Question 1

Determine the distance between the pair of points.
-$( 3 \sqrt { 6 } , 2 ) \text { and } ( 5 \sqrt { 6 } , 7 )$

Accepted Answer

A) 6 
B)  $\frac { 49 } { 2 }$ 
C) 7 
D) 49 
A) 6 
B)  $\frac { 49 } { 2 }$ 
C) 7 
D) 49 C

Question 2

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

Accepted Answer

A)    
B)    
A)    
B)    B

Question 3

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

Accepted Answer

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

Question 4

Determine the distance between the pair of points.
-(2, 5)and (-6, -6)

Accepted Answer

A) 88 
B)  $\sqrt { 185 }$ 
C)  $\sqrt { 57 }$ 
D) -3 
A) 88 
B)  $\sqrt { 185 }$ 
C)  $\sqrt { 57 }$ 
D) -3

Question 5

Determine the distance between the pair of points.
-(0, 0)and (-10, -8)

Accepted Answer

A) 164 
B)  $3 \sqrt { 2 }$ 
C)  $2 \sqrt { 41 }$ 
D) -18 
A) 164 
B)  $3 \sqrt { 2 }$ 
C)  $2 \sqrt { 41 }$ 
D) -18

Question 6

Find all real solutions to the system of equations using the substitution method.
-$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 39 \
x - y = 3
\end{array}$

Accepted Answer

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

Question 7

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l } 
3 x ^ { 2 } - 2 y ^ { 2 } = - 6 \
2 x ^ { 2 } + 4 y ^ { 2 } = 44
\end{array}$

Accepted Answer

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

Question 8

Graph the equation.
-$16 x ^ { 2 } + 9 y ^ { 2 } = 144$

Accepted Answer

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

Question 9

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the
equation.
-$25 x^{2}=4 y^{2}+100$

Accepted Answer

A)  $y = \pm \frac { 5 } { 2 } x$

B)  $y = \pm \frac { 2 } { 5 } x$

C)  $y = \pm \frac { 5 } { 2 } x$

D)  $y = \pm \frac { 2 } { 5 } x$

A)  $y = \pm \frac { 5 } { 2 } x$

B)  $y = \pm \frac { 2 } { 5 } x$

C)  $y = \pm \frac { 5 } { 2 } x$

D)  $y = \pm \frac { 2 } { 5 } x$

Question 10

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.
-$x = \frac { 1 } { 2 } y ^ { 2 } - 4 y + 9$

Accepted Answer

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

Question 11

Solve the problem.
-An arch for a bridge over a highway is in the form of a semi-ellipse. The top of the arch is 35 feet above ground. What should the span of the bridge be, rounded to the nearest hundredth of a foot, if the height 26 feet from the
Center is to be 12 feet above ground?

Accepted Answer

A) 27.68 ft 
B) 151.67 ft 
C) 55.36 ft 
D) 35.85 ft 
A) 27.68 ft 
B) 151.67 ft 
C) 55.36 ft 
D) 35.85 ft

Question 12

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { r } 
2 x ^ { 2 } + y ^ { 2 } = 66 \
x ^ { 2 } + y ^ { 2 } = 41
\end{array}$

Accepted Answer

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

Question 13

Determine the midpoint of the line segment between the pair of points.
-(6, 1)and (8, 5)

Accepted Answer

A) (- 1, - 2) 
B) (14, 6) 
C) (-2, -4) 
D) (7, 3) 
A) (- 1, - 2) 
B) (14, 6) 
C) (-2, -4) 
D) (7, 3)

Question 14

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.
-$y = - x ^ { 2 } - 6 x - 8$

Accepted Answer

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

Question 15

Solve the problem.
-A bridge is built in the shape of a semi-elliptical arch. It has a span of 118 feet. The height of the arch 30 feet from the center is to be 12 feet. Find the height of the arch at its center rounded to the nearest hundredth of a
Foot.

Accepted Answer

A) 12.41 ft 
B) 23.6 ft 
C) 13.94 ft 
D) 30.64 ft 
A) 12.41 ft 
B) 23.6 ft 
C) 13.94 ft 
D) 30.64 ft

Question 16

Graph the inequality.
-$25 x ^ { 2 } - 9 y ^ { 2 } \leq 225$

Accepted Answer

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

Question 17

Determine the distance between the pair of points.
-(2, -3)and (6, -1)

Accepted Answer

A)  $2 \sqrt { 5 }$ 
B) 2 
C) 12 
D)  $12 \sqrt { 3 }$ 
A)  $2 \sqrt { 5 }$ 
B) 2 
C) 12 
D)  $12 \sqrt { 3 }$

Question 18

Determine whether the graph of the quadratic function opens up or down.
-$f ( x ) = x ^ { 2 } + 8 x - 2$

Accepted Answer

A) down 
B) up 
A) down 
B) up

Question 19

Graph the inequality.
-$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } \leq 1$

Accepted Answer

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

Question 20

Solve the problem.
-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 equationn $h = - 16 t ^ { 2 } + 600$ where h is mea 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 516 feet from the ground, drops a
White ball 1.5 seconds after the yellow ball was dropped. The height of the white ball is given by the equation $h = - 16 ( t - 1.5 ) ^ { 2 } + 516$ where h is meas where h is meaured 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 sec; 456 ft 
B) 2.5 sec; 500 ft 
C) 2 sec; 536 ft 
D) 1.5 sec; 564 ft 
A) 3 sec; 456 ft 
B) 2.5 sec; 500 ft 
C) 2 sec; 536 ft 
D) 1.5 sec; 564 ft

Determine the distance between the pair of points. - $( 3 \sqrt { 6 } , 2 ) \text { and } ( 5 \sqrt { 6 } , 7 )$

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

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

Determine the distance between the pair of points. -(2, 5)and (-6, -6)

Determine the distance between the pair of points. -(0, 0)and (-10, -8)

Find all real solutions to the system of equations using the substitution method. - -=39 x-y=3

Find all real solutions to the system of equations using the addition method. - 3-2=-6 2+4=44

Graph the equation. - $16 x ^ { 2 } + 9 y ^ { 2 } = 144$ $Graph the equation. - 16 x ^ { 2 } + 9 y ^ { 2 } = 144$

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the equation. - $25 x^{2}=4 y^{2}+100$ $Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the equation. - 25 x^{2}=4 y^{2}+100$

Solve the problem. -An arch for a bridge over a highway is in the form of a semi-ellipse. The top of the arch is 35 feet above ground. What should the span of the bridge be, rounded to the nearest hundredth of a foot, if the height 26 feet from the Center is to be 12 feet above ground?

Find all real solutions to the system of equations using the addition method. - 2+=66 +=41

Determine the midpoint of the line segment between the pair of points. -(6, 1)and (8, 5)

Solve the problem. -A bridge is built in the shape of a semi-elliptical arch. It has a span of 118 feet. The height of the arch 30 feet from the center is to be 12 feet. Find the height of the arch at its center rounded to the nearest hundredth of a Foot.

Graph the inequality. - $25 x ^ { 2 } - 9 y ^ { 2 } \leq 225$ $Graph the inequality. - 25 x ^ { 2 } - 9 y ^ { 2 } \leq 225$

Determine the distance between the pair of points. -(2, -3)and (6, -1)

Determine whether the graph of the quadratic function opens up or down. - $f ( x ) = x ^ { 2 } + 8 x - 2$

Graph the inequality. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } \leq 1$ $Graph the inequality. - \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } \leq 1$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Sequences, Series, and Probability

Filters

Exam 11: Conic Sections

Determine the distance between the pair of points. - (36,2) and (56,7)( 3 \sqrt { 6 } , 2 ) \text { and } ( 5 \sqrt { 6 } , 7 )(36​,2) and (56​,7)

Graph the equation. - x2+y2=9x ^ { 2 } + y ^ { 2 } = 9x2+y2=9

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

Determine the distance between the pair of points. -(2, 5)and (-6, -6)

Determine the distance between the pair of points. -(0, 0)and (-10, -8)

Find all real solutions to the system of equations using the substitution method. - -=39 x-y=3

Find all real solutions to the system of equations using the addition method. - 3-2=-6 2+4=44

Graph the equation. - 16x2+9y2=14416 x ^ { 2 } + 9 y ^ { 2 } = 14416x2+9y2=144

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the equation. - 25x2=4y2+10025 x^{2}=4 y^{2}+10025x2=4y2+100

Write the equation in the form y=a(x−h)2+k or x=a(y−k)2+h\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}y=a(x−h)2+k or x=a(y−k)2+h h a nd then graph the equation. - x=12y2−4y+9x = \frac { 1 } { 2 } y ^ { 2 } - 4 y + 9x=21​y2−4y+9

Solve the problem. -An arch for a bridge over a highway is in the form of a semi-ellipse. The top of the arch is 35 feet above ground. What should the span of the bridge be, rounded to the nearest hundredth of a foot, if the height 26 feet from the Center is to be 12 feet above ground?

Find all real solutions to the system of equations using the addition method. - 2+=66 +=41

Determine the midpoint of the line segment between the pair of points. -(6, 1)and (8, 5)

Write the equation in the form y=a(x−h)2+k or x=a(y−k)2+h\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}y=a(x−h)2+k or x=a(y−k)2+h h a nd then graph the equation. - y=−x2−6x−8y = - x ^ { 2 } - 6 x - 8y=−x2−6x−8

Solve the problem. -A bridge is built in the shape of a semi-elliptical arch. It has a span of 118 feet. The height of the arch 30 feet from the center is to be 12 feet. Find the height of the arch at its center rounded to the nearest hundredth of a Foot.

Graph the inequality. - 25x2−9y2≤22525 x ^ { 2 } - 9 y ^ { 2 } \leq 22525x2−9y2≤225

Determine the distance between the pair of points. -(2, -3)and (6, -1)

Determine whether the graph of the quadratic function opens up or down. - f(x)=x2+8x−2f ( x ) = x ^ { 2 } + 8 x - 2f(x)=x2+8x−2

Graph the inequality. - x225+y249≤1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } \leq 125x2​+49y2​≤1

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Sequences, Series, and Probability

Filters

Determine the distance between the pair of points. - $( 3 \sqrt { 6 } , 2 ) \text { and } ( 5 \sqrt { 6 } , 7 )$

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

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

Graph the equation. - $16 x ^ { 2 } + 9 y ^ { 2 } = 144$ $Graph the equation. - 16 x ^ { 2 } + 9 y ^ { 2 } = 144$

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the equation. - $25 x^{2}=4 y^{2}+100$ $Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the equation. - 25 x^{2}=4 y^{2}+100$

Graph the inequality. - $25 x ^ { 2 } - 9 y ^ { 2 } \leq 225$ $Graph the inequality. - 25 x ^ { 2 } - 9 y ^ { 2 } \leq 225$

Determine whether the graph of the quadratic function opens up or down. - $f ( x ) = x ^ { 2 } + 8 x - 2$

Graph the inequality. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } \leq 1$ $Graph the inequality. - \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } \leq 1$