Question 1

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

Accepted Answer

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

Question 2

Write out the first five terms of the sequence.
-$$a _ { n } = n ^ { 2 } - n$$

Accepted Answer

A)  $2,6,12,20,30$ 
B)  $0,3,8,15,24$ 
C)  $0,2,6,12,20$ 
D)  $1,4,9,16,25$ 
A)  $2,6,12,20,30$ 
B)  $0,3,8,15,24$ 
C)  $0,2,6,12,20$ 
D)  $1,4,9,16,25$

Question 3

Provide an appropriate response.
-Suppose that $\mathrm { A } = \mathrm { C } \neq 0$ in the equation $\mathrm { Ax } { } ^ { 2 } + \mathrm { Bx } + \mathrm { Cy } { } ^ { 2 } + \mathrm { Dy } + \mathrm { E } = 0$. What kind of graph does this equation have?

Accepted Answer

The equati

Question 4

Write an equation for the ellipse.
-center at origin; length of major axis $16 ; y$-intercepts $( 0 , \pm 5 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 8 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 5 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 8 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 5 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$

Question 5

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence.
-$$a _ { 15 } = - 10 , a _ { 17 } = - 44$$

Accepted Answer

A)  $a _ { n } = 228 + 17 ( n - 1 ) , a _ { 6 } = 1180$ 
B)  $a _ { n } = 228 - 17 ( n - 1 ) , a _ { 6 } = 330$ 
C)  $a _ { n } = 228 - 17 ( n - 1 ) , a _ { 6 } = 143$ 
D)  $a _ { n } = 228 - 17 ( n - 1 ) , a _ { 6 } = 126$ 
A)  $a _ { n } = 228 + 17 ( n - 1 ) , a _ { 6 } = 1180$ 
B)  $a _ { n } = 228 - 17 ( n - 1 ) , a _ { 6 } = 330$ 
C)  $a _ { n } = 228 - 17 ( n - 1 ) , a _ { 6 } = 143$ 
D)  $a _ { n } = 228 - 17 ( n - 1 ) , a _ { 6 } = 126$

Question 6

Write an equation for the ellipse.
-foci at $( - 2,5 ) , ( - 2 , - 1 )$; major axis length of 10

Accepted Answer

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

Question 7

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$$x = 7 y ^ { 2 } + 8$$

Accepted Answer

A)  $y = \frac { \sqrt { x - 8 } } { \sqrt { 7 } }$ and $y = \frac { \sqrt { 8 - x } } { \sqrt { 7 } }$ 
B)  $y = \sqrt { \frac { x } { 7 } - 8 }$ and $y = - \sqrt { \frac { x } { 7 } - 8 }$ 
C)  $y = \frac { \sqrt { x - 8 } } { \sqrt { 7 } }$ and $y = - \frac { \sqrt { x - 8 } } { \sqrt { 7 } }$ 
D)  $y = \frac { \sqrt { x - 8 } } { 7 }$ and $y = - \frac { \sqrt { x - 8 } } { 7 }$ 
A)  $y = \frac { \sqrt { x - 8 } } { \sqrt { 7 } }$ and $y = \frac { \sqrt { 8 - x } } { \sqrt { 7 } }$ 
B)  $y = \sqrt { \frac { x } { 7 } - 8 }$ and $y = - \sqrt { \frac { x } { 7 } - 8 }$ 
C)  $y = \frac { \sqrt { x - 8 } } { \sqrt { 7 } }$ and $y = - \frac { \sqrt { x - 8 } } { \sqrt { 7 } }$ 
D)  $y = \frac { \sqrt { x - 8 } } { 7 }$ and $y = - \frac { \sqrt { x - 8 } } { 7 }$

Question 8

A ball is dropped from a height of 5.0 m. On each upward bounce the ball returns to $$\frac { 4 } { 5 }$$ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Accepted Answer

A)  25.0 m 
B)  50.0 m 
C)  46.0 m 
D)  45.0 m 
A)  25.0 m 
B)  50.0 m 
C)  46.0 m 
D)  45.0 m

Question 9

Use a graphing calculator to evaluate the series.
-$\sum _ { j = 1 } ^ { 9 } \left( 8 j ^ { 2 } - 5 \right)$

Accepted Answer

A)  1600.5 
B)  2235 
C)  2325 
D)  279 
A)  1600.5 
B)  2235 
C)  2325 
D)  279

Question 10

Find a general term aS1U1B1nS1U1B0 for the geometric sequence.
-$$8 , - 4,2 , - 1 , \frac { 1 } { 2 } ,$$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 8 } ( - 2 ) n - 1$ 
B)  $a _ { n } = 6 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 8 \left( - \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
A)  $a _ { n } = \frac { 1 } { 8 } ( - 2 ) n - 1$ 
B)  $a _ { n } = 6 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 8 \left( - \frac { 1 } { 2 } \right) ^ { n - 1 }$

Question 11

How many 5-card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 5 $$52 \text {-card deck }$$

Accepted Answer

A)  288 
B)  12 
C)  6 
D)  24 
A)  288 
B)  12 
C)  6 
D)  24

Question 12

A musician plans to perform 3 selections. In how many ways can she arrange the musical selections?

Accepted Answer

A)  9 
B)  18 
C)  6 
D)  3 
A)  9 
B)  18 
C)  6 
D)  3

Question 13

Find the sum of the first n terms of the following arithmetic sequence.
-$$a _ { 2 } = - 65 , a _ { 5 } = 220 ; \mathrm { n } = 10$$

Accepted Answer

A)  2675 
B)  $- 5875$ 
C)  3475 
D)  $- 3475$ 
A)  2675 
B)  $- 5875$ 
C)  3475 
D)  $- 3475$

Question 14

A town has a population of 2000 people and is increasing by 9% every year. What will the population be at the end of 8 years?

Accepted Answer

A)  4344 people 
B)  3440 people 
C)  3985 people 
D)  3656 people 
A)  4344 people 
B)  3440 people 
C)  3985 people 
D)  3656 people

Question 15

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$

Accepted Answer

Answers will vary. One possible proof fo

Question 16

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$5 + 5 \cdot \frac { 1 } { 5 } + 5 \cdot \left( \frac { 1 } { 5 } \right) ^ { 2 } + \ldots + 5 \cdot \left( \frac { 1 } { 5 } \right) ^ { n - 1 } = \frac { 5 \left( 1 - \left( \frac { 1 } { 5 } \right) ^ { n } \right) } { 1 - \frac { 1 } { 5 } }$$

Accepted Answer

Also, if the statement is true for @#LAT-DLM&, the

Question 17

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = ( 18 + n ) ^ { 1 / n }$$

Accepted Answer

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

Question 18

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence.
-$$a _ { 12 } = 73 x + 1 , a _ { 14 } = 75 x + 11$$

Accepted Answer

A)  $a _ { n } = ( 62 + n ) x - 54 + 5 n , a _ { 6 } = 68 x - 24$ 
B)  $a _ { n } = ( 62 + n ) x - 49 + 5 n , a _ { 6 } = 68 x - 79$ 
C)  $a _ { n } = ( 62 - n ) x - 54 - 5 n , a _ { 6 } = 56 x - 84$ 
D)  $a _ { n } = ( 61 + n ) x - 59 + 5 n , a _ { 6 } = 67 x - 29$ 
A)  $a _ { n } = ( 62 + n ) x - 54 + 5 n , a _ { 6 } = 68 x - 24$ 
B)  $a _ { n } = ( 62 + n ) x - 49 + 5 n , a _ { 6 } = 68 x - 79$ 
C)  $a _ { n } = ( 62 - n ) x - 54 - 5 n , a _ { 6 } = 56 x - 84$ 
D)  $a _ { n } = ( 61 + n ) x - 59 + 5 n , a _ { 6 } = 67 x - 29$

Question 19

List the elements in the sample space of the experiment.
-A group of 18 people are assigned numbers 1 through 18. List the sample space of the event choosing a person with a number 5 or less.

Accepted Answer

A)  {1, 2, 3, 4, 5} 
B)  {1, 2, 3, 4} 
C)  {18} 
D)  {1} 
A)  {1, 2, 3, 4, 5} 
B)  {1, 2, 3, 4} 
C)  {18} 
D)  {1}

Question 20

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { i = 4 } ^ { 7 } \frac { - 7 } { i }$$

Accepted Answer

A)  $419.65$ 
B)  $- 2.32$ 
C)  $- 5.32$ 
D)  $1.82$ 
A)  $419.65$ 
B)  $- 2.32$ 
C)  $- 5.32$ 
D)  $1.82$

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

Write out the first five terms of the sequence. - $a _ { n } = n ^ { 2 } - n$

Provide an appropriate response. -Suppose that $\mathrm { A } = \mathrm { C } \neq 0$ in the equation $\mathrm { Ax } { } ^ { 2 } + \mathrm { Bx } + \mathrm { Cy } { } ^ { 2 } + \mathrm { Dy } + \mathrm { E } = 0$ . What kind of graph does this equation have?

Write an equation for the ellipse. -center at origin; length of major axis $16 ; y$ -intercepts $( 0 , \pm 5 )$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. - $a _ { 15 } = - 10 , a _ { 17 } = - 44$

Write an equation for the ellipse. -foci at $( - 2,5 ) , ( - 2 , - 1 )$ ; major axis length of 10

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 7 y ^ { 2 } + 8$

A ball is dropped from a height of 5.0 m. On each upward bounce the ball returns to $\frac { 4 } { 5 }$ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Use a graphing calculator to evaluate the series. - $\sum _ { j = 1 } ^ { 9 } \left( 8 j ^ { 2 } - 5 \right)$

Find a general term a_n for the geometric sequence. - $8 , - 4,2 , - 1 , \frac { 1 } { 2 } ,$

How many 5-card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 5 $52 \text {-card deck }$

A musician plans to perform 3 selections. In how many ways can she arrange the musical selections?

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 2 } = - 65 , a _ { 5 } = 220 ; \mathrm { n } = 10$

A town has a population of 2000 people and is increasing by 9% every year. What will the population be at the end of 8 years?

Use mathematical induction to prove that the statement is true for every positive integer n. - $4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = ( 18 + n ) ^ { 1 / n }$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. - $a _ { 12 } = 73 x + 1 , a _ { 14 } = 75 x + 11$

List the elements in the sample space of the experiment. -A group of 18 people are assigned numbers 1 through 18. List the sample space of the event choosing a person with a number 5 or less.

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 4 } ^ { 7 } \frac { - 7 } { i }$

Review of Basic Concepts

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

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

Write out the first five terms of the sequence. - an=n2−na _ { n } = n ^ { 2 } - nan​=n2−n

Write an equation for the ellipse. -center at origin; length of major axis 16;y16 ; y16;y -intercepts (0,±5)( 0 , \pm 5 )(0,±5)

Find an and a6a _ { n } \text { and } a _ { 6 }an​ and a6​ for the following arithmetic sequence. - a15=−10,a17=−44a _ { 15 } = - 10 , a _ { 17 } = - 44a15​=−10,a17​=−44

Write an equation for the ellipse. -foci at (−2,5),(−2,−1)( - 2,5 ) , ( - 2 , - 1 )(−2,5),(−2,−1) ; major axis length of 10

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x=7y2+8x = 7 y ^ { 2 } + 8x=7y2+8

A ball is dropped from a height of 5.0 m. On each upward bounce the ball returns to 45\frac { 4 } { 5 }54​ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Use a graphing calculator to evaluate the series. - ∑j=19(8j2−5)\sum _ { j = 1 } ^ { 9 } \left( 8 j ^ { 2 } - 5 \right)∑j=19​(8j2−5)

Find a general term an for the geometric sequence. - 8,−4,2,−1,12,8 , - 4,2 , - 1 , \frac { 1 } { 2 } ,8,−4,2,−1,21​,

How many 5-card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 5 52-card deck 52 \text {-card deck }52-card deck

A musician plans to perform 3 selections. In how many ways can she arrange the musical selections?

Find the sum of the first n terms of the following arithmetic sequence. - a2=−65,a5=220;n=10a _ { 2 } = - 65 , a _ { 5 } = 220 ; \mathrm { n } = 10a2​=−65,a5​=220;n=10

A town has a population of 2000 people and is increasing by 9% every year. What will the population be at the end of 8 years?

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - an=(18+n)1/na _ { n } = ( 18 + n ) ^ { 1 / n }an​=(18+n)1/n

Find an and a6a _ { n } \text { and } a _ { 6 }an​ and a6​ for the following arithmetic sequence. - a12=73x+1,a14=75x+11a _ { 12 } = 73 x + 1 , a _ { 14 } = 75 x + 11a12​=73x+1,a14​=75x+11

List the elements in the sample space of the experiment. -A group of 18 people are assigned numbers 1 through 18. List the sample space of the event choosing a person with a number 5 or less.

Evaluate the sum. Round to two decimal places, if necessary. - ∑i=47−7i\sum _ { i = 4 } ^ { 7 } \frac { - 7 } { i }∑i=47​i−7​

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

Write out the first five terms of the sequence. - $a _ { n } = n ^ { 2 } - n$

Write an equation for the ellipse. -center at origin; length of major axis $16 ; y$ -intercepts $( 0 , \pm 5 )$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. - $a _ { 15 } = - 10 , a _ { 17 } = - 44$

Write an equation for the ellipse. -foci at $( - 2,5 ) , ( - 2 , - 1 )$ ; major axis length of 10

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 7 y ^ { 2 } + 8$

A ball is dropped from a height of 5.0 m. On each upward bounce the ball returns to $\frac { 4 } { 5 }$ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Use a graphing calculator to evaluate the series. - $\sum _ { j = 1 } ^ { 9 } \left( 8 j ^ { 2 } - 5 \right)$

Find a general term a_n for the geometric sequence. - $8 , - 4,2 , - 1 , \frac { 1 } { 2 } ,$

How many 5-card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 5 $52 \text {-card deck }$

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 2 } = - 65 , a _ { 5 } = 220 ; \mathrm { n } = 10$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = ( 18 + n ) ^ { 1 / n }$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. - $a _ { 12 } = 73 x + 1 , a _ { 14 } = 75 x + 11$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 4 } ^ { 7 } \frac { - 7 } { i }$