } } { 25 } + y ^ { 2 } = 1$

Graph the equation. - $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$

Find the center and the radius of the circle. - $( x + 1 ) ^ { 2 } + y ^ { 2 } = 16$

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

Graph the equation. - $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$

Graph the system. - $\left\{\begin{array}{r}y>x^{2} \\4 x+5 y \leq 20\end{array}\right.$ $Graph the system. - \left\{\begin{array}{r} y>x^{2} \\ 4 x+5 y \leq 20 \end{array}\right.$

Graph the equation. - $9 x^{2}+25 y^{2}=225$ $Graph the equation. - 9 x^{2}+25 y^{2}=225$