Question 1

Find the equation of the circle.
-

Accepted Answer

A)  $(x-4)^{2}+(y-2)^{2}=16$ 
B)  $(x-4)^{2}+(y-2)^{2}=2$ 
C)  $(x-4)^{2}-(y-2)^{2}=16$ 
D)  $(x-4)^{2}+(y-2)^{2}=4$ 
A)  $(x-4)^{2}+(y-2)^{2}=16$ 
B)  $(x-4)^{2}+(y-2)^{2}=2$ 
C)  $(x-4)^{2}-(y-2)^{2}=16$ 
D)  $(x-4)^{2}+(y-2)^{2}=4$

Question 2

Solve the system by the substitution method.
-$x^{2}+y^{2}=23$
$\mathrm{y}^{2}=2 \mathrm{x}+20$

Accepted Answer

A)  $(2, \sqrt{22}),(-3, \sqrt{14}),(2,-\sqrt{22}),(-3,-\sqrt{14})$ 
B)  $(1, \sqrt{22}),(-2, \sqrt{14}),(1,-\sqrt{22}),(-2,-\sqrt{14})$ 
C)  $(1, \sqrt{23}),(-3, \sqrt{23}),(1,-\sqrt{23}),(-3,-\sqrt{23})$ 
D)  $(1, \sqrt{22}),(-3, \sqrt{14}),(1,-\sqrt{22}),(-3,-\sqrt{14})$ 
A)  $(2, \sqrt{22}),(-3, \sqrt{14}),(2,-\sqrt{22}),(-3,-\sqrt{14})$ 
B)  $(1, \sqrt{22}),(-2, \sqrt{14}),(1,-\sqrt{22}),(-2,-\sqrt{14})$ 
C)  $(1, \sqrt{23}),(-3, \sqrt{23}),(1,-\sqrt{23}),(-3,-\sqrt{23})$ 
D)  $(1, \sqrt{22}),(-3, \sqrt{14}),(1,-\sqrt{22}),(-3,-\sqrt{14})$

Question 3

Find the midpoint of the line segment that connects the given points.
-$(0,-6)$ and $(-8,2)$

Accepted Answer

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

Question 4

Solve the problem.
-An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 6.25 inches tall and stand 50 inches apart. At some point along the road from the lowest point of the cable, the cable is 0.56 inches above the roadway. Find the distance between that point and the base of the nearest tower.

Accepted Answer

A)  $7.3 \mathrm{in}$. 
B)  $7.7 \mathrm{in.}$ 
C)  $17.5 \mathrm{in}$. 
D)  $17.7 \mathrm{in.}$ 
A)  $7.3 \mathrm{in}$. 
B)  $7.7 \mathrm{in.}$ 
C)  $17.5 \mathrm{in}$. 
D)  $17.7 \mathrm{in.}$

Question 5

Find the vertex of the parabola by completing the square.
-$x=y^{2}+2 y+6$

Accepted Answer

A)  $(5,-1)$ 
B)  $(1,7)$ 
C)  $(-1,5)$ 
D)  $(5,1)$ 
A)  $(5,-1)$ 
B)  $(1,7)$ 
C)  $(-1,5)$ 
D)  $(5,1)$

Question 6

Graph the parabola. State the vertex of the parabola.
-$x=y^{2}+4 y+2$

Accepted Answer

A)  vertex $ (-2,2) $
  
B)  vertex $ (-2,-2) $
  
C)  vertex $ (2,6) $
  
D)  vertex $ (-2,-2) $
  
A)  vertex $ (-2,2) $
  
B)  vertex $ (-2,-2) $
  
C)  vertex $ (2,6) $
  
D)  vertex $ (-2,-2) $

Question 7

Solve.
-A picture frame has a perimeter of $98 \mathrm{~cm}$ and a diagonal $\sqrt{1313} \mathrm{~cm}$. What are the dimensions?

Accepted Answer

A)  $17 \mathrm{~cm}$ by $32 \mathrm{~cm}$ 
B)  $17 \mathrm{~cm}$ by $33 \mathrm{~cm}$ 
C)  $18 \mathrm{~cm}$ by $31 \mathrm{~cm}$ 
D)  $18 \mathrm{~cm}$ by $32 \mathrm{~cm}$ 
A)  $17 \mathrm{~cm}$ by $32 \mathrm{~cm}$ 
B)  $17 \mathrm{~cm}$ by $33 \mathrm{~cm}$ 
C)  $18 \mathrm{~cm}$ by $31 \mathrm{~cm}$ 
D)  $18 \mathrm{~cm}$ by $32 \mathrm{~cm}$

Question 8

Find the standard-form equation of the hyperbola whose graph is shown.
-

Accepted Answer

A)  $\frac{y^{2}}{16}-\frac{x^{2}}{25}=1$ 
B)  $4 y^{2}-5 x^{2}=1$ 
C)  $16 y^{2}-25 x^{2}=1$ 
D)  $\frac{y^{2}}{4}-\frac{x^{2}}{5}=1$ 
A)  $\frac{y^{2}}{16}-\frac{x^{2}}{25}=1$ 
B)  $4 y^{2}-5 x^{2}=1$ 
C)  $16 y^{2}-25 x^{2}=1$ 
D)  $\frac{y^{2}}{4}-\frac{x^{2}}{5}=1$

Question 9

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$.
-$\frac{(x+2)^{2}}{9}+(y+1)^{2}=1$

Accepted Answer

A)  center $ (-2,-1), a=3, b=1 $
  
B)  center $ (-2,-1), a=1, b=3 $
  
C)  center $ (-2,-1), a=1, b=3 $
  
D)  center $ (-2,-1), a=3, b=1 $
  
A)  center $ (-2,-1), a=3, b=1 $
  
B)  center $ (-2,-1), a=1, b=3 $
  
C)  center $ (-2,-1), a=1, b=3 $
  
D)  center $ (-2,-1), a=3, b=1 $

Question 10

Solve the system by the substitution method.
-$x^{2}+y^{2}=104$
$\mathrm{x}^{2}-\mathrm{y}^{2}=96$

Accepted Answer

A)  $(10,-2),(10,2)$ 
B)  $(-10,-2),(-2,-10)$ 
C)  $(10,2),(-10,2),(10,-2),(-10,-2)$ 
D)  $(10,2),(2,10),(-10,-2),(-2,-10)$ 
A)  $(10,-2),(10,2)$ 
B)  $(-10,-2),(-2,-10)$ 
C)  $(10,2),(-10,2),(10,-2),(-10,-2)$ 
D)  $(10,2),(2,10),(-10,-2),(-2,-10)$

Question 11

Solve.
-The area of an ellipse given by the equation $\frac{(\mathrm{x}-\mathrm{h})^{2}}{\mathrm{a}^{2}}+\frac{(\mathrm{y}-\mathrm{k})^{2}}{\mathrm{~b}^{2}}=1$ is $\pi \mathrm{ab}$. A small park in the shape of an ellipse covers an area of 1432.57 square meters. The park measures 48 meters from east to west, what is the distance from north to south?

Accepted Answer

A)  $38 \mathrm{~m}$ 
B)  $576 \mathrm{~m}$ 
C)  $361 \mathrm{~m}$ 
D)  $48 \mathrm{~m}$ 
A)  $38 \mathrm{~m}$ 
B)  $576 \mathrm{~m}$ 
C)  $361 \mathrm{~m}$ 
D)  $48 \mathrm{~m}$

Question 12

Find the equation of the parabola of the form $x=a y^{2}+b y+c$ that passes through the given three points.
-$y^{2}=8 x$

Accepted Answer

A)  vertex: $ (0,0) $; focus $ (2,0) $; directrix $ x=-2 $
  
B)  vertex: $ (0,0) $; focus $ (1,0) $; directrix $ x=-1 $
  
C)  vertex: $ (0,0) $; focus $ (1,0) $; directrix $ x=-1 $
  
D)  vertex: $ (0,0) $; focus $ (2,0) $; directrix $ x=-2 $
  
A)  vertex: $ (0,0) $; focus $ (2,0) $; directrix $ x=-2 $
  
B)  vertex: $ (0,0) $; focus $ (1,0) $; directrix $ x=-1 $
  
C)  vertex: $ (0,0) $; focus $ (1,0) $; directrix $ x=-1 $
  
D)  vertex: $ (0,0) $; focus $ (2,0) $; directrix $ x=-2 $

Question 13

Graph the parabola. State the vertex of the parabola.
-$y =-(x+6)^2-1$

Accepted Answer

A)  vertex $ (1,6) $
  
B)  vertex $ (-6,-1) $
  
C)  vertex $ (-1,-6) $
  
D)  vertex $ (6,-1) $
  
A)  vertex $ (1,6) $
  
B)  vertex $ (-6,-1) $
  
C)  vertex $ (-1,-6) $
  
D)  vertex $ (6,-1) $

Question 14

Solve the system by the substitution method.
-y = x2 - 10x + 25 
x + y = 7

Accepted Answer

A)  $(6,13),(3,4)$ 
B)  $(5,2)$ 
C)  $(6,1),(3,4)$ 
D)  $(-6,13),(-3,10)$ 
A)  $(6,13),(3,4)$ 
B)  $(5,2)$ 
C)  $(6,1),(3,4)$ 
D)  $(-6,13),(-3,10)$

Question 15

Solve the problem.
-

Accepted Answer

A)  $(y+7)^{2}=4(x+2)$ 
B)  $(x+2)^{2}=-4(y+7)$ 
C)  $(x+7)^{2}=4(y+2)$ 
D)  $(y+2)^{2}=-4(x+7)$ 
A)  $(y+7)^{2}=4(x+2)$ 
B)  $(x+2)^{2}=-4(y+7)$ 
C)  $(x+7)^{2}=4(y+2)$ 
D)  $(y+2)^{2}=-4(x+7)$

Question 16

Find the equation of the circle.
-

Accepted Answer

A)  $(x-9)^{2}+(y-7)^{2}=25$ 
B)  $(x+9)^{2}+(y-7)^{2}=25$ 
C)  $(x+9)^{2}+(y+7)^{2}=25$ 
D)  $(x-9)^{2}+(y+7)^{2}=25$ 
A)  $(x-9)^{2}+(y-7)^{2}=25$ 
B)  $(x+9)^{2}+(y-7)^{2}=25$ 
C)  $(x+9)^{2}+(y+7)^{2}=25$ 
D)  $(x-9)^{2}+(y+7)^{2}=25$

Question 17

Solve.
-The diagonal of a Persian rug measures $10 \mathrm{ft}$. The area of the rug is $48 \mathrm{ft}^{2}$. Find the dimensions of the rug.

Accepted Answer

A)  $24 \mathrm{ft}$ by $24 \mathrm{ft}$ 
B)  $8 \mathrm{ft}$ by $6 \mathrm{ft}$ 
C)  $16 \mathrm{ft}$ by $3 \mathrm{ft}$ 
D)  $12 \mathrm{ft}$ by $4 \mathrm{ft}$ 
A)  $24 \mathrm{ft}$ by $24 \mathrm{ft}$ 
B)  $8 \mathrm{ft}$ by $6 \mathrm{ft}$ 
C)  $16 \mathrm{ft}$ by $3 \mathrm{ft}$ 
D)  $12 \mathrm{ft}$ by $4 \mathrm{ft}$

Question 18

Find the vertex of the parabola by completing the square.
-$x=-y^{2}+2 y-4$

Accepted Answer

A)  $(-5,-1)$ 
B)  $(-3,1)$ 
C)  $(5,1)$ 
D)  $(5,-1)$ 
A)  $(-5,-1)$ 
B)  $(-3,1)$ 
C)  $(5,1)$ 
D)  $(5,-1)$

Question 19

Solve the system by the substitution method.
-$y=3 x^{2}+6 x$
$\mathrm{y}=\mathrm{x}^{2}-4 \mathrm{x}+12$

Accepted Answer

A)  $(2,0),(-3,9)$ 
B)  $(-2,0),(-3,9)$ 
C)  $(1,9),(-6,72)$ 
D)  $(2,0),(3,45)$ 
A)  $(2,0),(-3,9)$ 
B)  $(-2,0),(-3,9)$ 
C)  $(1,9),(-6,72)$ 
D)  $(2,0),(3,45)$

Question 20

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$.
-$\frac{x^{2}}{49}+\frac{y^{2}}{24}=1$

Accepted Answer

A)  center $ (0,0), a=2 \sqrt{6}, b=7 $
  
B)  center $ (0,0), a=7, b=2 \sqrt{6} $
  
C)  center $ (0,0), a=7, b=2 \sqrt{6} $
  
D)  center $ (0,0), a=2 \sqrt{6}, b=7 $
  
A)  center $ (0,0), a=2 \sqrt{6}, b=7 $
  
B)  center $ (0,0), a=7, b=2 \sqrt{6} $
  
C)  center $ (0,0), a=7, b=2 \sqrt{6} $
  
D)  center $ (0,0), a=2 \sqrt{6}, b=7 $

Find the equation of the circle. -

Solve the system by the substitution method. - $x^{2}+y^{2}=23$ $\mathrm{y}^{2}=2 \mathrm{x}+20$

Find the midpoint of the line segment that connects the given points. - $(0,-6)$ and $(-8,2)$

Find the vertex of the parabola by completing the square. - $x=y^{2}+2 y+6$

Graph the parabola. State the vertex of the parabola. - $x=y^{2}+4 y+2$ $Graph the parabola. State the vertex of the parabola. - x=y^{2}+4 y+2$

Solve. -A picture frame has a perimeter of $98 \mathrm{~cm}$ and a diagonal $\sqrt{1313} \mathrm{~cm}$ . What are the dimensions?

Find the standard-form equation of the hyperbola whose graph is shown. -

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $\frac{(x+2)^{2}}{9}+(y+1)^{2}=1$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - \frac{(x+2)^{2}}{9}+(y+1)^{2}=1$

Solve the system by the substitution method. - $x^{2}+y^{2}=104$ $\mathrm{x}^{2}-\mathrm{y}^{2}=96$

Graph the parabola. State the vertex of the parabola. - $y =-(x+6)^2-1$

Solve the system by the substitution method. -y = x² - 10x + 25 x + y = 7

Solve the problem. -

Find the equation of the circle. -

Solve. -The diagonal of a Persian rug measures $10 \mathrm{ft}$ . The area of the rug is $48 \mathrm{ft}^{2}$ . Find the dimensions of the rug.

Find the vertex of the parabola by completing the square. - $x=-y^{2}+2 y-4$

Solve the system by the substitution method. - $y=3 x^{2}+6 x$ $\mathrm{y}=\mathrm{x}^{2}-4 \mathrm{x}+12$

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $\frac{x^{2}}{49}+\frac{y^{2}}{24}=1$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - \frac{x^{2}}{49}+\frac{y^{2}}{24}=1$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Conic Sections

Find the equation of the circle. -

Solve the system by the substitution method. - x2+y2=23x^{2}+y^{2}=23x2+y2=23 y2=2x+20\mathrm{y}^{2}=2 \mathrm{x}+20y2=2x+20

Find the midpoint of the line segment that connects the given points. - (0,−6)(0,-6)(0,−6) and (−8,2)(-8,2)(−8,2)

Find the vertex of the parabola by completing the square. - x=y2+2y+6x=y^{2}+2 y+6x=y2+2y+6

Graph the parabola. State the vertex of the parabola. - x=y2+4y+2x=y^{2}+4 y+2x=y2+4y+2

Solve. -A picture frame has a perimeter of 98 cm98 \mathrm{~cm}98 cm and a diagonal 1313 cm\sqrt{1313} \mathrm{~cm}1313​ cm . What are the dimensions?

Find the standard-form equation of the hyperbola whose graph is shown. -

Graph the ellipse. Give the coordinates of the center, as well as the values of aaa and bbb . - (x+2)29+(y+1)2=1\frac{(x+2)^{2}}{9}+(y+1)^{2}=19(x+2)2​+(y+1)2=1

Solve the system by the substitution method. - x2+y2=104x^{2}+y^{2}=104x2+y2=104 x2−y2=96\mathrm{x}^{2}-\mathrm{y}^{2}=96x2−y2=96

Find the equation of the parabola of the form x=ay2+by+cx=a y^{2}+b y+cx=ay2+by+c that passes through the given three points. - y2=8xy^{2}=8 xy2=8x

Graph the parabola. State the vertex of the parabola. - y=−(x+6)2−1y =-(x+6)^2-1y=−(x+6)2−1

Solve the system by the substitution method. -y = x2 - 10x + 25 x + y = 7

Solve the problem. -

Find the equation of the circle. -

Solve. -The diagonal of a Persian rug measures 10ft10 \mathrm{ft}10ft . The area of the rug is 48ft248 \mathrm{ft}^{2}48ft2 . Find the dimensions of the rug.

Find the vertex of the parabola by completing the square. - x=−y2+2y−4x=-y^{2}+2 y-4x=−y2+2y−4

Solve the system by the substitution method. - y=3x2+6xy=3 x^{2}+6 xy=3x2+6x y=x2−4x+12\mathrm{y}=\mathrm{x}^{2}-4 \mathrm{x}+12y=x2−4x+12

Graph the ellipse. Give the coordinates of the center, as well as the values of aaa and bbb . - x249+y224=1\frac{x^{2}}{49}+\frac{y^{2}}{24}=149x2​+24y2​=1

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Sequences, Series, and the Binomial Theorem

Filters

Solve the system by the substitution method. - $x^{2}+y^{2}=23$ $\mathrm{y}^{2}=2 \mathrm{x}+20$

Find the midpoint of the line segment that connects the given points. - $(0,-6)$ and $(-8,2)$

Find the vertex of the parabola by completing the square. - $x=y^{2}+2 y+6$

Graph the parabola. State the vertex of the parabola. - $x=y^{2}+4 y+2$ $Graph the parabola. State the vertex of the parabola. - x=y^{2}+4 y+2$

Solve. -A picture frame has a perimeter of $98 \mathrm{~cm}$ and a diagonal $\sqrt{1313} \mathrm{~cm}$ . What are the dimensions?

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $\frac{(x+2)^{2}}{9}+(y+1)^{2}=1$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - \frac{(x+2)^{2}}{9}+(y+1)^{2}=1$

Solve the system by the substitution method. - $x^{2}+y^{2}=104$ $\mathrm{x}^{2}-\mathrm{y}^{2}=96$

Graph the parabola. State the vertex of the parabola. - $y =-(x+6)^2-1$

Solve the system by the substitution method. -y = x² - 10x + 25 x + y = 7

Solve. -The diagonal of a Persian rug measures $10 \mathrm{ft}$ . The area of the rug is $48 \mathrm{ft}^{2}$ . Find the dimensions of the rug.

Find the vertex of the parabola by completing the square. - $x=-y^{2}+2 y-4$

Solve the system by the substitution method. - $y=3 x^{2}+6 x$ $\mathrm{y}=\mathrm{x}^{2}-4 \mathrm{x}+12$

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $\frac{x^{2}}{49}+\frac{y^{2}}{24}=1$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - \frac{x^{2}}{49}+\frac{y^{2}}{24}=1$