Question 1

Choose the equation that matches the graph.
-

Accepted Answer

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

Question 2

Match the equation of the parabola with the appropriate description.
-$$x = - 4 y ^ { 2 } + 5 y + 3$$

Accepted Answer

A)  Opens right 
B)  Opens left 
C)  Opens down 
D)  Opens up 
A)  Opens right 
B)  Opens left 
C)  Opens down 
D)  Opens up

Question 3

Graph the equation. Give the domain and range. Identify whether the equation is a function.
-$\frac{y}{6}=\sqrt{1-\frac{x^{2}}{16}}$

Accepted Answer

A)  
$[ - 4,4 ] ; [ - 6,0 ]$; function 
B) 
 
$[ - 4,4 ] ; [ - 1,0 ] ;$ not a function 
C) 
 
$[ - 4,4 ] ; [ 0,6 ] ;$ function 
D) 
 
$[ - 4,4 ] ; [ 0,1 ]$; not a function 
A)  
$[ - 4,4 ] ; [ - 6,0 ]$; function 
B) 
 
$[ - 4,4 ] ; [ - 1,0 ] ;$ not a function 
C) 
 
$[ - 4,4 ] ; [ 0,6 ] ;$ function 
D) 
 
$[ - 4,4 ] ; [ 0,1 ]$; not a function

Question 4

Graph the hyperbola.
-$$\frac { ( x + 2 ) ^ { 2 } } { 49 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$

Accepted Answer

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

Question 5

The series of sketches below starts with a square having sides of length 1 (one). In the following steps, squares
are constructed by joining, in order, the midpoints of the sides of the previous square. Develop a formula for the
perimeter of the nth square.

Accepted Answer

The answer of The series of sketches below starts with...

Question 6

A certain club initially has 160 members and membership increases by 2 members every month. If dues are $20/month, what is the total amount of dues collected during the first year?

Accepted Answer

A)  $41,040 
B)  $37,840 
C)  $37,400 
D)  $41,280 
A)  $41,040 
B)  $37,840 
C)  $37,400 
D)  $41,280

Question 7

Match the equation of the parabola with the appropriate description.
-$$y = 6 + 3 x - x ^ { 2 }$$

Accepted Answer

A)  Opens right 
B)  Opens up 
C)  Opens left 
D)  Opens down 
A)  Opens right 
B)  Opens up 
C)  Opens left 
D)  Opens down

Question 8

Find the eccentricity of the conic section shown in the graph.
- 
$y=-17$

Accepted Answer

A)  e=1 
B)  e=4 
C)  $= \frac { \sqrt { 17 } } { 4 }$ 
D)  $\mathrm { e } = \frac { 4 } { \sqrt { 17 } }$ 
A)  e=1 
B)  e=4 
C)  $= \frac { \sqrt { 17 } } { 4 }$ 
D)  $\mathrm { e } = \frac { 4 } { \sqrt { 17 } }$

Question 9

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$\text { If } 0 < a < 1 \text {, then } a ^n < 1 \text {. }$$ (Assume that a is a constant.)

Accepted Answer

Answers will vary. One possible proof fo

Question 10

If the police have 7 suspects, how many different sets of 5 suspects can they select for a lineup?

Accepted Answer

A)  21 
B)  2520 
C)  35 
D)  42 
A)  21 
B)  2520 
C)  35 
D)  42

Question 11

Match the equation of the ellipse with the appropriate description.
-$$49 x ^ { 2 } = 3136 - 16 y ^ { 2 }$$

Accepted Answer

A)  $x$-intercepts $( 64,0 ) , ( - 64,0 )$; y-intercepts $( 0,196 ) , ( 0 , - 196 )$ 
B)  $x$-intercepts $( 8,0 ) , ( - 8,0 )$; y-intercepts $( 0,56 ) , ( 0 , - 56 )$ 
C)  x-intercepts $( 8,0 ) , ( - 8,0 ) ; y$-intercepts $( 0,14 ) , ( 0 , - 14 )$ 
D)  x-intercepts $\left( \frac { 7 } { 4 } , 0 \right) , \left( - \frac { 7 } { 4 } , 0 \right) ; y$-intercepts $( 0,14 ) , ( 0 , - 14 )$ 
A)  $x$-intercepts $( 64,0 ) , ( - 64,0 )$; y-intercepts $( 0,196 ) , ( 0 , - 196 )$ 
B)  $x$-intercepts $( 8,0 ) , ( - 8,0 )$; y-intercepts $( 0,56 ) , ( 0 , - 56 )$ 
C)  x-intercepts $( 8,0 ) , ( - 8,0 ) ; y$-intercepts $( 0,14 ) , ( 0 , - 14 )$ 
D)  x-intercepts $\left( \frac { 7 } { 4 } , 0 \right) , \left( - \frac { 7 } { 4 } , 0 \right) ; y$-intercepts $( 0,14 ) , ( 0 , - 14 )$

Question 12

Explain why the graph of an ellipse does not satisfy the conditions for the graph of a function.

Accepted Answer

The graph of an elli

Question 13

Find the center, foci, and asymptotes of the hyperbola.
-$$\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  C: $( 2,2 ) ; F : ( 2 , - 3 ) , ( 2,7 ) ; A : y = \frac { 4 } { 3 } x - \frac { 2 } { 3 } , y = - \frac { 4 } { 3 } x - \frac { 14 } { 3 }$ 
B)  $C : ( 2,2 ) ; F : ( - 1,2 ) , ( 5,2 ) ; A : y = \frac { 9 } { 16 } x - \frac { 7 } { 8 } , y = - \frac { 9 } { 16 } x - \frac { 7 } { 8 }$ 
C)  $C : ( 2,2 ) ; F : ( 2 , - 1 ) , ( 2,5 ) ; A : y = \frac { 9 } { 16 } x - \frac { 1 } { 8 } , y = - \frac { 9 } { 16 } x - \frac { 7 } { 8 }$ 
D)  $C : ( 2,2 ) ; F : ( - 3,2 ) , ( 7,2 ) ; A : y = \frac { 3 } { 4 } x + \frac { 1 } { 2 } , y = - \frac { 3 } { 4 } x + \frac { 7 } { 2 }$ 
A)  C: $( 2,2 ) ; F : ( 2 , - 3 ) , ( 2,7 ) ; A : y = \frac { 4 } { 3 } x - \frac { 2 } { 3 } , y = - \frac { 4 } { 3 } x - \frac { 14 } { 3 }$ 
B)  $C : ( 2,2 ) ; F : ( - 1,2 ) , ( 5,2 ) ; A : y = \frac { 9 } { 16 } x - \frac { 7 } { 8 } , y = - \frac { 9 } { 16 } x - \frac { 7 } { 8 }$ 
C)  $C : ( 2,2 ) ; F : ( 2 , - 1 ) , ( 2,5 ) ; A : y = \frac { 9 } { 16 } x - \frac { 1 } { 8 } , y = - \frac { 9 } { 16 } x - \frac { 7 } { 8 }$ 
D)  $C : ( 2,2 ) ; F : ( - 3,2 ) , ( 7,2 ) ; A : y = \frac { 3 } { 4 } x + \frac { 1 } { 2 } , y = - \frac { 3 } { 4 } x + \frac { 7 } { 2 }$

Question 14

Provide an appropriate response.
-Under what condition is this statement true for all x and y? $$( x + y ) ^ { n } = x ^ { n } + y ^ { n }$$

Accepted Answer

The answer of Provide an appropriate response.
-Under what condition is...

Question 15

Decide whether the given sequence is finite or infinite.
-$$- 5 , - 4 , - 3 , - 2$$

Accepted Answer

A)  Finite 
B)  Infinite 
A)  Finite 
B)  Infinite

Question 16

A comet follows the hyperbolic path described by $\frac { x ^ { 2 } } { 10 } - \frac { y ^ { 2 } } { 2 } = 1$, where $x$ and $y$ are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?

Accepted Answer

A)  3.7 million mi 
B)  0.3 million mi 
C)  3.2 million mi 
D)  12 million mi 
A)  3.7 million mi 
B)  0.3 million mi 
C)  3.2 million mi 
D)  12 million mi

Question 17

Evaluate the expression.
-P(5, 0)

Accepted Answer

A)  120 
B)  0.5 
C)  240 
D)  1 
A)  120 
B)  0.5 
C)  240 
D)  1

Question 18

Match the equation of the parabola with the appropriate description.
-$$y - 6 = 2 ( x - 5 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( 5,6 )$ 
B)  Vertex at $( - 5 , - 6 )$ 
C)  Vertex at $( 10,6 )$ 
D)  Vertex at $( - 10 , - 6 )$ 
A)  Vertex at $( 5,6 )$ 
B)  Vertex at $( - 5 , - 6 )$ 
C)  Vertex at $( 10,6 )$ 
D)  Vertex at $( - 10 , - 6 )$

Question 19

Write an equation for the parabola.
-vertex (4, 8), focus (4, 10)

Accepted Answer

A)  $y - 8 = 8 ( x - 4 ) ^ { 2 }$ 
B)  $8 ( y - 8 ) = ( x - 4 ) ^ { 2 }$ 
C)  $2 ( y - 8 ) = ( x - 4 ) ^ { 2 }$ 
D)  $( y - 8 ) ^ { 2 } = 8 ( x - 4 )$ 
A)  $y - 8 = 8 ( x - 4 ) ^ { 2 }$ 
B)  $8 ( y - 8 ) = ( x - 4 ) ^ { 2 }$ 
C)  $2 ( y - 8 ) = ( x - 4 ) ^ { 2 }$ 
D)  $( y - 8 ) ^ { 2 } = 8 ( x - 4 )$

Question 20

Provide an appropriate response.
-Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither?

Accepted Answer

A)  Neither 
B)  Combination 
C)  Permutation 
A)  Neither 
B)  Combination 
C)  Permutation

Choose the equation that matches the graph. -

Match the equation of the parabola with the appropriate description. - $x = - 4 y ^ { 2 } + 5 y + 3$

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $\frac{y}{6}=\sqrt{1-\frac{x^{2}}{16}}$ $Graph the equation. Give the domain and range. Identify whether the equation is a function. - \frac{y}{6}=\sqrt{1-\frac{x^{2}}{16}}$

Graph the hyperbola. - $\frac { ( x + 2 ) ^ { 2 } } { 49 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { ( x + 2 ) ^ { 2 } } { 49 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$

The series of sketches below starts with a square having sides of length 1 (one). In the following steps, squares are constructed by joining, in order, the midpoints of the sides of the previous square. Develop a formula for the perimeter of the nth square.

A certain club initially has 160 members and membership increases by 2 members every month. If dues are $20/month, what is the total amount of dues collected during the first year?

Match the equation of the parabola with the appropriate description. - $y = 6 + 3 x - x ^ { 2 }$

Find the eccentricity of the conic section shown in the graph. - $y=-17$

Use mathematical induction to prove that the statement is true for every positive integer n. - $\text { If } 0 < a < 1 \text {, then } a ^n < 1 \text {. }$ (Assume that a is a constant.)

If the police have 7 suspects, how many different sets of 5 suspects can they select for a lineup?

Match the equation of the ellipse with the appropriate description. - $49 x ^ { 2 } = 3136 - 16 y ^ { 2 }$

Explain why the graph of an ellipse does not satisfy the conditions for the graph of a function.

Find the center, foci, and asymptotes of the hyperbola. - $\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$

Provide an appropriate response. -Under what condition is this statement true for all x and y? $( x + y ) ^ { n } = x ^ { n } + y ^ { n }$

Decide whether the given sequence is finite or infinite. - $- 5 , - 4 , - 3 , - 2$

Evaluate the expression. -P(5, 0)

Match the equation of the parabola with the appropriate description. - $y - 6 = 2 ( x - 5 ) ^ { 2 }$

Write an equation for the parabola. -vertex (4, 8), focus (4, 10)

Provide an appropriate response. -Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Exam 7: Arithmetic Sequence: Common Difference and First n Terms

Choose the equation that matches the graph. -

Match the equation of the parabola with the appropriate description. - x=−4y2+5y+3x = - 4 y ^ { 2 } + 5 y + 3x=−4y2+5y+3

Graph the equation. Give the domain and range. Identify whether the equation is a function. - y6=1−x216\frac{y}{6}=\sqrt{1-\frac{x^{2}}{16}}6y​=1−16x2​​

Graph the hyperbola. - (x+2)249−(y−2)236=1\frac { ( x + 2 ) ^ { 2 } } { 49 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 149(x+2)2​−36(y−2)2​=1

The series of sketches below starts with a square having sides of length 1 (one). In the following steps, squares are constructed by joining, in order, the midpoints of the sides of the previous square. Develop a formula for the perimeter of the nth square.

A certain club initially has 160 members and membership increases by 2 members every month. If dues are $20/month, what is the total amount of dues collected during the first year?

Match the equation of the parabola with the appropriate description. - y=6+3x−x2y = 6 + 3 x - x ^ { 2 }y=6+3x−x2

Find the eccentricity of the conic section shown in the graph. - y=−17y=-17y=−17

Use mathematical induction to prove that the statement is true for every positive integer n. - If 0<a<1, then an<1. \text { If } 0 < a < 1 \text {, then } a ^n < 1 \text {. } If 0<a<1, then an<1. (Assume that a is a constant.)

If the police have 7 suspects, how many different sets of 5 suspects can they select for a lineup?

Match the equation of the ellipse with the appropriate description. - 49x2=3136−16y249 x ^ { 2 } = 3136 - 16 y ^ { 2 }49x2=3136−16y2

Explain why the graph of an ellipse does not satisfy the conditions for the graph of a function.

Find the center, foci, and asymptotes of the hyperbola. - (x−2)216−(y−2)29=1\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y - 2 ) ^ { 2 } } { 9 } = 116(x−2)2​−9(y−2)2​=1

Provide an appropriate response. -Under what condition is this statement true for all x and y? (x+y)n=xn+yn( x + y ) ^ { n } = x ^ { n } + y ^ { n }(x+y)n=xn+yn

Decide whether the given sequence is finite or infinite. - −5,−4,−3,−2- 5 , - 4 , - 3 , - 2−5,−4,−3,−2

A comet follows the hyperbolic path described by x210−y22=1\frac { x ^ { 2 } } { 10 } - \frac { y ^ { 2 } } { 2 } = 110x2​−2y2​=1 , where xxx and yyy are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?

Evaluate the expression. -P(5, 0)

Match the equation of the parabola with the appropriate description. - y−6=2(x−5)2y - 6 = 2 ( x - 5 ) ^ { 2 }y−6=2(x−5)2

Write an equation for the parabola. -vertex (4, 8), focus (4, 10)

Provide an appropriate response. -Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Match the equation of the parabola with the appropriate description. - $x = - 4 y ^ { 2 } + 5 y + 3$

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $\frac{y}{6}=\sqrt{1-\frac{x^{2}}{16}}$ $Graph the equation. Give the domain and range. Identify whether the equation is a function. - \frac{y}{6}=\sqrt{1-\frac{x^{2}}{16}}$

Graph the hyperbola. - $\frac { ( x + 2 ) ^ { 2 } } { 49 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { ( x + 2 ) ^ { 2 } } { 49 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$

Match the equation of the parabola with the appropriate description. - $y = 6 + 3 x - x ^ { 2 }$

Find the eccentricity of the conic section shown in the graph. - $y=-17$

Use mathematical induction to prove that the statement is true for every positive integer n. - $\text { If } 0 < a < 1 \text {, then } a ^n < 1 \text {. }$ (Assume that a is a constant.)

Match the equation of the ellipse with the appropriate description. - $49 x ^ { 2 } = 3136 - 16 y ^ { 2 }$

Find the center, foci, and asymptotes of the hyperbola. - $\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$

Provide an appropriate response. -Under what condition is this statement true for all x and y? $( x + y ) ^ { n } = x ^ { n } + y ^ { n }$

Decide whether the given sequence is finite or infinite. - $- 5 , - 4 , - 3 , - 2$

Match the equation of the parabola with the appropriate description. - $y - 6 = 2 ( x - 5 ) ^ { 2 }$