Question 1

Provide an appropriate response.
-For $\frac { 8 } { 15 } , x , \frac { 13 } { 10 }$ to be a geometric sequence, $x$ must be:

Accepted Answer

A)  $\sqrt { \frac { 195 } { 80 } }$ 
B)  $\sqrt { \frac { 150 } { 104 } }$ 
C)  $\sqrt { \frac { 104 } { 150 } }$ 
D)  $\sqrt { \frac { 80 } { 195 } }$ 
A)  $\sqrt { \frac { 195 } { 80 } }$ 
B)  $\sqrt { \frac { 150 } { 104 } }$ 
C)  $\sqrt { \frac { 104 } { 150 } }$ 
D)  $\sqrt { \frac { 80 } { 195 } }$

Question 2

Match the equation of the parabola with the appropriate description.
-$$y - 11 = 2 ( x + 3 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( 3 , - 11 )$ 
B)  Vertex at $( - 11,3 )$ 
C)  Vertex at $( - 3,11 )$ 
D)  Vertex at $( 11 , - 3 )$ 
A)  Vertex at $( 3 , - 11 )$ 
B)  Vertex at $( - 11,3 )$ 
C)  Vertex at $( - 3,11 )$ 
D)  Vertex at $( 11 , - 3 )$

Question 3

Decide whether the given sequence is finite or infinite.
-$$a _ { 1 } = 5 ; \text { for } 2 \leq n \leq 50 , a _ { n } = 8 \cdot a _ { n - 1 }$$

Accepted Answer

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

Question 4

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).
-$$a _ { 3 } = 4 , d = - 2 , n = 5$$

Accepted Answer

A)  $8,6,4,2,0$ 
B)  $8,6,3,2,0$ 
C)  $10,8,6,4,2$ 
D)  $6,4,2,0 , - 2$ 
A)  $8,6,4,2,0$ 
B)  $8,6,3,2,0$ 
C)  $10,8,6,4,2$ 
D)  $6,4,2,0 , - 2$

Question 5

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { i = 2 } ^ { 5 } ( 3 i - 3 )$$

Accepted Answer

A)  27 
B)  24 
C)  30 
D)  18 
A)  27 
B)  24 
C)  30 
D)  18

Question 6

Write an equation for the parabola.
-vertex $( - 3,5 )$, focus $( - 14,5 )$

Accepted Answer

A)  $x + 3 = - 44 ( y - 5 ) ^ { 2 }$ 
B)  $x + 5 = - 14 ( y - 3 ) ^ { 2 }$ 
C)  $- 44 ( x - 3 ) = ( y + 5 ) ^ { 2 }$ 
D)  $( y - 5 ) ^ { 2 } = - 44 ( x + 3 )$ 
A)  $x + 3 = - 44 ( y - 5 ) ^ { 2 }$ 
B)  $x + 5 = - 14 ( y - 3 ) ^ { 2 }$ 
C)  $- 44 ( x - 3 ) = ( y + 5 ) ^ { 2 }$ 
D)  $( y - 5 ) ^ { 2 } = - 44 ( x + 3 )$

Question 7

Write the binomial expansion of the expression.
-$$( - 2 m + 4 n ) ^ { 4 }$$

Accepted Answer

A)  $16 m ^ { 4 } - 128 m ^ { 3 } n - 384 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } - 256 n ^ { 4 }$ 
B)  $16 m ^ { 4 } - 2048 m ^ { 3 } n + 2304 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } + 256 n ^ { 4 }$ 
C)  $16 m ^ { 4 } - 2048 m ^ { 3 } n - 2304 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } - 256 n ^ { 4 }$ 
D)  $16 m ^ { 4 } - 128 m ^ { 3 } n + 384 m ^ { 2 } n ^ { 2 } - 512 m ^ { 3 } + 256 n ^ { 4 }$ 
A)  $16 m ^ { 4 } - 128 m ^ { 3 } n - 384 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } - 256 n ^ { 4 }$ 
B)  $16 m ^ { 4 } - 2048 m ^ { 3 } n + 2304 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } + 256 n ^ { 4 }$ 
C)  $16 m ^ { 4 } - 2048 m ^ { 3 } n - 2304 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } - 256 n ^ { 4 }$ 
D)  $16 m ^ { 4 } - 128 m ^ { 3 } n + 384 m ^ { 2 } n ^ { 2 } - 512 m ^ { 3 } + 256 n ^ { 4 }$

Question 8

List the elements in the sample space of the experiment.
-A box contains 13 white cards numbered 1 through 13. List the sample space of the event choosing one card with a number greater than 6.

Accepted Answer

A)  {7, 8, 9, 10, 11, 12, 13} 
B)  {1, 2, 3, . . . 13} 
C)  {6, 7, 8, 9, 10, 11, 12, 13} 
D)  {11} 
A)  {7, 8, 9, 10, 11, 12, 13} 
B)  {1, 2, 3, . . . 13} 
C)  {6, 7, 8, 9, 10, 11, 12, 13} 
D)  {11}

Question 9

A rectangular board is 4 units by 12 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?

Accepted Answer

A)  5.7 units 
B)  2.0 units 
C)  0.3 units 
D)  4.0 units 
A)  5.7 units 
B)  2.0 units 
C)  0.3 units 
D)  4.0 units

Question 10

Find the eccentricity of the conic section shown in the graph.
-  $y = \frac { 2 } { 5 } x$

Accepted Answer

A)  $e = \frac { 21 } { 5 }$ 
B)  $e = \frac { 29 } { 2 }$ 
C)  $e = \frac { \sqrt { 29 } } { 5 }$ 
D) e=1 
A)  $e = \frac { 21 } { 5 }$ 
B)  $e = \frac { 29 } { 2 }$ 
C)  $e = \frac { \sqrt { 29 } } { 5 }$ 
D) e=1

Question 11

Find the nth term of the geometric sequence.
-$$\mathrm { a } _ { 1 } = \frac { 1 } { 3 } , \mathrm { r } = \frac { 1 } { 2 } , \mathrm { n } = 5$$

Accepted Answer

A)  $a _ { 5 } = \frac { 1 } { 96 }$ 
B)  $a _ { 5 } = \frac { 1 } { 48 }$ 
C)  $a _ { 5 } = \frac { 1 } { 24 }$ 
D)  $a _ { 5 } = \frac { 1 } { 162 }$ 
A)  $a _ { 5 } = \frac { 1 } { 96 }$ 
B)  $a _ { 5 } = \frac { 1 } { 48 }$ 
C)  $a _ { 5 } = \frac { 1 } { 24 }$ 
D)  $a _ { 5 } = \frac { 1 } { 162 }$

Question 12

Write an equation for the parabola with vertex at the origin.
-Through $( \sqrt { 7 } , 7 )$, opening upward

Accepted Answer

A)  $y = x ^ { 2 }$ 
B)  $y = 7 x ^ { 2 }$ 
C)  $x = \frac { \sqrt { 7 } } { 7 } y ^ { 2 }$ 
D)  $x = y ^ { 2 }$ 
A)  $y = x ^ { 2 }$ 
B)  $y = 7 x ^ { 2 }$ 
C)  $x = \frac { \sqrt { 7 } } { 7 } y ^ { 2 }$ 
D)  $x = y ^ { 2 }$

Question 13

Evaluate the sum.
-$$\sum _ { j = 1 } ^ { 13 } ( 8 j + 7 )$$

Accepted Answer

A)  735 
B)  708 
C)  631 
D)  819 
A)  735 
B)  708 
C)  631 
D)  819

Question 14

Four boys and three girls are seated, in a row, at random, to watch a play. What is the probability that 
a) a girl is seated at each end of the row?
b) one of the boys is seated in the middle seat?
c) boys and girls are seated alternately?

Accepted Answer

A)  a) $\frac { 1 } { 7 }$ b) $\frac { 3 } { 7 }$ c) $\frac { 1 } { 35 }$ 
B)  a) $\frac { 1 } { 7 }$ b) $\frac { 4 } { 7 } \quad$ c) $\frac { 1 } { 35 }$ 
C)  a) $\frac { 3 } { 7 }$ b) $\frac { 4 } { 7 }$ c) $\frac { 1 } { 7 }$ 
D)  a) $\frac { 2 } { 7 }$ b) $\frac { 1 } { 7 } \quad$ c) $\frac { 1 } { 35 }$ 
A)  a) $\frac { 1 } { 7 }$ b) $\frac { 3 } { 7 }$ c) $\frac { 1 } { 35 }$ 
B)  a) $\frac { 1 } { 7 }$ b) $\frac { 4 } { 7 } \quad$ c) $\frac { 1 } { 35 }$ 
C)  a) $\frac { 3 } { 7 }$ b) $\frac { 4 } { 7 }$ c) $\frac { 1 } { 7 }$ 
D)  a) $\frac { 2 } { 7 }$ b) $\frac { 1 } { 7 } \quad$ c) $\frac { 1 } { 35 }$

Question 15

What are the odds in favor of drawing an even number from these cards?

Accepted Answer

A)  2 to 3 
B)  3 to 2 
C)  2 to 5 
D)  5 to 2 
A)  2 to 3 
B)  3 to 2 
C)  2 to 5 
D)  5 to 2

Question 16

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence.
-$$a _ { 10 } = 40 , a _ { 11 } = 6$$

Accepted Answer

A)  $a _ { n } = 346 + 34 ( n - 1 ) , a _ { 6 } = 550$ 
B)  $a _ { n } = 346 - 34 ( n - 1 ) , a _ { 6 } = 142$ 
C)  $a _ { n } = 346 - 34 ( n - 1 ) , a _ { 6 } = 176$ 
D)  $a _ { n } = 346 + 34 ( n - 1 ) , a _ { 6 } = 516$ 
A)  $a _ { n } = 346 + 34 ( n - 1 ) , a _ { 6 } = 550$ 
B)  $a _ { n } = 346 - 34 ( n - 1 ) , a _ { 6 } = 142$ 
C)  $a _ { n } = 346 - 34 ( n - 1 ) , a _ { 6 } = 176$ 
D)  $a _ { n } = 346 + 34 ( n - 1 ) , a _ { 6 } = 516$

Question 17

Find a general term aS1U1B1nS1U1B0 for the geometric sequence.
-$$a _ { 2 } = - 1 , a _ { 9 } = \frac { 1 } { 128 }$$

Accepted Answer

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

Question 18

Find the future value of the annuity.
-A sequence of yearly payments of $6000 is invested at the end of each of 12 years at an interest rate of 2.1%, compounded annually. What is the total amount of the annuity after 12 years?

Accepted Answer

A)  $81,926.57 
B)  $79,926.57 
C)  $80,426.57 
D)  $80,926.57 
A)  $81,926.57 
B)  $79,926.57 
C)  $80,426.57 
D)  $80,926.57

Question 19

Graph the ellipse.
-$$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$$

Accepted Answer

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

Question 20

Use a calculator to evaluate the expression.
-$${ } _ { 52 } C _ { 5 }$$

Accepted Answer

A)  62,375,040 
B)  311,875,200 
C)  5,197,920 
D)  2,598,960 
A)  62,375,040 
B)  311,875,200 
C)  5,197,920 
D)  2,598,960

Provide an appropriate response. -For $\frac { 8 } { 15 } , x , \frac { 13 } { 10 }$ to be a geometric sequence, $x$ must be:

Match the equation of the parabola with the appropriate description. - $y - 11 = 2 ( x + 3 ) ^ { 2 }$

Decide whether the given sequence is finite or infinite. - $a _ { 1 } = 5 ; \text { for } 2 \leq n \leq 50 , a _ { n } = 8 \cdot a _ { n - 1 }$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $a _ { 3 } = 4 , d = - 2 , n = 5$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 2 } ^ { 5 } ( 3 i - 3 )$

Write an equation for the parabola. -vertex $( - 3,5 )$ , focus $( - 14,5 )$

Write the binomial expansion of the expression. - $( - 2 m + 4 n ) ^ { 4 }$

List the elements in the sample space of the experiment. -A box contains 13 white cards numbered 1 through 13. List the sample space of the event choosing one card with a number greater than 6.

A rectangular board is 4 units by 12 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - y = \frac { 2 } { 5 } x$ $y = \frac { 2 } { 5 } x$

Find the nth term of the geometric sequence. - $\mathrm { a } _ { 1 } = \frac { 1 } { 3 } , \mathrm { r } = \frac { 1 } { 2 } , \mathrm { n } = 5$

Write an equation for the parabola with vertex at the origin. -Through $( \sqrt { 7 } , 7 )$ , opening upward

Evaluate the sum. - $\sum _ { j = 1 } ^ { 13 } ( 8 j + 7 )$

Four boys and three girls are seated, in a row, at random, to watch a play. What is the probability that a) a girl is seated at each end of the row? b) one of the boys is seated in the middle seat? c) boys and girls are seated alternately?

What are the odds in favor of drawing an even number from these cards?

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. - $a _ { 10 } = 40 , a _ { 11 } = 6$

Find a general term a_n for the geometric sequence. - $a _ { 2 } = - 1 , a _ { 9 } = \frac { 1 } { 128 }$

Find the future value of the annuity. -A sequence of yearly payments of $6000 is invested at the end of each of 12 years at an interest rate of 2.1%, compounded annually. What is the total amount of the annuity after 12 years?

Graph the ellipse. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$ $Graph the ellipse. - \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

Use a calculator to evaluate the expression. - ${ } _ { 52 } C _ { 5 }$

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

Provide an appropriate response. -For 815,x,1310\frac { 8 } { 15 } , x , \frac { 13 } { 10 }158​,x,1013​ to be a geometric sequence, xxx must be:

Match the equation of the parabola with the appropriate description. - y−11=2(x+3)2y - 11 = 2 ( x + 3 ) ^ { 2 }y−11=2(x+3)2

Decide whether the given sequence is finite or infinite. - a1=5; for 2≤n≤50,an=8⋅an−1a _ { 1 } = 5 ; \text { for } 2 \leq n \leq 50 , a _ { n } = 8 \cdot a _ { n - 1 }a1​=5; for 2≤n≤50,an​=8⋅an−1​

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - a3=4,d=−2,n=5a _ { 3 } = 4 , d = - 2 , n = 5a3​=4,d=−2,n=5

Evaluate the sum. Round to two decimal places, if necessary. - ∑i=25(3i−3)\sum _ { i = 2 } ^ { 5 } ( 3 i - 3 )∑i=25​(3i−3)

Write an equation for the parabola. -vertex (−3,5)( - 3,5 )(−3,5) , focus (−14,5)( - 14,5 )(−14,5)

Write the binomial expansion of the expression. - (−2m+4n)4( - 2 m + 4 n ) ^ { 4 }(−2m+4n)4

List the elements in the sample space of the experiment. -A box contains 13 white cards numbered 1 through 13. List the sample space of the event choosing one card with a number greater than 6.

A rectangular board is 4 units by 12 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?

Find the eccentricity of the conic section shown in the graph. - y=25xy = \frac { 2 } { 5 } xy=52​x

Find the nth term of the geometric sequence. - a1=13,r=12,n=5\mathrm { a } _ { 1 } = \frac { 1 } { 3 } , \mathrm { r } = \frac { 1 } { 2 } , \mathrm { n } = 5a1​=31​,r=21​,n=5

Write an equation for the parabola with vertex at the origin. -Through (7,7)( \sqrt { 7 } , 7 )(7​,7) , opening upward

Evaluate the sum. - ∑j=113(8j+7)\sum _ { j = 1 } ^ { 13 } ( 8 j + 7 )∑j=113​(8j+7)

Four boys and three girls are seated, in a row, at random, to watch a play. What is the probability that a) a girl is seated at each end of the row? b) one of the boys is seated in the middle seat? c) boys and girls are seated alternately?

What are the odds in favor of drawing an even number from these cards?

Find an and a6a _ { n } \text { and } a _ { 6 }an​ and a6​ for the following arithmetic sequence. - a10=40,a11=6a _ { 10 } = 40 , a _ { 11 } = 6a10​=40,a11​=6

Find a general term an for the geometric sequence. - a2=−1,a9=1128a _ { 2 } = - 1 , a _ { 9 } = \frac { 1 } { 128 }a2​=−1,a9​=1281​

Find the future value of the annuity. -A sequence of yearly payments of $6000 is invested at the end of each of 12 years at an interest rate of 2.1%, compounded annually. What is the total amount of the annuity after 12 years?

Graph the ellipse. - x216+y264=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 116x2​+64y2​=1

Use a calculator to evaluate the expression. - 52C5{ } _ { 52 } C _ { 5 }52​C5​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Provide an appropriate response. -For $\frac { 8 } { 15 } , x , \frac { 13 } { 10 }$ to be a geometric sequence, $x$ must be:

Match the equation of the parabola with the appropriate description. - $y - 11 = 2 ( x + 3 ) ^ { 2 }$

Decide whether the given sequence is finite or infinite. - $a _ { 1 } = 5 ; \text { for } 2 \leq n \leq 50 , a _ { n } = 8 \cdot a _ { n - 1 }$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $a _ { 3 } = 4 , d = - 2 , n = 5$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 2 } ^ { 5 } ( 3 i - 3 )$

Write an equation for the parabola. -vertex $( - 3,5 )$ , focus $( - 14,5 )$

Write the binomial expansion of the expression. - $( - 2 m + 4 n ) ^ { 4 }$

Find the eccentricity of the conic section shown in the graph. - $Find the eccentricity of the conic section shown in the graph. - y = \frac { 2 } { 5 } x$ $y = \frac { 2 } { 5 } x$

Find the nth term of the geometric sequence. - $\mathrm { a } _ { 1 } = \frac { 1 } { 3 } , \mathrm { r } = \frac { 1 } { 2 } , \mathrm { n } = 5$

Write an equation for the parabola with vertex at the origin. -Through $( \sqrt { 7 } , 7 )$ , opening upward

Evaluate the sum. - $\sum _ { j = 1 } ^ { 13 } ( 8 j + 7 )$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. - $a _ { 10 } = 40 , a _ { 11 } = 6$

Find a general term a_n for the geometric sequence. - $a _ { 2 } = - 1 , a _ { 9 } = \frac { 1 } { 128 }$

Graph the ellipse. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$ $Graph the ellipse. - \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

Use a calculator to evaluate the expression. - ${ } _ { 52 } C _ { 5 }$