Question 1

Find the distance between the pair of points. Round to the nearest tenth if necessary.
-$(-7,-7)$ and $(7,3)$

Accepted Answer

A)  4 
B)  $2 \sqrt{74} \approx 17.2$ 
C)  $96 \sqrt{6} \approx 235.2$ 
D)  96 
A)  4 
B)  $2 \sqrt{74} \approx 17.2$ 
C)  $96 \sqrt{6} \approx 235.2$ 
D)  96

Question 2

Solve.
-Find the dimensions of a rectangular enclosure with perimeter $54 \mathrm{yd}$ and area $176 \mathrm{yd}^{2}$.

Accepted Answer

A)  12 yd by $16 y d$ 
B)  11 yd by $15 y d$ 
C)  11 yd by $16 y d$ 
D)  12 yd by $15 y d$ 
A)  12 yd by $16 y d$ 
B)  11 yd by $15 y d$ 
C)  11 yd by $16 y d$ 
D)  12 yd by $15 y d$

Question 3

Graph the parabola. State the vertex of the parabola.
-$y=x^{2}+3$

Accepted Answer

A)  vertex $(0,-3)$
  
B)  vertex $(0,3)$
  
C)  vertex $(-3,0)$
  
D)  vertex $(3,0)$
  
A)  vertex $(0,-3)$
  
B)  vertex $(0,3)$
  
C)  vertex $(-3,0)$
  
D)  vertex $(3,0)$

Question 4

Solve the system by the substitution method.
-$y^{2}-x^{2}=10$
$\mathrm{x}-8=\mathrm{y}$

Accepted Answer

A)  $\left(-\frac{37}{8},-\frac{73}{4}\right)$ 
B)  $\left(-\frac{37}{8},-\frac{9}{4}\right)$ 
C)  $\left(\frac{27}{8}, 7\right)$ 
D)  $\left(\frac{27}{8},-\frac{37}{8}\right)$ 
A)  $\left(-\frac{37}{8},-\frac{73}{4}\right)$ 
B)  $\left(-\frac{37}{8},-\frac{9}{4}\right)$ 
C)  $\left(\frac{27}{8}, 7\right)$ 
D)  $\left(\frac{27}{8},-\frac{37}{8}\right)$

Question 5

Find an equation of the circle with the given center and radius.
-Center (0, - 6), radius 2

Accepted Answer

A)  $x^{2}+(y-6)^{2}=2$ 
B)  $(x+6)^{2}+y^{2}=4$ 
C)  $x^{2}+(y+6)^{2}=4$ 
D)  $(x-6)^{2}+y^{2}=4$ 
A)  $x^{2}+(y-6)^{2}=2$ 
B)  $(x+6)^{2}+y^{2}=4$ 
C)  $x^{2}+(y+6)^{2}=4$ 
D)  $(x-6)^{2}+y^{2}=4$

Question 6

Find the equation of the circle.
-

Accepted Answer

A)  $x^{2}+y^{2}=5$ 
B)  $x^{2}+y^{2}=9$ 
C)  $x^{2}+y^{2}=10$ 
D)  $x^{2}+y^{2}=25$ 
A)  $x^{2}+y^{2}=5$ 
B)  $x^{2}+y^{2}=9$ 
C)  $x^{2}+y^{2}=10$ 
D)  $x^{2}+y^{2}=25$

Question 7

Find the distance between the pair of points. Round to the nearest tenth if necessary.
-$(6,1)$ and $(-7,-3)$

Accepted Answer

A)  52 
B)  $3 \sqrt{17} \approx 12.4$ 
C)  9 
D)  $\sqrt{185} \approx 13.6$ 
A)  52 
B)  $3 \sqrt{17} \approx 12.4$ 
C)  9 
D)  $\sqrt{185} \approx 13.6$

Question 8

Find an equation of the circle with the given center and radius.
-Center $(-9,0)$, radius 3

Accepted Answer

A)  $(x+9)^{2}+y^{2}=9$ 
B)  $x^{2}+(y-9)^{2}=3$ 
C)  $(x-9)^{2}+y^{2}=9$ 
D)  $x^{2}+(y+9)^{2}=3$ 
A)  $(x+9)^{2}+y^{2}=9$ 
B)  $x^{2}+(y-9)^{2}=3$ 
C)  $(x-9)^{2}+y^{2}=9$ 
D)  $x^{2}+(y+9)^{2}=3$

Question 9

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

Accepted Answer

A)  $\frac{(y+2)^{2}}{9}-\frac{(x+5)^{2}}{16}=1$ 
B)  $\frac{(y-2)^{2}}{16}-\frac{(x-5)^{2}}{9}=1$ 
C)  $\frac{(y-2)^{2}}{9}-\frac{(x-5)^{2}}{16}=1$ 
D)  $\frac{(y+2)^{2}}{16}-\frac{(x+5)^{2}}{9}=1$ 
A)  $\frac{(y+2)^{2}}{9}-\frac{(x+5)^{2}}{16}=1$ 
B)  $\frac{(y-2)^{2}}{16}-\frac{(x-5)^{2}}{9}=1$ 
C)  $\frac{(y-2)^{2}}{9}-\frac{(x-5)^{2}}{16}=1$ 
D)  $\frac{(y+2)^{2}}{16}-\frac{(x+5)^{2}}{9}=1$

Question 10

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 homeowner is building an elliptical swimming pool that is 28 feet from end to end at its longest point, and 14 feet from side to side at its widest point. Find the area covered by the swimming pool. Round to the nearest tenth of a foot if necessary.

Accepted Answer

A)  $615.8 \mathrm{ft}^{2}$ 
B)  $1231.5 \mathrm{ft}^{2}$ 
C)  $30,171.8 \mathrm{ft}^{2}$ 
D)  $307.9 \mathrm{ft}^{2}$ 
A)  $615.8 \mathrm{ft}^{2}$ 
B)  $1231.5 \mathrm{ft}^{2}$ 
C)  $30,171.8 \mathrm{ft}^{2}$ 
D)  $307.9 \mathrm{ft}^{2}$

Question 11

Solve the system by the substitution method.
-$36 x^{2}+49 y^{2}=1764$
$7 y-6 x=42$

Accepted Answer

A)  $(0,6),(-7,0)$ 
B)  $(0,7),(0,-6)$ 
C)  $(0,-6),(7,0)$ 
D)  $(0,-7),(6,0)$ 
A)  $(0,6),(-7,0)$ 
B)  $(0,7),(0,-6)$ 
C)  $(0,-6),(7,0)$ 
D)  $(0,-7),(6,0)$

Question 12

Find the distance between the pair of points. Round to the nearest tenth if necessary.
-$(2,-1)$ and $(4,-5)$

Accepted Answer

A)  12 
B)  6 
C)  $2 \sqrt{5} \approx 4.5$ 
D)  $12 \sqrt{3} \approx 20.8$ 
A)  12 
B)  6 
C)  $2 \sqrt{5} \approx 4.5$ 
D)  $12 \sqrt{3} \approx 20.8$

Question 13

Find an equation of the circle with the given center and radius.
-Center $(9,-7)$, radius $\sqrt{7}$

Accepted Answer

A)  $(x+7)^{2}+(y-9)^{2}=49$ 
B)  $(x+9)^{2}+(y-7)^{2}=7$ 
C)  $(x-7)^{2}+(y+9)^{2}=49$ 
D)  $(x-9)^{2}+(y+7)^{2}=7$ 
A)  $(x+7)^{2}+(y-9)^{2}=49$ 
B)  $(x+9)^{2}+(y-7)^{2}=7$ 
C)  $(x-7)^{2}+(y+9)^{2}=49$ 
D)  $(x-9)^{2}+(y+7)^{2}=7$

Question 14

Graph the circle. State the center and radius of the circle
-$x^{2}+y^{2}=100$

Accepted Answer

A)  center $(0,0) ; r=10$
  
B)  center $(0,0) ; \mathrm{r}=10$
  
C)  center $(0,0) ; r=10$
  
D)  center $(0,0) ; r=10$
  
A)  center $(0,0) ; r=10$
  
B)  center $(0,0) ; \mathrm{r}=10$
  
C)  center $(0,0) ; r=10$
  
D)  center $(0,0) ; r=10$

Question 15

Solve the system by the substitution method.
-$2 x^{2}+3 y^{2}=8$
$x^{2}+3 y^{2}=4$

Accepted Answer

A)  $(-2 \mathrm{i}, 0)$, (2i, 0) 
B)  $(-2,-\sqrt{3}),(-2, \sqrt{3}),(2,-\sqrt{3}),(2, \sqrt{3})$ 
C)  $(2,0)$ 
D)  $(-2,0),(2,0)$ 
A)  $(-2 \mathrm{i}, 0)$, (2i, 0) 
B)  $(-2,-\sqrt{3}),(-2, \sqrt{3}),(2,-\sqrt{3}),(2, \sqrt{3})$ 
C)  $(2,0)$ 
D)  $(-2,0),(2,0)$

Question 16

Find an equation of the circle with the given center and radius.
-Center $(-9,0)$, radius $\sqrt{3}$

Accepted Answer

A)  $(x+9)^{2}+y^{2}=3$ 
B)  $(x-9)^{2}+y^{2}=3$ 
C)  $x^{2}+(y-9)^{2}=9$ 
D)  $x^{2}+(y+9)^{2}=9$ 
A)  $(x+9)^{2}+y^{2}=3$ 
B)  $(x-9)^{2}+y^{2}=3$ 
C)  $x^{2}+(y-9)^{2}=9$ 
D)  $x^{2}+(y+9)^{2}=9$

Question 17

Solve the system by the substitution method.
-$x^{2}+y^{2}=61$ $\mathrm{x}-\mathrm{y}=1$

Accepted Answer

A)  $(5,-6),(6,-5)$ 
B)  $(-5,-6),(6,5)$ 
C)  $(-5,6),(-6,5)$ 
D)  $(5,6),(6,5)$ 
A)  $(5,-6),(6,-5)$ 
B)  $(-5,-6),(6,5)$ 
C)  $(-5,6),(-6,5)$ 
D)  $(5,6),(6,5)$

Question 18

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$.
-$\frac{(y-4)^{2}}{9}-(x+1)^{2}=1$

Accepted Answer

A)  center $ (-1,4), a=1, b=3 $
  
B)  center $ (-1,4), a=3, b=1 $
  
C)  center $ (-1,4), a=1, b=3 $
  
D)  center $ (-1,4), a=3, b=1 $
  
A)  center $ (-1,4), a=1, b=3 $
  
B)  center $ (-1,4), a=3, b=1 $
  
C)  center $ (-1,4), a=1, b=3 $
  
D)  center $ (-1,4), a=3, b=1 $

Question 19

Graph the parabola. State the vertex of the parabola.
-$x=-(y+3)^{2}+6$

Accepted Answer

A)  vertex $ (-3,6) $
  
B)  vertex $ (3,-6) $
  
C)  vertex $ (6,-3) $
  
D)  vertex $ (6,3) $
  
A)  vertex $ (-3,6) $
  
B)  vertex $ (3,-6) $
  
C)  vertex $ (6,-3) $
  
D)  vertex $ (6,3) $

Question 20

Find the equation of the parabola of the form $x=a y^{2}+b y+c$ that passes through the given three points.
-$(x+3)^{2}=-16(y-1)$

Accepted Answer

A)  vertex: $(-3,1)$; focus $(-3,-3)$; directrix $y=5$
  
B)  vertex: $(-3,1)$; focus $(-3,-3)$; directrix $y=5$
  
C)  vertex: $(-3,1)$; focus $(-3,-1)$; directrix $y=3$
  
D)  vertex: $(-3,1)$; focus $(-3,-1)$; directrix $y=3$
  
A)  vertex: $(-3,1)$; focus $(-3,-3)$; directrix $y=5$
  
B)  vertex: $(-3,1)$; focus $(-3,-3)$; directrix $y=5$
  
C)  vertex: $(-3,1)$; focus $(-3,-1)$; directrix $y=3$
  
D)  vertex: $(-3,1)$; focus $(-3,-1)$; directrix $y=3$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $(-7,-7)$ and $(7,3)$

Solve. -Find the dimensions of a rectangular enclosure with perimeter $54 \mathrm{yd}$ and area $176 \mathrm{yd}^{2}$ .

Graph the parabola. State the vertex of the parabola. - $y=x^{2}+3$ $Graph the parabola. State the vertex of the parabola. - y=x^{2}+3$

Solve the system by the substitution method. - $y^{2}-x^{2}=10$ $\mathrm{x}-8=\mathrm{y}$

Find an equation of the circle with the given center and radius. -Center (0, - 6), radius 2

Find the equation of the circle. -

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $(6,1)$ and $(-7,-3)$

Find an equation of the circle with the given center and radius. -Center $(-9,0)$ , radius 3

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

Solve the system by the substitution method. - $36 x^{2}+49 y^{2}=1764$ $7 y-6 x=42$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $(2,-1)$ and $(4,-5)$

Find an equation of the circle with the given center and radius. -Center $(9,-7)$ , radius $\sqrt{7}$

Graph the circle. State the center and radius of the circle - $x^{2}+y^{2}=100$ $Graph the circle. State the center and radius of the circle - x^{2}+y^{2}=100$

Solve the system by the substitution method. - $2 x^{2}+3 y^{2}=8$ $x^{2}+3 y^{2}=4$

Find an equation of the circle with the given center and radius. -Center $(-9,0)$ , radius $\sqrt{3}$

Solve the system by the substitution method. - $x^{2}+y^{2}=61$ $\mathrm{x}-\mathrm{y}=1$

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $\frac{(y-4)^{2}}{9}-(x+1)^{2}=1$ $Graph the hyperbola. Give the coordinates of the center as well as the values of a and b . - \frac{(y-4)^{2}}{9}-(x+1)^{2}=1$

Graph the parabola. State the vertex of the parabola. - $x=-(y+3)^{2}+6$ $Graph the parabola. State the vertex of the parabola. - x=-(y+3)^{2}+6$

Find the equation of the parabola of the form $x=a y^{2}+b y+c$ that passes through the given three points. - $(x+3)^{2}=-16(y-1)$ $Find the equation of the parabola of the form x=a y^{2}+b y+c that passes through the given three points. - (x+3)^{2}=-16(y-1)$

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 distance between the pair of points. Round to the nearest tenth if necessary. - (−7,−7)(-7,-7)(−7,−7) and (7,3)(7,3)(7,3)

Solve. -Find the dimensions of a rectangular enclosure with perimeter 54yd54 \mathrm{yd}54yd and area 176yd2176 \mathrm{yd}^{2}176yd2 .

Graph the parabola. State the vertex of the parabola. - y=x2+3y=x^{2}+3y=x2+3

Solve the system by the substitution method. - y2−x2=10y^{2}-x^{2}=10y2−x2=10 x−8=y\mathrm{x}-8=\mathrm{y}x−8=y