Question 1

Solve.
-The sum of the squares of two numbers is 106. The difference of the two numbers is 4. Find the two numbers.

Accepted Answer

A)  5 and 9 
B)  $- 9$ and $5 ; - 5$ and 9 
C)  $- 9$ and $- 5 ; 5$ and 9 
D)  $- 9$ and $- 5$ 
A)  5 and 9 
B)  $- 9$ and $5 ; - 5$ and 9 
C)  $- 9$ and $- 5 ; 5$ and 9 
D)  $- 9$ and $- 5$

Question 2

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.
-$x = y ^ { 2 } + 16 y - 1$

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 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.
-$x=-2 y^{2}-8 y-7$

Accepted Answer

A)  vertex $( - 2,1 )$
  
B)  vertex $( - 1,2 )$
  
C)  vertex $( 1 , - 2 )$
  
D)  vertex $( 1,2 )$

Question 5

Graph the equation.
-$16 x^{2}+4 y^{2}=64$

Accepted Answer

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

Question 6

Find the center and the radius of the circle.
-$x ^ { 2 } + y ^ { 2 } + 6 x + 16 y + 9 = 0$

Accepted Answer

A)  center $( 8,3 )$, radius $= 64$ 
B)  center $( - 3 , - 8 )$, radius $= 8$ 
C)  center $( 3,8 )$, radius $= 64$ 
D)  center $( - 8 , - 3 )$, radius $= 8$ 
A)  center $( 8,3 )$, radius $= 64$ 
B)  center $( - 3 , - 8 )$, radius $= 8$ 
C)  center $( 3,8 )$, radius $= 64$ 
D)  center $( - 8 , - 3 )$, radius $= 8$

Question 7

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + 3 y ^ { 2 } = 6 \
x ^ { 2 } - 3 y ^ { 2 } = 8
\end{array} \right.$

Accepted Answer

A)  $( \sqrt { 7 } , 1 ) , ( \sqrt { 7 } , - 1 )$ 
B)  $\varnothing$ 
C)  $( \sqrt { 7 } , 1 ) , ( - \sqrt { 7 } , - 1 )$ 
D)  $( \sqrt { 7 } , 1 ) , ( \sqrt { 7 } , - 1 ) , ( - \sqrt { 7 } , 1 ) , ( - \sqrt { 7 } , - 1 )$ 
A)  $( \sqrt { 7 } , 1 ) , ( \sqrt { 7 } , - 1 )$ 
B)  $\varnothing$ 
C)  $( \sqrt { 7 } , 1 ) , ( - \sqrt { 7 } , - 1 )$ 
D)  $( \sqrt { 7 } , 1 ) , ( \sqrt { 7 } , - 1 ) , ( - \sqrt { 7 } , 1 ) , ( - \sqrt { 7 } , - 1 )$

Question 8

Graph the system.
-$\left\{ \begin{aligned}
x ^ { 2 } + y ^ { 2 } & \leq 49 \
x & < y ^ { 2 }
\end{aligned} \right.$

Accepted Answer

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

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.
-$x=-(y-3)^{2}+2$

Accepted Answer

A)  vertex $( 2,3 )$
  
B)  vertex $( 2,3 )$
  
C)  vertex $( - 3 , - 2 )$
  
D)  vertex $( - 2 , - 3 )$
  
A)  vertex $( 2,3 )$
  
B)  vertex $( 2,3 )$
  
C)  vertex $( - 3 , - 2 )$
  
D)  vertex $( - 2 , - 3 )$

Question 10

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 13 \
x + y = 5
\end{array} \right.$

Accepted Answer

A)  $( 3 , - 2 ) , ( 2 , - 3 )$ 
B)  $( - 3 , - 2 ) , ( - 2 , - 3 )$ 
C)  $( 3,2 ) , ( 2,3 )$ 
D)  $( - 3,2 ) , ( - 2,3 )$ 
A)  $( 3 , - 2 ) , ( 2 , - 3 )$ 
B)  $( - 3 , - 2 ) , ( - 2 , - 3 )$ 
C)  $( 3,2 ) , ( 2,3 )$ 
D)  $( - 3,2 ) , ( - 2,3 )$

Question 11

Graph the system.
-$\left\{\begin{aligned}
x^{2}+y^{2} & \geq 9 \
x^{2}+y^{2} &<36 \
y & \leq 0
\end{aligned}\right.$

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Sketch the graph of the equation.
-$16 x^{2}+25 y^{2}=400$

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{aligned}
x ^ { 2 } + y ^ { 2 } & = 4 \
y & = \frac { 1 } { 2 } x ^ { 2 } - 2
\end{aligned} \right.$

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Find the center and the radius of the circle.
-$x ^ { 2 } + ( y - 8 ) ^ { 2 } = 64$

Accepted Answer

A)  center $( 0 , - 8 )$; radius $= 8$ 
B)  center $( 8,0 )$; radius $= 8$ 
C)  center $( 0,8 )$; radius $= 8$ 
D)  center $( 0,8 )$; radius $= 64$ 
A)  center $( 0 , - 8 )$; radius $= 8$ 
B)  center $( 8,0 )$; radius $= 8$ 
C)  center $( 0,8 )$; radius $= 8$ 
D)  center $( 0,8 )$; radius $= 64$

Question 19

Solve the system.
-$\left\{ \begin{array} { l } 
y = x ^ { 2 } - 8 x + 16 \
y = - x + 6
\end{array} \right.$

Accepted Answer

A)  $( 4,2 )$ 
B)  $( 2,4 ) , ( 5,1 )$ 
C)  $( 2,8 ) , ( 5,1 )$ 
D)  $( - 2,8 ) , ( - 5,11 )$ 
A)  $( 4,2 )$ 
B)  $( 2,4 ) , ( 5,1 )$ 
C)  $( 2,8 ) , ( 5,1 )$ 
D)  $( - 2,8 ) , ( - 5,11 )$

Question 20

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

Accepted Answer

A)  vertex $( 5 , - 2 )$
  
B)  vertex $( - 5,2 )$
  
C)  vertex $( - 2,5 )$
  
D)  vertex $( 2,5 )$
  
A)  vertex $( 5 , - 2 )$
  
B)  vertex $( - 5,2 )$
  
C)  vertex $( - 2,5 )$
  
D)  vertex $( 2,5 )$

Solve. -The sum of the squares of two numbers is 106. The difference of the two numbers is 4. Find the two numbers.

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. - $x = y ^ { 2 } + 16 y - 1$

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

Graph the equation. - $16 x^{2}+4 y^{2}=64$ $Graph the equation. - 16 x^{2}+4 y^{2}=64$

Find the center and the radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 6 x + 16 y + 9 = 0$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + 3 y ^ { 2 } = 6 \\x ^ { 2 } - 3 y ^ { 2 } = 8\end{array} \right.$

Graph the system. - $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & \leq 49 \\x & < y ^ { 2 }\end{aligned} \right.$ $Graph the system. - \left\{ \begin{aligned} x ^ { 2 } + y ^ { 2 } & \leq 49 \\ x & < y ^ { 2 } \end{aligned} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 13 \\x + y = 5\end{array} \right.$

Graph the system. - $\left\{\begin{aligned}x^{2}+y^{2} & \geq 9 \\x^{2}+y^{2} &<36 \\y & \leq 0\end{aligned}\right.$ $Graph the system. - \left\{\begin{aligned} x^{2}+y^{2} & \geq 9 \\ x^{2}+y^{2} &<36 \\ y & \leq 0 \end{aligned}\right.$

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

Sketch the graph of the equation. - $16 x^{2}+25 y^{2}=400$ $Sketch the graph of the equation. - 16 x^{2}+25 y^{2}=400$

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

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 4 \\y & = \frac { 1 } { 2 } x ^ { 2 } - 2\end{aligned} \right.$

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

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

Find the center and the radius of the circle. - $x ^ { 2 } + ( y - 8 ) ^ { 2 } = 64$

Solve the system. - $\left\{ \begin{array} { l } y = x ^ { 2 } - 8 x + 16 \\y = - x + 6\end{array} \right.$

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 sum of the squares of two numbers is 106. The difference of the two numbers is 4. Find the two numbers.

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=y2+16y−1x = y ^ { 2 } + 16 y - 1x=y2+16y−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. - x=−4y2x=-4 y^{2}x=−4y2

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=−2y2−8y−7x=-2 y^{2}-8 y-7x=−2y2−8y−7

Graph the equation. - 16x2+4y2=6416 x^{2}+4 y^{2}=6416x2+4y2=64

Find the center and the radius of the circle. - x2+y2+6x+16y+9=0x ^ { 2 } + y ^ { 2 } + 6 x + 16 y + 9 = 0x2+y2+6x+16y+9=0

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

Graph the system. - {x2+y2≤49x<y2\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & \leq 49 \\x & < y ^ { 2 }\end{aligned} \right.{x2+y2x​≤49<y2​

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−3)2+2x=-(y-3)^{2}+2x=−(y−3)2+2

Solve the nonlinear system of equations for real solutions. - {x2+y2=13x+y=5\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 13 \\x + y = 5\end{array} \right.{x2+y2=13x+y=5​

Graph the system. - {x2+y2≥9x2+y2<36y≤0\left\{\begin{aligned}x^{2}+y^{2} & \geq 9 \\x^{2}+y^{2} &<36 \\y & \leq 0\end{aligned}\right.⎩⎨⎧​x2+y2x2+y2y​≥9<36≤0​

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

Sketch the graph of the equation. - 16x2+25y2=40016 x^{2}+25 y^{2}=40016x2+25y2=400

Graph the equation. - 25x2+y2=2525 x^{2}+y^{2}=2525x2+y2=25

Solve the nonlinear system of equations for real solutions. - {x2+y2=4y=12x2−2\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 4 \\y & = \frac { 1 } { 2 } x ^ { 2 } - 2\end{aligned} \right.⎩⎨⎧​x2+y2y​=4=21​x2−2​

Graph the equation. - x29−y249=1\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 49 } = 19x2​−49y2​=1

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

Find the center and the radius of the circle. - x2+(y−8)2=64x ^ { 2 } + ( y - 8 ) ^ { 2 } = 64x2+(y−8)2=64

Solve the system. - {y=x2−8x+16y=−x+6\left\{ \begin{array} { l } y = x ^ { 2 } - 8 x + 16 \\y = - x + 6\end{array} \right.{y=x2−8x+16y=−x+6​

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)2+5y=(x+2)^{2}+5y=(x+2)2+5

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

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. - $x = y ^ { 2 } + 16 y - 1$

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

Graph the equation. - $16 x^{2}+4 y^{2}=64$ $Graph the equation. - 16 x^{2}+4 y^{2}=64$

Find the center and the radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 6 x + 16 y + 9 = 0$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + 3 y ^ { 2 } = 6 \\x ^ { 2 } - 3 y ^ { 2 } = 8\end{array} \right.$

Graph the system. - $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & \leq 49 \\x & < y ^ { 2 }\end{aligned} \right.$ $Graph the system. - \left\{ \begin{aligned} x ^ { 2 } + y ^ { 2 } & \leq 49 \\ x & < y ^ { 2 } \end{aligned} \right.$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 13 \\x + y = 5\end{array} \right.$

Graph the system. - $\left\{\begin{aligned}x^{2}+y^{2} & \geq 9 \\x^{2}+y^{2} &<36 \\y & \leq 0\end{aligned}\right.$ $Graph the system. - \left\{\begin{aligned} x^{2}+y^{2} & \geq 9 \\ x^{2}+y^{2} &<36 \\ y & \leq 0 \end{aligned}\right.$

Sketch the graph of the equation. - $16 x^{2}+25 y^{2}=400$ $Sketch the graph of the equation. - 16 x^{2}+25 y^{2}=400$

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

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 4 \\y & = \frac { 1 } { 2 } x ^ { 2 } - 2\end{aligned} \right.$

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

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

Find the center and the radius of the circle. - $x ^ { 2 } + ( y - 8 ) ^ { 2 } = 64$

Solve the system. - $\left\{ \begin{array} { l } y = x ^ { 2 } - 8 x + 16 \\y = - x + 6\end{array} \right.$