Question 1

Evaluate the series, if it converges.
-$$9 - \frac { 9 } { 5 } + \frac { 9 } { 25 } - \frac { 9 } { 125 } + \ldots$$

Accepted Answer

A)  Does not converge 
B)  $\frac { 15 } { 2 }$ 
C)  $\frac { 5 } { 6 }$ 
D)  $- \frac { 3 } { 2 }$ 
A)  Does not converge 
B)  $\frac { 15 } { 2 }$ 
C)  $\frac { 5 } { 6 }$ 
D)  $- \frac { 3 } { 2 }$

Question 2

Use a calculator to evaluate the expression.
-$${ } _ { 60 } \mathrm { P } _ { 5 }$$

Accepted Answer

A)  5,461,512 
B)  655,381,440 
C)  10,923,024 
D)  131,076,288 
A)  5,461,512 
B)  655,381,440 
C)  10,923,024 
D)  131,076,288

Question 3

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$0.63 ^ { n } < 0.63 ^ { n - 1 }$$

Accepted Answer

Answers will vary. One possible proof fo

Question 4

A musician plans to perform 5 selections for a concert. If he can choose from 8 different selections, how many ways can he arrange his program?

Accepted Answer

A)  32,768 
B)  56 
C)  40 
D)  6720 
A)  32,768 
B)  56 
C)  40 
D)  6720

Question 5

Write an equation for the parabola with vertex at the origin.
-Through $( 6 , - 6 \sqrt { 6 } )$, symmetric with respect to the $x$-axis

Accepted Answer

A)  $y ^ { 2 } = 36 x$ 
B)  $x = \sqrt { 6 } y ^ { 2 }$ 
C)  $x ^ { 2 } = - \sqrt { 6 } y$ 
D)  $x = 36 y ^ { 2 }$ 
A)  $y ^ { 2 } = 36 x$ 
B)  $x = \sqrt { 6 } y ^ { 2 }$ 
C)  $x ^ { 2 } = - \sqrt { 6 } y$ 
D)  $x = 36 y ^ { 2 }$

Question 6

Provide an appropriate response.
-In the ellipse $\frac { ( y + 3 ) ^ { 2 } } { 36 } + \frac { ( x - 6 ) ^ { 2 } } { 16 } = 1$, what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Accepted Answer

A)  Horizontal: $y = 3$; Vertical: $x = 6$ 
B)  Horizontal: $y = 6$; Vertical: $x = - 3$ 
C)  Horizontal: $y = 3$; Vertical: $x = - 6$ 
D)  Horizontal: $y = - 3$; Vertical: $x = 6$ 
A)  Horizontal: $y = 3$; Vertical: $x = 6$ 
B)  Horizontal: $y = 6$; Vertical: $x = - 3$ 
C)  Horizontal: $y = 3$; Vertical: $x = - 6$ 
D)  Horizontal: $y = - 3$; Vertical: $x = 6$

Question 7

Find the first six terms of the sequence.
-$$a _ { 1 } = 3 , a _ { 2 } = 4 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$$

Accepted Answer

A)  3, 4, 7, 11, 18, 29 
B)  3, 4, 6, 9, 12, 15 
C)  3, 4, 12, 48, 576, 27,648 
D)  3, 4, 7, 8, 11, 11 
A)  3, 4, 7, 11, 18, 29 
B)  3, 4, 6, 9, 12, 15 
C)  3, 4, 12, 48, 576, 27,648 
D)  3, 4, 7, 8, 11, 11

Question 8

Find the sum of the first n terms of the following arithmetic sequence.
-$$\mathrm { a } _ { 1 } = - 12 , \mathrm {~d} = - 1 ; \mathrm { n } = 5$$

Accepted Answer

A)  $- 60$ 
B)  $- 17$ 
C)  $- 70$ 
D)  7 
A)  $- 60$ 
B)  $- 17$ 
C)  $- 70$ 
D)  7

Question 9

A nuclear cooling tower cross section is a hyperbola having a diameter of 52 ft at the center. The distance between the two foci is 96 ft. What is the equation for the hyperbola?

Accepted Answer

A)  $\frac { x ^ { 2 } } { 676 } - \frac { y ^ { 2 } } { 1628 } = 5$ 
B)  $\frac { x ^ { 2 } } { 676 } - \frac { y ^ { 2 } } { 1628 } = 1$ 
C)  $\frac { x ^ { 2 } } { 676 } - \frac { y ^ { 2 } } { 2304 } = 1$ 
D)  $\frac { x ^ { 2 } } { 676 } - \frac { y ^ { 2 } } { 1630 } = 1$ 
A)  $\frac { x ^ { 2 } } { 676 } - \frac { y ^ { 2 } } { 1628 } = 5$ 
B)  $\frac { x ^ { 2 } } { 676 } - \frac { y ^ { 2 } } { 1628 } = 1$ 
C)  $\frac { x ^ { 2 } } { 676 } - \frac { y ^ { 2 } } { 2304 } = 1$ 
D)  $\frac { x ^ { 2 } } { 676 } - \frac { y ^ { 2 } } { 1630 } = 1$

Question 10

Write an equation for the hyperbola.
-$x$-intercepts $( \pm 5,0 )$; center at origin; passing through $( 5 \sqrt { 5 } , 6 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 36 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 36 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$

Question 11

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 girls?

Accepted Answer

A)  0.06252 
B)  0.15625 
C)  0.31255 
D)  0.03125 
A)  0.06252 
B)  0.15625 
C)  0.31255 
D)  0.03125

Question 12

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or 8?

Accepted Answer

A)  $\frac { 13 } { 2 }$ 
B)  9 
C)  $\frac { 9 } { 26 }$ 
D)  $\frac { 2 } { 13 }$ 
A)  $\frac { 13 } { 2 }$ 
B)  9 
C)  $\frac { 9 } { 26 }$ 
D)  $\frac { 2 } { 13 }$

Question 13

A cross-section of an irrigation canal is a parabola. If the surface of the water is 33 ft wide and the canal is 5 ft deep at the center, how deep is it 1 ft from the edge?

Accepted Answer

A)  0.3 ft 
B)  0.6 ft 
C)  4.7 ft 
D)  4.4 ft 
A)  0.3 ft 
B)  0.6 ft 
C)  4.7 ft 
D)  4.4 ft

Question 14

Graph the parabola.
-$$x = ( y + 5 ) ^ { 2 } + 7$$

Accepted Answer

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

Question 15

Find the sum of the geometric series.
-$$\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 4 } { 3 } ( 4 ) ^ { \mathrm { k } }$$

Accepted Answer

A)  $\frac { 5411 } { 3 }$ 
B)  $\frac { 5456 } { 3 }$ 
C)  $\frac { 5483 } { 3 }$ 
D)  $\frac { 5510 } { 3 }$ 
A)  $\frac { 5411 } { 3 }$ 
B)  $\frac { 5456 } { 3 }$ 
C)  $\frac { 5483 } { 3 }$ 
D)  $\frac { 5510 } { 3 }$

Question 16

Find the probability.
-A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?

Accepted Answer

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

Question 17

Write an equation for the ellipse.
-minor axis from $( - 3 , - 2 )$ to $( 1 , - 2 )$; major axis from $( - 1 , - 7 )$ to $( - 1,3 )$

Accepted Answer

A)  $\frac { ( \mathrm { x } - 1 ) ^ { 2 } } { 4 } + \frac { ( \mathrm { y } - 2 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$ 
A)  $\frac { ( \mathrm { x } - 1 ) ^ { 2 } } { 4 } + \frac { ( \mathrm { y } - 2 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$

Question 18

Find the nth term of the geometric sequence.
-$2 , - 6,18 , \ldots ; \mathrm { n } = 9$

Accepted Answer

A)  $- 4374$ 
B)  13,122 
C)  6561 
D)  118,098 
A)  $- 4374$ 
B)  13,122 
C)  6561 
D)  118,098

Question 19

Write out the first five terms of the sequence.
-$$a _ { n } = \frac { 8 n - 1 } { n ^ { 2 } + 8 n }$$

Accepted Answer

A)  $\frac { 7 } { 9 } , \frac { 3 } { 4 } , \frac { 23 } { 33 } , \frac { 31 } { 48 } , \frac { 3 } { 5 }$ 
B)  $1 , \frac { 17 } { 20 } , \frac { 25 } { 33 } , \frac { 11 } { 16 } , \frac { 41 } { 65 }$ 
C)  $\frac { 7 } { 9 } , \frac { 5 } { 4 } , \frac { 23 } { 17 } , \frac { 31 } { 24 } , \frac { 13 } { 11 }$ 
D)  $\frac { 7 } { 8 } , \frac { 15 } { 16 } , \frac { 23 } { 24 } , \frac { 31 } { 32 } , \frac { 39 } { 40 }$ 
A)  $\frac { 7 } { 9 } , \frac { 3 } { 4 } , \frac { 23 } { 33 } , \frac { 31 } { 48 } , \frac { 3 } { 5 }$ 
B)  $1 , \frac { 17 } { 20 } , \frac { 25 } { 33 } , \frac { 11 } { 16 } , \frac { 41 } { 65 }$ 
C)  $\frac { 7 } { 9 } , \frac { 5 } { 4 } , \frac { 23 } { 17 } , \frac { 31 } { 24 } , \frac { 13 } { 11 }$ 
D)  $\frac { 7 } { 8 } , \frac { 15 } { 16 } , \frac { 23 } { 24 } , \frac { 31 } { 32 } , \frac { 39 } { 40 }$

Question 20

Find the first six terms of the sequence.
-$$a _ { 1 } = 7 , a _ { 2 } = 7 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$$

Accepted Answer

A)  7, 7, 14, 14, 21, 21 
B)  7, 7, 14, 21, 35, 56 
C)  7, 7, 14, 21, 28, 35 
D)  7, 7, 49, 343, 16,807, 5,764,801 
A)  7, 7, 14, 14, 21, 21 
B)  7, 7, 14, 21, 35, 56 
C)  7, 7, 14, 21, 28, 35 
D)  7, 7, 49, 343, 16,807, 5,764,801

Evaluate the series, if it converges. - $9 - \frac { 9 } { 5 } + \frac { 9 } { 25 } - \frac { 9 } { 125 } + \ldots$

Use a calculator to evaluate the expression. - ${ } _ { 60 } \mathrm { P } _ { 5 }$

Use mathematical induction to prove that the statement is true for every positive integer n. - $0.63 ^ { n } < 0.63 ^ { n - 1 }$

A musician plans to perform 5 selections for a concert. If he can choose from 8 different selections, how many ways can he arrange his program?

Write an equation for the parabola with vertex at the origin. -Through $( 6 , - 6 \sqrt { 6 } )$ , symmetric with respect to the $x$ -axis

Provide an appropriate response. -In the ellipse $\frac { ( y + 3 ) ^ { 2 } } { 36 } + \frac { ( x - 6 ) ^ { 2 } } { 16 } = 1$ , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Find the first six terms of the sequence. - $a _ { 1 } = 3 , a _ { 2 } = 4 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Find the sum of the first n terms of the following arithmetic sequence. - $\mathrm { a } _ { 1 } = - 12 , \mathrm {~d} = - 1 ; \mathrm { n } = 5$

A nuclear cooling tower cross section is a hyperbola having a diameter of 52 ft at the center. The distance between the two foci is 96 ft. What is the equation for the hyperbola?

Write an equation for the hyperbola. - $x$ -intercepts $( \pm 5,0 )$ ; center at origin; passing through $( 5 \sqrt { 5 } , 6 )$

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 girls?

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or 8?

A cross-section of an irrigation canal is a parabola. If the surface of the water is 33 ft wide and the canal is 5 ft deep at the center, how deep is it 1 ft from the edge?

Graph the parabola. - $x = ( y + 5 ) ^ { 2 } + 7$ $Graph the parabola. - x = ( y + 5 ) ^ { 2 } + 7$

Find the sum of the geometric series. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 4 } { 3 } ( 4 ) ^ { \mathrm { k } }$

Find the probability. -A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?

Write an equation for the ellipse. -minor axis from $( - 3 , - 2 )$ to $( 1 , - 2 )$ ; major axis from $( - 1 , - 7 )$ to $( - 1,3 )$

Find the nth term of the geometric sequence. - $2 , - 6,18 , \ldots ; \mathrm { n } = 9$

Write out the first five terms of the sequence. - $a _ { n } = \frac { 8 n - 1 } { n ^ { 2 } + 8 n }$

Find the first six terms of the sequence. - $a _ { 1 } = 7 , a _ { 2 } = 7 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

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

Evaluate the series, if it converges. - 9−95+925−9125+…9 - \frac { 9 } { 5 } + \frac { 9 } { 25 } - \frac { 9 } { 125 } + \ldots9−59​+259​−1259​+…

Use a calculator to evaluate the expression. - 60P5{ } _ { 60 } \mathrm { P } _ { 5 }60​P5​

Use mathematical induction to prove that the statement is true for every positive integer n. - 0.63n<0.63n−10.63 ^ { n } < 0.63 ^ { n - 1 }0.63n<0.63n−1

A musician plans to perform 5 selections for a concert. If he can choose from 8 different selections, how many ways can he arrange his program?

Write an equation for the parabola with vertex at the origin. -Through (6,−66)( 6 , - 6 \sqrt { 6 } )(6,−66​) , symmetric with respect to the xxx -axis

Provide an appropriate response. -In the ellipse (y+3)236+(x−6)216=1\frac { ( y + 3 ) ^ { 2 } } { 36 } + \frac { ( x - 6 ) ^ { 2 } } { 16 } = 136(y+3)2​+16(x−6)2​=1 , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Find the first six terms of the sequence. - a1=3,a2=4; for n≥3,an=an−1+an−2a _ { 1 } = 3 , a _ { 2 } = 4 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }a1​=3,a2​=4; for n≥3,an​=an−1​+an−2​

Find the sum of the first n terms of the following arithmetic sequence. - a1=−12, d=−1;n=5\mathrm { a } _ { 1 } = - 12 , \mathrm {~d} = - 1 ; \mathrm { n } = 5a1​=−12, d=−1;n=5

A nuclear cooling tower cross section is a hyperbola having a diameter of 52 ft at the center. The distance between the two foci is 96 ft. What is the equation for the hyperbola?

Write an equation for the hyperbola. - xxx -intercepts (±5,0)( \pm 5,0 )(±5,0) ; center at origin; passing through (55,6)( 5 \sqrt { 5 } , 6 )(55​,6)

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 girls?

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or 8?

A cross-section of an irrigation canal is a parabola. If the surface of the water is 33 ft wide and the canal is 5 ft deep at the center, how deep is it 1 ft from the edge?

Graph the parabola. - x=(y+5)2+7x = ( y + 5 ) ^ { 2 } + 7x=(y+5)2+7

Find the sum of the geometric series. - ∑k=1543(4)k\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 4 } { 3 } ( 4 ) ^ { \mathrm { k } }∑k=15​34​(4)k

Find the probability. -A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?

Write an equation for the ellipse. -minor axis from (−3,−2)( - 3 , - 2 )(−3,−2) to (1,−2)( 1 , - 2 )(1,−2) ; major axis from (−1,−7)( - 1 , - 7 )(−1,−7) to (−1,3)( - 1,3 )(−1,3)

Find the nth term of the geometric sequence. - 2,−6,18,…;n=92 , - 6,18 , \ldots ; \mathrm { n } = 92,−6,18,…;n=9

Write out the first five terms of the sequence. - an=8n−1n2+8na _ { n } = \frac { 8 n - 1 } { n ^ { 2 } + 8 n }an​=n2+8n8n−1​

Find the first six terms of the sequence. - a1=7,a2=7; for n≥3,an=an−1+an−2a _ { 1 } = 7 , a _ { 2 } = 7 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }a1​=7,a2​=7; for n≥3,an​=an−1​+an−2​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Evaluate the series, if it converges. - $9 - \frac { 9 } { 5 } + \frac { 9 } { 25 } - \frac { 9 } { 125 } + \ldots$

Use a calculator to evaluate the expression. - ${ } _ { 60 } \mathrm { P } _ { 5 }$

Use mathematical induction to prove that the statement is true for every positive integer n. - $0.63 ^ { n } < 0.63 ^ { n - 1 }$

Write an equation for the parabola with vertex at the origin. -Through $( 6 , - 6 \sqrt { 6 } )$ , symmetric with respect to the $x$ -axis

Provide an appropriate response. -In the ellipse $\frac { ( y + 3 ) ^ { 2 } } { 36 } + \frac { ( x - 6 ) ^ { 2 } } { 16 } = 1$ , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Find the first six terms of the sequence. - $a _ { 1 } = 3 , a _ { 2 } = 4 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Find the sum of the first n terms of the following arithmetic sequence. - $\mathrm { a } _ { 1 } = - 12 , \mathrm {~d} = - 1 ; \mathrm { n } = 5$

Write an equation for the hyperbola. - $x$ -intercepts $( \pm 5,0 )$ ; center at origin; passing through $( 5 \sqrt { 5 } , 6 )$

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 girls?

Graph the parabola. - $x = ( y + 5 ) ^ { 2 } + 7$ $Graph the parabola. - x = ( y + 5 ) ^ { 2 } + 7$

Find the sum of the geometric series. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 4 } { 3 } ( 4 ) ^ { \mathrm { k } }$

Write an equation for the ellipse. -minor axis from $( - 3 , - 2 )$ to $( 1 , - 2 )$ ; major axis from $( - 1 , - 7 )$ to $( - 1,3 )$

Find the nth term of the geometric sequence. - $2 , - 6,18 , \ldots ; \mathrm { n } = 9$

Write out the first five terms of the sequence. - $a _ { n } = \frac { 8 n - 1 } { n ^ { 2 } + 8 n }$

Find the first six terms of the sequence. - $a _ { 1 } = 7 , a _ { 2 } = 7 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$