Question 1

Solve.
-A picture frame has a perimeter of $102 \mathrm {~cm}$ and a diagonal $\sqrt { 1445 } \mathrm {~cm}$. What are the dimensions?

Accepted Answer

A)  $17 \mathrm {~cm}$ by $34 \mathrm {~cm}$ 
B)  $18 \mathrm {~cm}$ by $33 \mathrm {~cm}$ 
C)  $17 \mathrm {~cm}$ by $35 \mathrm {~cm}$ 
D)  $18 \mathrm {~cm}$ by $34 \mathrm {~cm}$ 
A)  $17 \mathrm {~cm}$ by $34 \mathrm {~cm}$ 
B)  $18 \mathrm {~cm}$ by $33 \mathrm {~cm}$ 
C)  $17 \mathrm {~cm}$ by $35 \mathrm {~cm}$ 
D)  $18 \mathrm {~cm}$ by $34 \mathrm {~cm}$ A

Question 2

Solve the system by the substitution method.
-$$\begin{array} { l } 
5 x ^ { 2 } - y ^ { 2 } = 10 \
y = x ^ { 2 } - 2
\end{array}$$

Accepted Answer

A)  $( - \sqrt { 7 } , 5 ) , ( \sqrt { 7 } , 5 )$ 
B)  $( - \sqrt { 2 } , 0 ) , ( \sqrt { 2 } , 0 ) , ( - \sqrt { 7 } , 5 ) , ( \sqrt { 7 } , 5 )$ 
C)  $( - \sqrt { 2 } , 0 ) , ( \sqrt { 2 } , 0 )$ 
D)  $( 0 , - \sqrt { 2 } ) , ( 0 , \sqrt { 2 } ) , ( 5 , - \sqrt { 7 } ) , ( 5 , \sqrt { 7 } )$ 
A)  $( - \sqrt { 7 } , 5 ) , ( \sqrt { 7 } , 5 )$ 
B)  $( - \sqrt { 2 } , 0 ) , ( \sqrt { 2 } , 0 ) , ( - \sqrt { 7 } , 5 ) , ( \sqrt { 7 } , 5 )$ 
C)  $( - \sqrt { 2 } , 0 ) , ( \sqrt { 2 } , 0 )$ 
D)  $( 0 , - \sqrt { 2 } ) , ( 0 , \sqrt { 2 } ) , ( 5 , - \sqrt { 7 } ) , ( 5 , \sqrt { 7 } )$ B

Question 3

Solve the system by the substitution method.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 36 \
y = x ^ { 2 } - 6
\end{array}$

Accepted Answer

A)  $( 0,6 ) , ( - \sqrt { 11 } , 5 )$ 
B)  $( 0 , - 6 ) , ( \sqrt { 11 } , 5 )$ 
C)  $( - \sqrt { 11 } , 5 ) , ( 0 , - 6 ) , ( \sqrt { 11 } , 5 )$ 
D)  $( 0,6 ) , ( \sqrt { 11 } , 5 )$ 
A)  $( 0,6 ) , ( - \sqrt { 11 } , 5 )$ 
B)  $( 0 , - 6 ) , ( \sqrt { 11 } , 5 )$ 
C)  $( - \sqrt { 11 } , 5 ) , ( 0 , - 6 ) , ( \sqrt { 11 } , 5 )$ 
D)  $( 0,6 ) , ( \sqrt { 11 } , 5 )$ C

Question 4

Find the midpoint of the line segment that connects the given points.
-$( 3,6 )$ and $( 0,2 )$

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , 2 \right)$ 
B)  $\left( \frac { 3 } { 2 } , 4 \right)$ 
C)  $( 3,4 )$ 
D)  3,8 ) 
A)  $\left( \frac { 3 } { 2 } , 2 \right)$ 
B)  $\left( \frac { 3 } { 2 } , 4 \right)$ 
C)  $( 3,4 )$ 
D)  3,8 )

Question 5

Find an equation of the circle with the given center and radius.
-A bridge with a semi-elliptical arch extends over a river as shown. Find an equation of the ellipse that represents the arch of the bridge.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 324 } = 1$ 
B)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 144 } = 1$ 
D)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 144 } = 1$ 
A)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 324 } = 1$ 
B)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 144 } = 1$ 
D)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 144 } = 1$

Question 6

Solve.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation $h = - 16 t ^ { 2 } + 600$ where $h$ is measured in feet and $t$ is the number of seconds since the yellow ball was dropped. A second person, in the same building but on a lower floor that is 348 feet from the ground, drops a white ball $3.5$ seconds after the yellow ball was dropped. The height of the white ball is given by the equation $h = - 16 ( t - 3.5 ) ^ { 2 } + 348$ where $h$ is measured in feet and $t$ is the number of seconds since the yellow ball was dropped. Find the time that the balls are the same distance above the ground and find this distance.

Accepted Answer

A)  $3 \mathrm { sec } ; 456 \mathrm { ft }$ 
B)  $4 \mathrm { sec } ; 344 \mathrm { ft }$ 
C)  $3.5 \mathrm { sec } ; 404 \mathrm { ft }$ 
D)  $4.5 \mathrm { sec } ; 276 \mathrm { ft }$ 
A)  $3 \mathrm { sec } ; 456 \mathrm { ft }$ 
B)  $4 \mathrm { sec } ; 344 \mathrm { ft }$ 
C)  $3.5 \mathrm { sec } ; 404 \mathrm { ft }$ 
D)  $4.5 \mathrm { sec } ; 276 \mathrm { ft }$

Question 7

Find an equation of the circle with the given center and radius.
-Center (0, -10), radius 5

Accepted Answer

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

Question 8

Find an equation of the circle with the given center and radius.
-A one-way street passes under an overpass, which is in the form of the top half of an ellipse, as shown in the figure. Suppose that a truck 26 feet wide passes directly under the overpass. What is the maximum possible height of this truck to the nearest tenth of a foot?

Accepted Answer

A)  $5.2 \mathrm { ft }$ 
B)  $8.9 \mathrm { ft }$ 
C)  $7.8 \mathrm { ft }$ 
D)  $10.4 \mathrm { ft }$ 
A)  $5.2 \mathrm { ft }$ 
B)  $8.9 \mathrm { ft }$ 
C)  $7.8 \mathrm { ft }$ 
D)  $10.4 \mathrm { ft }$

Question 9

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

Accepted Answer

A)  $( - 1 , - 2 )$ 
B)  $( 1,0 )$ 
C)  $( - 2 , - 1 )$ 
D)  $( - 2,1 )$ 
A)  $( - 1 , - 2 )$ 
B)  $( 1,0 )$ 
C)  $( - 2 , - 1 )$ 
D)  $( - 2,1 )$

Question 10

Solve the system by the substitution method.
-$$\begin{array} { l } 
49 x ^ { 2 } + 64 y ^ { 2 } = 3136 \
8 y + 7 x = 56
\end{array}$$

Accepted Answer

A)  $( 0,8 ) , ( 7,0 )$ 
B)  $( 0,7 ) , ( 8,0 )$ 
C)  $( 0 , - 8 ) , ( 0 , - 7 )$ 
D)  $( 0 , - 7 ) , ( - 8,0 )$ 
A)  $( 0,8 ) , ( 7,0 )$ 
B)  $( 0,7 ) , ( 8,0 )$ 
C)  $( 0 , - 8 ) , ( 0 , - 7 )$ 
D)  $( 0 , - 7 ) , ( - 8,0 )$

Question 11

Graph the hyperbola. Give the coordinates of the center as well as the values of a and b.
-A Ferris wheel has a diameter of 340 feet and the bottom of the Ferris wheel is 10 feet above the ground. How far to the left or right is a car that is 166 feet above the ground? Round to the nearest
Tenth if necessary.

Accepted Answer

A)  170 
B)  340 
C)  $339.7$ 
D)  $169.4$ 
A)  170 
B)  340 
C)  $339.7$ 
D)  $169.4$

Question 12

Find an equation of the circle with the given center and radius.
-Center $( 9,2 )$, radius $\sqrt { 7 }$

Accepted Answer

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

Question 13

Solve.
-$$x ^ { 2 } + 6 x + y ^ { 2 } - 8 y + 21 = 0$$

Accepted Answer

A)  $( 3 , - 4 ) ; r = 4$ 
B)  $( - 3,4 ) ; r = 2$ 
C)  $( - 3,4 ) ; r = 4$ 
D)  $( 3 , - 4 ) ; r = 2$ 
A)  $( 3 , - 4 ) ; r = 4$ 
B)  $( - 3,4 ) ; r = 2$ 
C)  $( - 3,4 ) ; r = 4$ 
D)  $( 3 , - 4 ) ; r = 2$

Question 14

Graph the hyperbola. Give the coordinates of the center as well as the values of a and b.
-A Ferris wheel has a diameter of 320 feet and the bottom of the Ferris wheel is 11 feet above the ground. Find the equation of the wheel if the origin is placed on the ground directly below the
Center of the wheel, as illustrated.

Accepted Answer

A)  $x ^ { 2 } + ( y - 171 ) ^ { 2 } = 25,600$ 
B)  $x ^ { 2 } + ( y - 160 ) ^ { 2 } = 25,600$ 
C)  $x ^ { 2 } + y ^ { 2 } = 25,600$ 
D)  $x ^ { 2 } + ( y - 160 ) ^ { 2 } = 102,400$ 
A)  $x ^ { 2 } + ( y - 171 ) ^ { 2 } = 25,600$ 
B)  $x ^ { 2 } + ( y - 160 ) ^ { 2 } = 25,600$ 
C)  $x ^ { 2 } + y ^ { 2 } = 25,600$ 
D)  $x ^ { 2 } + ( y - 160 ) ^ { 2 } = 102,400$

Question 15

Solve the system by the substitution method.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
y ^ { 2 } = 2 x + 22
\end{array}$

Accepted Answer

A)  $( 1,2 \sqrt { 6 } ) , ( - 2,4 ) , ( 1 , - 2 \sqrt { 6 } ) , ( - 2 , - 4 )$ 
B)  $( 1,5 ) , ( - 3,5 ) , ( 1 , - 5 ) , ( - 3 , - 5 )$ 
C)  $( 2,2 \sqrt { 6 } ) , ( - 3,4 ) , ( 2 , - 2 \sqrt { 6 } ) , ( - 3 , - 4 )$ 
D)  $( 1,2 \sqrt { 6 } ) , ( - 3,4 ) , ( 1 , - 2 \sqrt { 6 } ) , ( - 3 , - 4 )$ 
A)  $( 1,2 \sqrt { 6 } ) , ( - 2,4 ) , ( 1 , - 2 \sqrt { 6 } ) , ( - 2 , - 4 )$ 
B)  $( 1,5 ) , ( - 3,5 ) , ( 1 , - 5 ) , ( - 3 , - 5 )$ 
C)  $( 2,2 \sqrt { 6 } ) , ( - 3,4 ) , ( 2 , - 2 \sqrt { 6 } ) , ( - 3 , - 4 )$ 
D)  $( 1,2 \sqrt { 6 } ) , ( - 3,4 ) , ( 1 , - 2 \sqrt { 6 } ) , ( - 3 , - 4 )$

Question 16

Find the distance between the pair of points. Round to the nearest tenth if necessary.
-$( - 5 , - 18 )$ and $( 55,58 )$

Accepted Answer

A)  4100 
B)  900 
C)  $4 \sqrt { 586 } \approx 96.8$ 
D)  $10 \sqrt { 41 } \approx 64$ 
A)  4100 
B)  900 
C)  $4 \sqrt { 586 } \approx 96.8$ 
D)  $10 \sqrt { 41 } \approx 64$

Question 17

Solve.
-$$x ^ { 2 } + y ^ { 2 } + 12 x - 8 y + 27 = 0$$

Accepted Answer

A)  $( 6 , - 4 ) ; r = 25$ 
B)  $( - 6,4 ) ; r = 5$ 
C)  $( - 4,6 ) ; \mathrm { r } = 25$ 
D)  $( 4 , - 6 ) ; r = 5$ 
A)  $( 6 , - 4 ) ; r = 25$ 
B)  $( - 6,4 ) ; r = 5$ 
C)  $( - 4,6 ) ; \mathrm { r } = 25$ 
D)  $( 4 , - 6 ) ; r = 5$

Question 18

Find an equation of the circle with the given center and radius.
-Center (0, -4), radius 15

Accepted Answer

A)  $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 15$ 
B)  $( x + 4 ) ^ { 2 } + y ^ { 2 } = 225$ 
C)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = 225$ 
D)  $x ^ { 2 } + ( y + 4 ) ^ { 2 } = 15$ 
A)  $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 15$ 
B)  $( x + 4 ) ^ { 2 } + y ^ { 2 } = 225$ 
C)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = 225$ 
D)  $x ^ { 2 } + ( y + 4 ) ^ { 2 } = 15$

Question 19

Find an equation of the circle with the given center and radius.
-Center (-4, 0), radius 11

Accepted Answer

A)  (x + 4)2 + y2 = 121 
B)  x2 + (y + 4)2 = 11 
C)  x2 + (y - 4)2 = 11 
D)  (x - 4)2 + y2 = 121 
A)  (x + 4)2 + y2 = 121 
B)  x2 + (y + 4)2 = 11 
C)  x2 + (y - 4)2 = 11 
D)  (x - 4)2 + y2 = 121

Question 20

Solve.
-$$x ^ { 2 } + y ^ { 2 } - 8 x - 8 y + 28 = 0$$

Accepted Answer

A)  $( 4,4 ) , r = 2$ 
B)  $( - 4 , - 4 ) , r = 2$ 
C)  $( 4,4 ) , \mathrm { r } = 4$ 
D)  $( - 4 , - 4 ) , r = 4$ 
A)  $( 4,4 ) , r = 2$ 
B)  $( - 4 , - 4 ) , r = 2$ 
C)  $( 4,4 ) , \mathrm { r } = 4$ 
D)  $( - 4 , - 4 ) , r = 4$

Solve. -A picture frame has a perimeter of $102 \mathrm {~cm}$ and a diagonal $\sqrt { 1445 } \mathrm {~cm}$ . What are the dimensions?

Solve the system by the substitution method. - 5-=10 y=-2

Solve the system by the substitution method. - +=36 y=-6

Find the midpoint of the line segment that connects the given points. - $( 3,6 )$ and $( 0,2 )$

Find an equation of the circle with the given center and radius. -A bridge with a semi-elliptical arch extends over a river as shown. Find an equation of the ellipse that represents the arch of the bridge.

Find an equation of the circle with the given center and radius. -Center (0, -10), radius 5

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

Solve the system by the substitution method. - 49+64=3136 8y+7x=56

Find an equation of the circle with the given center and radius. -Center $( 9,2 )$ , radius $\sqrt { 7 }$

Solve. - $x ^ { 2 } + 6 x + y ^ { 2 } - 8 y + 21 = 0$

Solve the system by the substitution method. - +=25 =2x+22

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $( - 5 , - 18 )$ and $( 55,58 )$

Solve. - $x ^ { 2 } + y ^ { 2 } + 12 x - 8 y + 27 = 0$

Find an equation of the circle with the given center and radius. -Center (0, -4), radius 15

Find an equation of the circle with the given center and radius. -Center (-4, 0), radius 11

Solve. - $x ^ { 2 } + y ^ { 2 } - 8 x - 8 y + 28 = 0$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Sequences, Series, and the Binomial Theorem

Filters

Exam 13: Conic Sections

Solve. -A picture frame has a perimeter of 102 cm102 \mathrm {~cm}102 cm and a diagonal 1445 cm\sqrt { 1445 } \mathrm {~cm}1445​ cm . What are the dimensions?