Question 1

Determine the two equations necessary to graph the hyperbola with a graphing calculator.
-$$y ^ { 2 } - 64 x ^ { 2 } = 64$$

Accepted Answer

A)  $y = 8 \sqrt { x ^ { 2 } + 1 }$ and $y = - 8 \sqrt { x ^ { 2 } + 1 }$ 
B)  $y = 8 + \sqrt { x ^ { 2 } }$ and $- y = - 8 - \sqrt { x ^ { 2 } }$ 
C)  $y = 8 + \sqrt { x ^ { 2 } }$ and $y = 8 - \sqrt { x ^ { 2 } }$ 
D)  $y = 8 x ^ { 2 } + 8$ and $y = - 8 x ^ { 2 } - 8$ 
A)  $y = 8 \sqrt { x ^ { 2 } + 1 }$ and $y = - 8 \sqrt { x ^ { 2 } + 1 }$ 
B)  $y = 8 + \sqrt { x ^ { 2 } }$ and $- y = - 8 - \sqrt { x ^ { 2 } }$ 
C)  $y = 8 + \sqrt { x ^ { 2 } }$ and $y = 8 - \sqrt { x ^ { 2 } }$ 
D)  $y = 8 x ^ { 2 } + 8$ and $y = - 8 x ^ { 2 } - 8$

Question 2

Find the sum of the geometric series.
-$$\sum _ { k = 1 } ^ { 5 } 2 ( - 3 ) ^ { k }$$

Accepted Answer

A)  75 
B)  12 
C)  $- 366$ 
D)  $- 1230$ 
A)  75 
B)  12 
C)  $- 366$ 
D)  $- 1230$

Question 3

A stack of poles has 36 poles in the bottom row, 35 poles in the next row, and so on, with 10 poles in the top row. How many poles are there in the stack?

Accepted Answer

A)  611 
B)  555 
C)  621 
D)  631 
A)  611 
B)  555 
C)  621 
D)  631

Question 4

Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = 6 ( \mathrm { x } - 9 ) ^ { 2 } - 7$ is a parabola with axis of symmetry ــــــــــــــــand vertexـــــــــــــــــــــــ

Accepted Answer

A)  $x = 9 ; ( 9 , - 7 )$ 
B)  $\ { x = 6 ; ( - 9 , - 7 ) }$ 
C)  $( - 9 , - 7 ) ; x = - 9$ 
D)  $x = 9 ; ( - 9 , - 7 )$ 
A)  $x = 9 ; ( 9 , - 7 )$ 
B)  $\ { x = 6 ; ( - 9 , - 7 ) }$ 
C)  $( - 9 , - 7 ) ; x = - 9$ 
D)  $x = 9 ; ( - 9 , - 7 )$

Question 5

Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ What is the probability of having at least four girls?

Accepted Answer

A)  0.0313 
B)  0.1875 
C)  0.3125 
D)  0.1563 
A)  0.0313 
B)  0.1875 
C)  0.3125 
D)  0.1563

Question 6

Discuss the symmetries exhibited by an ellipse centered at the origin.

Accepted Answer

An ellipse centered at the ori

Question 7

There are 5 women running in a race. How many first, second, and third place possibilities can occur?

Accepted Answer

A)  10 
B)  125 
C)  60 
D)  15 
A)  10 
B)  125 
C)  60 
D)  15

Question 8

Find the common ratio r for the given infinite geometric sequence.
-4, 16, 64, 256, 1024, . . .

Accepted Answer

A)  4 
B)  $- 4$ 
C)  16 
D)  $\frac { 1 } { 4 }$ 
A)  4 
B)  $- 4$ 
C)  16 
D)  $\frac { 1 } { 4 }$

Question 9

Find a general term aS1U1B1nS1U1B0 for the geometric sequence.
-$$a _ { 1 } = \frac { 1 } { 4 } , r = 8$$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 4 } \cdot 8 ^ { n - 1 }$ 
B)  $a _ { n } = \frac { 1 } { 4 } + \frac { 7 } { 4 } ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 4 } \right) n - 1 + \frac { 7 } { 4 }$ 
D)  $a _ { n } = \frac { 1 } { 4 } + 8 ( n - 1 )$ 
A)  $a _ { n } = \frac { 1 } { 4 } \cdot 8 ^ { n - 1 }$ 
B)  $a _ { n } = \frac { 1 } { 4 } + \frac { 7 } { 4 } ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 4 } \right) n - 1 + \frac { 7 } { 4 }$ 
D)  $a _ { n } = \frac { 1 } { 4 } + 8 ( n - 1 )$

Question 10

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$6 ^ { n } > n$$

Accepted Answer

Answers will vary. One possible proof fo

Question 11

Identify the type of graph.
$6 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 0$

Accepted Answer

A)  The graph is a circle with center  (1,-3) . 
B)  The graph is an ellipse with center  (1,-3) . 
C)  The graph is the point  (-1,3) . 
D)  The equation has no graph. 
A)  The graph is a circle with center  (1,-3) . 
B)  The graph is an ellipse with center  (1,-3) . 
C)  The graph is the point  (-1,3) . 
D)  The equation has no graph.

Question 12

Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ . What is the probability of having no more than three boys?

Accepted Answer

A)  0.8125 
B)  0.9688 
C)  0.5000 
D)  0.3125 
A)  0.8125 
B)  0.9688 
C)  0.5000 
D)  0.3125

Question 13

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = 56 e ^ { n }$$

Accepted Answer

A)  Diverges 
B)  Converges 
A)  Diverges 
B)  Converges

Question 14

Give the focus, directrix, and axis for the parabola.
-$x ^ { 2 } = 40 y$

Accepted Answer

A)  $( 10,0 ) , y = 10 , y$-axis 
B)  $( 10,0 ) , x = 10 , x$-axis 
C)  $( 0 , - 10 ) , x = - 10 , x$-axis 
D)  $( 0,10 )$, $y = - 10$, y-axis 
A)  $( 10,0 ) , y = 10 , y$-axis 
B)  $( 10,0 ) , x = 10 , x$-axis 
C)  $( 0 , - 10 ) , x = - 10 , x$-axis 
D)  $( 0,10 )$, $y = - 10$, y-axis

Question 15

Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 2, 7, or 6?

Accepted Answer

A)  $\frac { 1 } { 10 }$ 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 3 } { 10 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $\frac { 1 } { 10 }$ 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 3 } { 10 }$ 
D)  $\frac { 1 } { 2 }$

Question 16

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).
-$$\mathrm { a } _ { 1 } = 2 - \sqrt { 8 } , \mathrm { a } _ { 2 } = 2 , \mathrm { n } = 4$$

Accepted Answer

A)  $0,0 - \sqrt { 8 } , 3 - 3 \sqrt { 8 } , 4 - 4 \sqrt { 8 }$ 
B)  $2 - \sqrt { 8 } , 3 - \sqrt { 8 } , 4 - \sqrt { 8 } , 5 - \sqrt { 8 }$ 
C)  $0,2 - \sqrt { 8 } , 2,2 + \sqrt { 8 }$ 
D)  $2 - \sqrt { 8 } , 2,2 + \sqrt { 8 } , 2 + 2 \sqrt { 8 }$ 
A)  $0,0 - \sqrt { 8 } , 3 - 3 \sqrt { 8 } , 4 - 4 \sqrt { 8 }$ 
B)  $2 - \sqrt { 8 } , 3 - \sqrt { 8 } , 4 - \sqrt { 8 } , 5 - \sqrt { 8 }$ 
C)  $0,2 - \sqrt { 8 } , 2,2 + \sqrt { 8 }$ 
D)  $2 - \sqrt { 8 } , 2,2 + \sqrt { 8 } , 2 + 2 \sqrt { 8 }$

Question 17

A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius of 578 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 490
Km to 261 km.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 839 ^ { 2 } } + \frac { y ^ { 2 } } { 1068 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 261 } + \frac { y ^ { 2 } } { 490 } = 1$ 
C)  $\frac { x ^ { 2 } } { 1068 ^ { 2 } } + \frac { y ^ { 2 } } { 839 ^ { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { 490 } + \frac { y ^ { 2 } } { 261 } = 1$ 
A)  $\frac { x ^ { 2 } } { 839 ^ { 2 } } + \frac { y ^ { 2 } } { 1068 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 261 } + \frac { y ^ { 2 } } { 490 } = 1$ 
C)  $\frac { x ^ { 2 } } { 1068 ^ { 2 } } + \frac { y ^ { 2 } } { 839 ^ { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { 490 } + \frac { y ^ { 2 } } { 261 } = 1$

Question 18

Identify the type of graph.
-$$\frac { x ^ { 2 } } { 10 } = 1 - \frac { y ^ { 2 } } { 2 }$$

Accepted Answer

A)  The graph is an ellipse with foci on the y-axis. 
B)  The graph is a hyperbola with foci on the y-axis. 
C)  The graph is an ellipse with foci on the x-axis. 
D)  The graph is a hyperbola with foci on the x-axis. 
A)  The graph is an ellipse with foci on the y-axis. 
B)  The graph is a hyperbola with foci on the y-axis. 
C)  The graph is an ellipse with foci on the x-axis. 
D)  The graph is a hyperbola with foci on the x-axis.

Question 19

Provide an appropriate response.
-Consider the selections of particular thirteen card bridge hands. Is this a combination, a permutation, or neither?

Accepted Answer

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

Question 20

During the first day of an epidemic 8000 people get sick, during the second day 16,000 people get sick, and so on with the number of people getting sick increasing by 8000 each day. The epidemic peaks after 30 days with
8000 fewer people getting sick on the 31st day than on the 30th day, and so forth. What is the total number of
People who get sick?

Accepted Answer

A)  7,320,000 
B)  6,960,000 
C)  7,440,000 
D)  7,200,000 
A)  7,320,000 
B)  6,960,000 
C)  7,440,000 
D)  7,200,000

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - $y ^ { 2 } - 64 x ^ { 2 } = 64$

Find the sum of the geometric series. - $\sum _ { k = 1 } ^ { 5 } 2 ( - 3 ) ^ { k }$

A stack of poles has 36 poles in the bottom row, 35 poles in the next row, and so on, with 10 poles in the top row. How many poles are there in the stack?

Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = 6 ( \mathrm { x } - 9 ) ^ { 2 } - 7$ is a parabola with axis of symmetry ــــــــــــــــand vertexـــــــــــــــــــــــ

Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ What is the probability of having at least four girls?

Discuss the symmetries exhibited by an ellipse centered at the origin.

There are 5 women running in a race. How many first, second, and third place possibilities can occur?

Find the common ratio r for the given infinite geometric sequence. -4, 16, 64, 256, 1024, . . .

Find a general term a_n for the geometric sequence. - $a _ { 1 } = \frac { 1 } { 4 } , r = 8$

Use mathematical induction to prove that the statement is true for every positive integer n. - $6 ^ { n } > n$

Identify the type of graph. $6 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 0$

Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ . What is the probability of having no more than three boys?

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = 56 e ^ { n }$

Give the focus, directrix, and axis for the parabola. - $x ^ { 2 } = 40 y$

Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 2, 7, or 6?

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\mathrm { a } _ { 1 } = 2 - \sqrt { 8 } , \mathrm { a } _ { 2 } = 2 , \mathrm { n } = 4$

A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius of 578 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 490 Km to 261 km.

Identify the type of graph. - $\frac { x ^ { 2 } } { 10 } = 1 - \frac { y ^ { 2 } } { 2 }$

Provide an appropriate response. -Consider the selections of particular thirteen card bridge hands. 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

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - y2−64x2=64y ^ { 2 } - 64 x ^ { 2 } = 64y2−64x2=64

Find the sum of the geometric series. - ∑k=152(−3)k\sum _ { k = 1 } ^ { 5 } 2 ( - 3 ) ^ { k }∑k=15​2(−3)k

A stack of poles has 36 poles in the bottom row, 35 poles in the next row, and so on, with 10 poles in the top row. How many poles are there in the stack?

Fill in the blanks to complete the statement. The graph of P(x)=6(x−9)2−7\mathrm { P } ( \mathrm { x } ) = 6 ( \mathrm { x } - 9 ) ^ { 2 } - 7P(x)=6(x−9)2−7 is a parabola with axis of symmetry ــــــــــــــــand vertexـــــــــــــــــــــــ

Suppose that a family has 5 children and that the probability of having a girl is 12\frac { 1 } { 2 }21​ What is the probability of having at least four girls?

Discuss the symmetries exhibited by an ellipse centered at the origin.

There are 5 women running in a race. How many first, second, and third place possibilities can occur?

Find the common ratio r for the given infinite geometric sequence. -4, 16, 64, 256, 1024, . . .

Find a general term an for the geometric sequence. - a1=14,r=8a _ { 1 } = \frac { 1 } { 4 } , r = 8a1​=41​,r=8

Use mathematical induction to prove that the statement is true for every positive integer n. - 6n>n6 ^ { n } > n6n>n

Identify the type of graph. 6x2−12x+3y2+18y−21=06 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 06x2−12x+3y2+18y−21=0

Suppose that a family has 5 children and that the probability of having a girl is 12\frac { 1 } { 2 }21​ . What is the probability of having no more than three boys?

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - an=56ena _ { n } = 56 e ^ { n }an​=56en

Give the focus, directrix, and axis for the parabola. - x2=40yx ^ { 2 } = 40 yx2=40y

Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 2, 7, or 6?

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - a1=2−8,a2=2,n=4\mathrm { a } _ { 1 } = 2 - \sqrt { 8 } , \mathrm { a } _ { 2 } = 2 , \mathrm { n } = 4a1​=2−8​,a2​=2,n=4

A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius of 578 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 490 Km to 261 km.

Identify the type of graph. - x210=1−y22\frac { x ^ { 2 } } { 10 } = 1 - \frac { y ^ { 2 } } { 2 }10x2​=1−2y2​

Provide an appropriate response. -Consider the selections of particular thirteen card bridge hands. 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

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - $y ^ { 2 } - 64 x ^ { 2 } = 64$

Find the sum of the geometric series. - $\sum _ { k = 1 } ^ { 5 } 2 ( - 3 ) ^ { k }$

Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = 6 ( \mathrm { x } - 9 ) ^ { 2 } - 7$ is a parabola with axis of symmetry ــــــــــــــــand vertexـــــــــــــــــــــــ

Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ What is the probability of having at least four girls?

Find a general term a_n for the geometric sequence. - $a _ { 1 } = \frac { 1 } { 4 } , r = 8$

Use mathematical induction to prove that the statement is true for every positive integer n. - $6 ^ { n } > n$

Identify the type of graph. $6 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 0$

Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ . What is the probability of having no more than three boys?

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = 56 e ^ { n }$

Give the focus, directrix, and axis for the parabola. - $x ^ { 2 } = 40 y$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\mathrm { a } _ { 1 } = 2 - \sqrt { 8 } , \mathrm { a } _ { 2 } = 2 , \mathrm { n } = 4$

Identify the type of graph. - $\frac { x ^ { 2 } } { 10 } = 1 - \frac { y ^ { 2 } } { 2 }$