Question 1

Graph the inequality.
-$( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } \geq 4$

Accepted Answer

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

Question 2

Solve the problem.
-The perimeter of a rectangle is 34 inches and its area is 42 square inches. What are its dimensions?

Accepted Answer

A) 2 in. by 15 in. 
B) 2 in. by 13 in. 
C) 4 in. by 13 in. 
D) 3 in. by 14 in. 
A) 2 in. by 15 in. 
B) 2 in. by 13 in. 
C) 4 in. by 13 in. 
D) 3 in. by 14 in.

Question 3

Solve the problem.
-Simple interest is calculated using the formula, interest = principal · rate · time or i = prt. Jenny Brooks invested a certain amount of money saved for 1 year at a certain annual interest rate (simple interest)yielded $16.83 in
Interest. If we had added $34 to the principal and reduced the interest rate by 2 percentage point(s), the interest
Would have been the same. Find the principal and the rate.

Accepted Answer

A) $3.43, 442% 
B) $153.00, 11% 
C) $13.00, 11% 
D) $13.00, 9% 
A) $3.43, 442% 
B) $153.00, 11% 
C) $13.00, 11% 
D) $13.00, 9%

Question 4

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.
-$y = x ^ { 2 } + 4 x - 5$

Accepted Answer

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

Question 5

Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain bothth $x ^ { 2 }$ 2 and $y ^ { 2 }$ terms, divide both terms, divide bothsides of the equation by the constant term to put the equation in a more recognizable form.
-$8 x ^ { 2 } + 17 y ^ { 2 } = 20$

Accepted Answer

A) Hyperbola 
B) Parabola 
C) Circle 
D) Ellipse 
A) Hyperbola 
B) Parabola 
C) Circle 
D) Ellipse

Question 6

Graph the equation.
-$49 x ^ { 2 } + y ^ { 2 } = 49$

Accepted Answer

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

Question 7

Find the equation of the ellipse satisfying the given conditions.
-(0, 6), (0, -6), (3, 0), (-3, 0)are the endpoints of the major and minor axes.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 144 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 36 } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 144 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 36 } = 1$

Question 8

Write the equation of the circle with the given center and radius.
-$\text { Center } ( 0 , - 8 ) , \quad \text { radius } \sqrt { 17 }$

Accepted Answer

A)  $( x + 8 ) ^ { 2 } + y ^ { 2 } = 289$ 
B)  $( x - 8 ) ^ { 2 } + y ^ { 2 } = 289$ 
C)  $x ^ { 2 } + ( y - 8 ) ^ { 2 } = 17$ 
D)  $x ^ { 2 } + ( y + 8 ) ^ { 2 } = 17$ 
A)  $( x + 8 ) ^ { 2 } + y ^ { 2 } = 289$ 
B)  $( x - 8 ) ^ { 2 } + y ^ { 2 } = 289$ 
C)  $x ^ { 2 } + ( y - 8 ) ^ { 2 } = 17$ 
D)  $x ^ { 2 } + ( y + 8 ) ^ { 2 } = 17$

Question 9

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
y \geq x ^ { 2 } - 10 x + 25 \
x ^ { 2 } + y ^ { 2 } > 36
\end{array}$

Accepted Answer

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

Question 10

Solve the problem.
-The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 34 feet and the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use
This road. They are both 8 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an overall height of
11 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

Accepted Answer

A) Neither Truck 1 nor Truck 2 can pass under the bridge. 
B) Truck 1 can pass under the bridge, but Truck 2 cannot. 
C) Truck 2 can pass under the bridge, but Truck 1 cannot. 
D) Both Truck 1 and Truck 2 can pass under the bridge. 
A) Neither Truck 1 nor Truck 2 can pass under the bridge. 
B) Truck 1 can pass under the bridge, but Truck 2 cannot. 
C) Truck 2 can pass under the bridge, but Truck 1 cannot. 
D) Both Truck 1 and Truck 2 can pass under the bridge.

Question 11

Graph the equation.
-$x = \frac { 1 } { 2 } ( y - 4 ) ^ { 2 } + 1$

Accepted Answer

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

Question 12

Graph the equation.
-$( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

Accepted Answer

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

Question 13

Graph the inequality.
-$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } \geq 1$

Accepted Answer

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

Question 14

Write the following equation in standard form. Determine the center of the ellipse.
-$16 x ^ { 2 } + 64 x + 9 y ^ { 2 } - 54 y + 1 = 0$

Accepted Answer

A) (-1, 3) 
B) (-2, 3) 
C) (3, -2) 
D) (2, 3) 
A) (-1, 3) 
B) (-2, 3) 
C) (3, -2) 
D) (2, 3)

Question 15

Solve the problem.
-For the given cost and revenue equations, find the break-even point(s)C $C = 80 x , R = 0.2 x ^ { 2 } - 90 x$

Accepted Answer

A) 850 
B) 0 
C) 0 and 850 
D) 0 andR = 80x. 170 
A) 850 
B) 0 
C) 0 and 850 
D) 0 andR = 80x. 170

Question 16

Write the equation of the circle. Assume the radius is a whole number.
-

Accepted Answer

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

Question 17

Graph the equation.
-$\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Accepted Answer

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

Question 18

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.
-$y = - 3 x ^ { 2 } + 18 x - 31$

Accepted Answer

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

Question 19

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 80 \
x ^ { 2 } - y ^ { 2 } = - 48
\end{array}$

Accepted Answer

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

Question 20

Determine the equations of the asymptotes for the equation.
-$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$

Accepted Answer

A)  $y = \pm \frac { 16 } { 25 } x$ 
B)  $y = \pm \frac { 5 } { 4 } x$ 
C)  $y = \pm \frac { 25 } { 16 } x$ 
D)  $y = \pm \frac { 4 } { 5 } x$ 
A)  $y = \pm \frac { 16 } { 25 } x$ 
B)  $y = \pm \frac { 5 } { 4 } x$ 
C)  $y = \pm \frac { 25 } { 16 } x$ 
D)  $y = \pm \frac { 4 } { 5 } x$

Graph the inequality. - $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } \geq 4$ $Graph the inequality. - ( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } \geq 4$

Solve the problem. -The perimeter of a rectangle is 34 inches and its area is 42 square inches. What are its dimensions?

Graph the equation. - $49 x ^ { 2 } + y ^ { 2 } = 49$ $Graph the equation. - 49 x ^ { 2 } + y ^ { 2 } = 49$

Find the equation of the ellipse satisfying the given conditions. -(0, 6), (0, -6), (3, 0), (-3, 0)are the endpoints of the major and minor axes.

Write the equation of the circle with the given center and radius. - $\text { Center } ( 0 , - 8 ) , \quad \text { radius } \sqrt { 17 }$

Determine the solution to the system of inequalities. - y\geq-10x+25 +>36 $Determine the solution to the system of inequalities. - \begin{array} { l } y \geq x ^ { 2 } - 10 x + 25 \\ x ^ { 2 } + y ^ { 2 } > 36 \end{array}$

Graph the equation. - $x = \frac { 1 } { 2 } ( y - 4 ) ^ { 2 } + 1$ $Graph the equation. - x = \frac { 1 } { 2 } ( y - 4 ) ^ { 2 } + 1$

Graph the equation. - $( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$ $Graph the equation. - ( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

Graph the inequality. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } \geq 1$ $Graph the inequality. - \frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } \geq 1$

Write the following equation in standard form. Determine the center of the ellipse. - $16 x ^ { 2 } + 64 x + 9 y ^ { 2 } - 54 y + 1 = 0$

Solve the problem. -For the given cost and revenue equations, find the break-even point(s)C $C = 80 x , R = 0.2 x ^ { 2 } - 90 x$

Write the equation of the circle. Assume the radius is a whole number. -

Graph the equation. - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Find all real solutions to the system of equations using the addition method. - +=80 -=-48

Determine the equations of the asymptotes for the equation. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$

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

Graph the inequality. - (x+1)2+(y−4)2≥4( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } \geq 4(x+1)2+(y−4)2≥4

Solve the problem. -The perimeter of a rectangle is 34 inches and its area is 42 square inches. What are its dimensions?

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+4x−5y = x ^ { 2 } + 4 x - 5y=x2+4x−5

Graph the equation. - 49x2+y2=4949 x ^ { 2 } + y ^ { 2 } = 4949x2+y2=49

Find the equation of the ellipse satisfying the given conditions. -(0, 6), (0, -6), (3, 0), (-3, 0)are the endpoints of the major and minor axes.

Write the equation of the circle with the given center and radius. - Center (0,−8), radius 17\text { Center } ( 0 , - 8 ) , \quad \text { radius } \sqrt { 17 } Center (0,−8), radius 17​

Determine the solution to the system of inequalities. - y\geq-10x+25 +>36

Graph the equation. - x=12(y−4)2+1x = \frac { 1 } { 2 } ( y - 4 ) ^ { 2 } + 1x=21​(y−4)2+1

Graph the equation. - (x−3)2+y2=4( x - 3 ) ^ { 2 } + y ^ { 2 } = 4(x−3)2+y2=4

Graph the inequality. - x225−y29≥1\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } \geq 125x2​−9y2​≥1

Write the following equation in standard form. Determine the center of the ellipse. - 16x2+64x+9y2−54y+1=016 x ^ { 2 } + 64 x + 9 y ^ { 2 } - 54 y + 1 = 016x2+64x+9y2−54y+1=0

Solve the problem. -For the given cost and revenue equations, find the break-even point(s)C C=80x,R=0.2x2−90xC = 80 x , R = 0.2 x ^ { 2 } - 90 xC=80x,R=0.2x2−90x

Write the equation of the circle. Assume the radius is a whole number. -

Graph the equation. - x24+y29=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 14x2​+9y2​=1

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=−3x2+18x−31y = - 3 x ^ { 2 } + 18 x - 31y=−3x2+18x−31

Find all real solutions to the system of equations using the addition method. - +=80 -=-48

Determine the equations of the asymptotes for the equation. - x225−y216=1\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 125x2​−16y2​=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

Graph the inequality. - $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } \geq 4$ $Graph the inequality. - ( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } \geq 4$

Graph the equation. - $49 x ^ { 2 } + y ^ { 2 } = 49$ $Graph the equation. - 49 x ^ { 2 } + y ^ { 2 } = 49$

Write the equation of the circle with the given center and radius. - $\text { Center } ( 0 , - 8 ) , \quad \text { radius } \sqrt { 17 }$

Determine the solution to the system of inequalities. - y\geq-10x+25 +>36 $Determine the solution to the system of inequalities. - \begin{array} { l } y \geq x ^ { 2 } - 10 x + 25 \\ x ^ { 2 } + y ^ { 2 } > 36 \end{array}$

Graph the equation. - $x = \frac { 1 } { 2 } ( y - 4 ) ^ { 2 } + 1$ $Graph the equation. - x = \frac { 1 } { 2 } ( y - 4 ) ^ { 2 } + 1$

Graph the equation. - $( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$ $Graph the equation. - ( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

Graph the inequality. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } \geq 1$ $Graph the inequality. - \frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } \geq 1$

Write the following equation in standard form. Determine the center of the ellipse. - $16 x ^ { 2 } + 64 x + 9 y ^ { 2 } - 54 y + 1 = 0$

Solve the problem. -For the given cost and revenue equations, find the break-even point(s)C $C = 80 x , R = 0.2 x ^ { 2 } - 90 x$

Graph the equation. - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Determine the equations of the asymptotes for the equation. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$