Question 1

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
10 x ^ { 2 } + y ^ { 2 } = 100 \
10 x ^ { 2 } - y ^ { 2 } = 100
\end{array} \right.$

Accepted Answer

A)  $( \sqrt { 10 } , 0 ) , ( - \sqrt { 10 } , 0 )$ 
B)  $( 0,10 ) , ( 0 , - 10 )$ 
C)  $( 0 , \sqrt { 10 } ) , ( 0 , - \sqrt { 10 } )$ 
D)  $( 10,0 ) , ( - 10,0 )$ 
A)  $( \sqrt { 10 } , 0 ) , ( - \sqrt { 10 } , 0 )$ 
B)  $( 0,10 ) , ( 0 , - 10 )$ 
C)  $( 0 , \sqrt { 10 } ) , ( 0 , - \sqrt { 10 } )$ 
D)  $( 10,0 ) , ( - 10,0 )$

Question 2

Graph the equation.
-$9 x^{2}-4 y^{2}=36$

Accepted Answer

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

Question 3

Graph the equation.
-$\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$

Accepted Answer

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

Question 4

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola.
-$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$

Accepted Answer

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

Question 5

Sketch the graph of the equation.
-$y=x^{2}-4 x-2$

Accepted Answer

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

Question 6

Graph the system.
-Which graph best resembles the graph of $x = a ( y - k ) ^ { 2 } + h$ if $a  0$, and $k < 0$ ?
Graph 1
 
Graph 2
 
Graph 3
 
Graph 4

Accepted Answer

A)  Graph 4 
B)  Graph 1 
C)  Graph 2 
D)  Graph 3 
A)  Graph 4 
B)  Graph 1 
C)  Graph 2 
D)  Graph 3

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

A)  vertex $( 0 , - 2 )$
  
B)  vertex $( 0,0 )$
  
C)  vertex $( 0,0 )$
  
D)  vertex $( 0,0 )$
  
A)  vertex $( 0 , - 2 )$
  
B)  vertex $( 0,0 )$
  
C)  vertex $( 0,0 )$
  
D)  vertex $( 0,0 )$

Question 9

Solve the system.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 89 \
x ^ { 2 } - y ^ { 2 } = - 39
\end{array} \right.$

Accepted Answer

A)  $( - 5 , - 8 ) , ( - 8 , - 5 )$ 
B)  $( 5 , - 8 ) , ( 5,8 )$ 
C)  $( 5,8 ) , ( 8,5 ) , ( - 5 , - 8 ) , ( - 8 , - 5 )$ 
D)  $( 5,8 ) , ( - 5,8 ) , ( 5 , - 8 ) , ( - 5 , - 8 )$ 
A)  $( - 5 , - 8 ) , ( - 8 , - 5 )$ 
B)  $( 5 , - 8 ) , ( 5,8 )$ 
C)  $( 5,8 ) , ( 8,5 ) , ( - 5 , - 8 ) , ( - 8 , - 5 )$ 
D)  $( 5,8 ) , ( - 5,8 ) , ( 5 , - 8 ) , ( - 5 , - 8 )$

Question 10

Graph the inequality.
-$\frac{x^{2}}{4}+\frac{y^{2}}{16} \leq 1$

Accepted Answer

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

Question 11

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 41 \
x - y = 1
\end{array} \right.$

Accepted Answer

A)  $( 5,4 ) , ( - 4 , - 5 )$ 
B)  $( - 5,4 ) , ( - 4,5 )$ 
C)  $( - 5 , - 4 ) , ( - 4 , - 5 )$ 
D)  $( 5 , - 4 ) , ( 4 , - 5 )$ 
A)  $( 5,4 ) , ( - 4 , - 5 )$ 
B)  $( - 5,4 ) , ( - 4,5 )$ 
C)  $( - 5 , - 4 ) , ( - 4 , - 5 )$ 
D)  $( 5 , - 4 ) , ( 4 , - 5 )$

Question 12

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
3 x ^ { 2 } - 5 y ^ { 2 } = 28 \
4 x ^ { 2 } + 3 y ^ { 2 } = 76
\end{array} \right.$

Accepted Answer

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

Question 13

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

Accepted Answer

A)  center $\left( \frac { 3 } { 2 } , 0 \right)$; radius $= \frac { 3 } { 2 }$
  
B)  center $\left( 0 , \frac { 3 } { 2 } \right) ;$ radius $= \frac { 3 } { 2 }$
  
C)  center $( 0,0 )$; radius $= 3$
  
D)  center $( 0,0 )$; radius $= \sqrt { 3 }$
  
A)  center $\left( \frac { 3 } { 2 } , 0 \right)$; radius $= \frac { 3 } { 2 }$
  
B)  center $\left( 0 , \frac { 3 } { 2 } \right) ;$ radius $= \frac { 3 } { 2 }$
  
C)  center $( 0,0 )$; radius $= 3$
  
D)  center $( 0,0 )$; radius $= \sqrt { 3 }$

Question 14

Graph the inequality.
-$\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } > 1$

Accepted Answer

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

Question 15

Solve.
-Comet's orbit the Sun in elongated ellipses. Consider the Sun as the origin of a rectangular coordina system. Suppose that the equation of the path of the comet is
$\frac { ( \mathrm { x } - 646,000,000 ) ^ { 2 } } { 6.022 \times 10 ^ { 23 } } + \frac { ( \mathrm { y } + 374,000,000 ) ^ { 2 } } { 3.011 \times 10 ^ { 22 } } = 1$
Find the center of the path of the comet.

Accepted Answer

A)  $( - 646,000,000 , - 374,000,000 )$ 
B)  $( - 646,000,000,374,000,000 )$ 
C)  $( 646,000,000,374,000,000 )$ 
D)  $( 646,000,000 , - 374,000,000 )$ e 
A)  $( - 646,000,000 , - 374,000,000 )$ 
B)  $( - 646,000,000,374,000,000 )$ 
C)  $( 646,000,000,374,000,000 )$ 
D)  $( 646,000,000 , - 374,000,000 )$ e

Question 16

Graph the system.
-$\left\{ \begin{array} { r } 
2 x + 3 y \geq 6 \
x - y \geq 3 \
y \leq 2
\end{array} \right.$

Accepted Answer

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

Question 17

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { r } 
x ^ { 2 } + 3 y ^ { 2 } = 8 \
y = x
\end{array} \right.$

Accepted Answer

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

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.
-$x ^ { 2 } + 4 x + y ^ { 2 } + 6 y - 2 = 0$

Accepted Answer

A)  center $( - 2 , - 3 )$; radius $= 15$
  
B)  center $( 2 , - 3 )$; radius $= \sqrt { 15 }$
  
C)  center $( - 2 , - 3 )$; radius $= \sqrt { 15 }$
  
D)  center $( 2,3 )$; radius $= \sqrt { 15 }$
  
A)  center $( - 2 , - 3 )$; radius $= 15$
  
B)  center $( 2 , - 3 )$; radius $= \sqrt { 15 }$
  
C)  center $( - 2 , - 3 )$; radius $= \sqrt { 15 }$
  
D)  center $( 2,3 )$; radius $= \sqrt { 15 }$

Question 19

Sketch the graph of the equation.
-$x=y^{2}+10 y+31$

Accepted Answer

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

Question 20

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { r } 
20 x - y = 1 \
x y = 1
\end{array} \right.$

Accepted Answer

A)  $\left( \frac { 1 } { 4 } , 4 \right) , \left( - \frac { 1 } { 5 } , - 5 \right)$ 
B)  $\left( 4 , \frac { 1 } { 4 } \right) , \left( - 5 , - \frac { 1 } { 5 } \right)$ 
C)  $\varnothing$ 
D)  $( - 4,4 ) , ( 5 , - 5 )$ 
A)  $\left( \frac { 1 } { 4 } , 4 \right) , \left( - \frac { 1 } { 5 } , - 5 \right)$ 
B)  $\left( 4 , \frac { 1 } { 4 } \right) , \left( - 5 , - \frac { 1 } { 5 } \right)$ 
C)  $\varnothing$ 
D)  $( - 4,4 ) , ( 5 , - 5 )$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } 10 x ^ { 2 } + y ^ { 2 } = 100 \\10 x ^ { 2 } - y ^ { 2 } = 100\end{array} \right.$

Graph the equation. - $9 x^{2}-4 y^{2}=36$ $Graph the equation. - 9 x^{2}-4 y^{2}=36$

Graph the equation. - $\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$

Sketch the graph of the equation. - $y=x^{2}-4 x-2$ $Sketch the graph of the equation. - y=x^{2}-4 x-2$

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

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

Solve the system. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 89 \\x ^ { 2 } - y ^ { 2 } = - 39\end{array} \right.$

Graph the inequality. - $\frac{x^{2}}{4}+\frac{y^{2}}{16} \leq 1$ $Graph the inequality. - \frac{x^{2}}{4}+\frac{y^{2}}{16} \leq 1$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 41 \\x - y = 1\end{array} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } 3 x ^ { 2 } - 5 y ^ { 2 } = 28 \\4 x ^ { 2 } + 3 y ^ { 2 } = 76\end{array} \right.$

Graph the inequality. - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } > 1$ $Graph the inequality. - \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } > 1$

Graph the system. - $\left\{ \begin{array} { r } 2 x + 3 y \geq 6 \\x - y \geq 3 \\y \leq 2\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { r } 2 x + 3 y \geq 6 \\ x - y \geq 3 \\ y \leq 2 \end{array} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { r } x ^ { 2 } + 3 y ^ { 2 } = 8 \\y = x\end{array} \right.$

Sketch the graph of the equation. - $x=y^{2}+10 y+31$ $Sketch the graph of the equation. - x=y^{2}+10 y+31$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { r } 20 x - y = 1 \\x y = 1\end{array} \right.$

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

Solve the nonlinear system of equations for real solutions. - {10x2+y2=10010x2−y2=100\left\{ \begin{array} { l } 10 x ^ { 2 } + y ^ { 2 } = 100 \\10 x ^ { 2 } - y ^ { 2 } = 100\end{array} \right.{10x2+y2=10010x2−y2=100​

Graph the equation. - 9x2−4y2=369 x^{2}-4 y^{2}=369x2−4y2=36

Graph the equation. - (x−2)225−(y+1)29=1\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 9 } = 125(x−2)2​−9(y+1)2​=1

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - x225+y29=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 125x2​+9y2​=1

Sketch the graph of the equation. - y=x2−4x−2y=x^{2}-4 x-2y=x2−4x−2

Graph the system. -Which graph best resembles the graph of x=a(y−k)2+hx = a ( y - k ) ^ { 2 } + hx=a(y−k)2+h if a<0,h>0a < 0 , h > 0a<0,h>0 , and k<0k < 0k<0 ? Graph 1 Graph 2 Graph 3 Graph 4

Graph the inequality. - y≤x2+6x+4y \leq x^{2}+6 x+4y≤x2+6x+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=−2x2y=-2 x^{2}y=−2x2

Solve the system. - {x2+y2=89x2−y2=−39\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 89 \\x ^ { 2 } - y ^ { 2 } = - 39\end{array} \right.{x2+y2=89x2−y2=−39​

Graph the inequality. - x24+y216≤1\frac{x^{2}}{4}+\frac{y^{2}}{16} \leq 14x2​+16y2​≤1

Solve the nonlinear system of equations for real solutions. - {x2+y2=41x−y=1\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 41 \\x - y = 1\end{array} \right.{x2+y2=41x−y=1​

Solve the nonlinear system of equations for real solutions. - {3x2−5y2=284x2+3y2=76\left\{ \begin{array} { l } 3 x ^ { 2 } - 5 y ^ { 2 } = 28 \\4 x ^ { 2 } + 3 y ^ { 2 } = 76\end{array} \right.{3x2−5y2=284x2+3y2=76​

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=9x^{2}+y^{2}=9x2+y2=9

Graph the inequality. - x24+y249>1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } > 14x2​+49y2​>1

Graph the system. - {2x+3y≥6x−y≥3y≤2\left\{ \begin{array} { r } 2 x + 3 y \geq 6 \\x - y \geq 3 \\y \leq 2\end{array} \right.⎩⎨⎧​2x+3y≥6x−y≥3y≤2​

Solve the nonlinear system of equations for real solutions. - {x2+3y2=8y=x\left\{ \begin{array} { r } x ^ { 2 } + 3 y ^ { 2 } = 8 \\y = x\end{array} \right.{x2+3y2=8y=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. - x2+4x+y2+6y−2=0x ^ { 2 } + 4 x + y ^ { 2 } + 6 y - 2 = 0x2+4x+y2+6y−2=0

Sketch the graph of the equation. - x=y2+10y+31x=y^{2}+10 y+31x=y2+10y+31

Solve the nonlinear system of equations for real solutions. - {20x−y=1xy=1\left\{ \begin{array} { r } 20 x - y = 1 \\x y = 1\end{array} \right.{20x−y=1xy=1​

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. - $\left\{ \begin{array} { l } 10 x ^ { 2 } + y ^ { 2 } = 100 \\10 x ^ { 2 } - y ^ { 2 } = 100\end{array} \right.$

Graph the equation. - $9 x^{2}-4 y^{2}=36$ $Graph the equation. - 9 x^{2}-4 y^{2}=36$

Graph the equation. - $\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$

Sketch the graph of the equation. - $y=x^{2}-4 x-2$ $Sketch the graph of the equation. - y=x^{2}-4 x-2$

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

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

Solve the system. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 89 \\x ^ { 2 } - y ^ { 2 } = - 39\end{array} \right.$

Graph the inequality. - $\frac{x^{2}}{4}+\frac{y^{2}}{16} \leq 1$ $Graph the inequality. - \frac{x^{2}}{4}+\frac{y^{2}}{16} \leq 1$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 41 \\x - y = 1\end{array} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } 3 x ^ { 2 } - 5 y ^ { 2 } = 28 \\4 x ^ { 2 } + 3 y ^ { 2 } = 76\end{array} \right.$

Graph the inequality. - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } > 1$ $Graph the inequality. - \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } > 1$

Graph the system. - $\left\{ \begin{array} { r } 2 x + 3 y \geq 6 \\x - y \geq 3 \\y \leq 2\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { r } 2 x + 3 y \geq 6 \\ x - y \geq 3 \\ y \leq 2 \end{array} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { r } x ^ { 2 } + 3 y ^ { 2 } = 8 \\y = x\end{array} \right.$

Sketch the graph of the equation. - $x=y^{2}+10 y+31$ $Sketch the graph of the equation. - x=y^{2}+10 y+31$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { r } 20 x - y = 1 \\x y = 1\end{array} \right.$