Question 1

Graph the hyperbola.
-$16 x^{2}-9 y^{2}=144$

Accepted Answer

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

Question 2

Suppose that an insect population density, in thousands, during year n can be modeled by the recursively defined sequence: $$a _ { 1 } = 1 ; a _ { n } = 2.98 a _ { n - 1 } - 0.17 a _ { n - 1 } ^ { 2 } \quad \text { for } n > 1$$ Use technology to graph the sequence for n = 1, 2, 3, . . . , 20 . Describe what happens to the population density
Function.

Accepted Answer

A)  The insect population increases every year. 
B)  The insect population stabilizes near 11.65 thousand. 
C)  The insect population stabilizes near 12.58 thousand. 
D)  The insect population stabilizes near 8.45 thousand. 
A)  The insect population increases every year. 
B)  The insect population stabilizes near 11.65 thousand. 
C)  The insect population stabilizes near 12.58 thousand. 
D)  The insect population stabilizes near 8.45 thousand.

Question 3

In how many ways can a class president and a class secretary be chosen from a group of 4 candidates?

Accepted Answer

A)  8 
B)  24 
C)  7 
D)  12 
A)  8 
B)  24 
C)  7 
D)  12

Question 4

Find the eccentricity $ e $ of the ellipse.
-$$x ^ { 2 } + 2 y ^ { 2 } = 6$$

Accepted Answer

A)  $\sqrt { 2 }$ 
B)  $\sqrt { 6 }$ 
C)  $\frac { \sqrt { 6 } } { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$ 
A)  $\sqrt { 2 }$ 
B)  $\sqrt { 6 }$ 
C)  $\frac { \sqrt { 6 } } { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$

Question 5

Evaluate the series, if it converges.
-$$\sum _ { k = 1 } ^ { \infty } \left( \frac { 3 } { 8 } \right) ^ { k }$$

Accepted Answer

A)  Does not converge. 
B)  $\frac { 3 } { 5 }$ 
C)  $ - \frac { 3 } { 5 }$ 
D)  $\frac { 8 } { 5 }$ 
A)  Does not converge. 
B)  $\frac { 3 } { 5 }$ 
C)  $ - \frac { 3 } { 5 }$ 
D)  $\frac { 8 } { 5 }$

Question 6

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 3 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x + 3 ) ^ { 2 } } { 4 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x + 3 ) ^ { 2 } } { 16 } - \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1$ 
A)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 3 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x + 3 ) ^ { 2 } } { 4 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x + 3 ) ^ { 2 } } { 16 } - \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1$

Question 7

Match the equation of the ellipse with the appropriate description.
-$$\frac { x ^ { 2 } } { 9 } = 1 - \frac { y ^ { 2 } } { 25 }$$

Accepted Answer

A)  $x$-intercepts $( 3,0 ) , ( - 3,0 ) ; y$-intercepts $( 0,5 ) , ( 0 , - 5 )$ 
B)  $x$-intercepts $( 5,0 ) , ( - 5,0 )$; y-intercepts $( 0,3 ) , ( 0 , - 3 )$ 
C)  $x$-intercepts $( 25,0 ) , ( - 25,0 ) ; y$-intercepts $( 0,9 ) , ( 0 , - 9 )$ 
D)  x-intercepts $( 9,0 ) , ( - 9,0 )$; $y$-intercepts $( 0,25 ) , ( 0 , - 25 )$ 
A)  $x$-intercepts $( 3,0 ) , ( - 3,0 ) ; y$-intercepts $( 0,5 ) , ( 0 , - 5 )$ 
B)  $x$-intercepts $( 5,0 ) , ( - 5,0 )$; y-intercepts $( 0,3 ) , ( 0 , - 3 )$ 
C)  $x$-intercepts $( 25,0 ) , ( - 25,0 ) ; y$-intercepts $( 0,9 ) , ( 0 , - 9 )$ 
D)  x-intercepts $( 9,0 ) , ( - 9,0 )$; $y$-intercepts $( 0,25 ) , ( 0 , - 25 )$

Question 8

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

Accepted Answer

A)  C: $( 0,0 ) ; F : ( 0 , - 5 ) , ( 0,5 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$ 
B)  $\mathrm { C } : ( 0,0 ) ; \mathrm { F } : ( 0 , - 4 ) , ( 0,4 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }$ 
C)  C: $( 0,0 ) ; F : ( - 5,0 ) , ( 5,0 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
D)  C: $( 0,0 ) ; F : ( - 4,0 ) , ( 4,0 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
A)  C: $( 0,0 ) ; F : ( 0 , - 5 ) , ( 0,5 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$ 
B)  $\mathrm { C } : ( 0,0 ) ; \mathrm { F } : ( 0 , - 4 ) , ( 0,4 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }$ 
C)  C: $( 0,0 ) ; F : ( - 5,0 ) , ( 5,0 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
D)  C: $( 0,0 ) ; F : ( - 4,0 ) , ( 4,0 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$

Question 9

Evaluate the expression.
-$9 C 5$

Accepted Answer

A)  $\frac { 9 } { 20 }$ 
B)  126 
C)  15120 
D)  3024 
A)  $\frac { 9 } { 20 }$ 
B)  126 
C)  15120 
D)  3024

Question 10

Graph the hyperbola.
-$$\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 4 } = 1$$

Accepted Answer

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

Question 11

Bruce agrees to go to work for Jim at a rate of 1¢ for the first day, 2¢ for the second day, 4¢ for the third day, 8¢ for the fourth day, and so on. What will Bruce's daily pay be on day 14, and how much total wages will he have
Earned at the end of that day?

Accepted Answer

A)  Pay on day $14 = \$ 81.92$; Total pay through day $14 = \$ 81.91$ 
B)  Pay on day $14 = \$ 163.84$; Total pay through day $14 = \$ 163.83$ 
C)  Pay on day $14 = \$ 163.84$; Total pay through day $14 = \$ 81.91$ 
D)  Pay on day $14 = \$ 81.92$; Total pay through day $14 = \$ 163.83$ 
A)  Pay on day $14 = \$ 81.92$; Total pay through day $14 = \$ 81.91$ 
B)  Pay on day $14 = \$ 163.84$; Total pay through day $14 = \$ 163.83$ 
C)  Pay on day $14 = \$ 163.84$; Total pay through day $14 = \$ 81.91$ 
D)  Pay on day $14 = \$ 81.92$; Total pay through day $14 = \$ 163.83$

Question 12

Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 5 shirts chosen from the 8 shirts in his closet. In how many ways can this be done?

Accepted Answer

A)  20,160 
B)  2,419,200 
C)  840 
D)  100,800 
A)  20,160 
B)  2,419,200 
C)  840 
D)  100,800

Question 13

A bag contains 8 apples and 6 oranges. If you select 7 pieces of fruit without looking, how many ways can you get exactly 6 apples?

Accepted Answer

A)  168 
B)  2016 
C)  56 
D)  336 
A)  168 
B)  2016 
C)  56 
D)  336

Question 14

Write the binomial expansion of the expression.
-$$\left( 2 x ^ { 2 } - y \right) ^ { 5 }$$

Accepted Answer

A)  $- 32 x^{ 10} + 80 x ^ { 8 } y - 80 x ^ { 6 } y ^ { 2 } + 40 x ^ { 4 } y ^ { 3 } - 10 x ^ { 2 } y ^ { 4 } + y ^ { 5 }$ 
B)  $32 x ^ { 10 } - 80 x ^ { 8 } y + 80 x ^ { 6 } y ^ { 2 } - 40 x ^ { 4 } y ^ { 3 } + 10 x ^ { 2 } y ^ { 4 } - y ^ { 5 }$ 
C)  $32 x ^ { 10 } - 80 x ^ { 8 } y - 80 x ^ { 6 } y ^ { 2 } - 40 x ^ { 4 } y ^ { 3 } - 10 x ^ { 2 } y ^ { 4 } - y ^ { 5 }$ 
D)  $32 x ^ { 10 } + 80 x ^ { 8 } y + 80 x ^ { 6 } y ^ { 2 } + 40 x ^ { 4 } y ^ { 3 } + 10 x ^ { 2 } y ^ { 4 } + y ^ { 5 }$ 
A)  $- 32 x^{ 10} + 80 x ^ { 8 } y - 80 x ^ { 6 } y ^ { 2 } + 40 x ^ { 4 } y ^ { 3 } - 10 x ^ { 2 } y ^ { 4 } + y ^ { 5 }$ 
B)  $32 x ^ { 10 } - 80 x ^ { 8 } y + 80 x ^ { 6 } y ^ { 2 } - 40 x ^ { 4 } y ^ { 3 } + 10 x ^ { 2 } y ^ { 4 } - y ^ { 5 }$ 
C)  $32 x ^ { 10 } - 80 x ^ { 8 } y - 80 x ^ { 6 } y ^ { 2 } - 40 x ^ { 4 } y ^ { 3 } - 10 x ^ { 2 } y ^ { 4 } - y ^ { 5 }$ 
D)  $32 x ^ { 10 } + 80 x ^ { 8 } y + 80 x ^ { 6 } y ^ { 2 } + 40 x ^ { 4 } y ^ { 3 } + 10 x ^ { 2 } y ^ { 4 } + y ^ { 5 }$

Question 15

Provide an appropriate response.
-What is the common ratio in the geometric sequence $\left. a _ { n } = \log \left[ 2 ^ { \left( 9 ^ { n } - 1 \right.} \right) \right]$ ?

Accepted Answer

A)  9 
B)  $\log 2$ 
C)  $\log 9$ 
D)  2 
A)  9 
B)  $\log 2$ 
C)  $\log 9$ 
D)  2

Question 16

How many relay teams of 4 members can be chosen from a 6 member team to run in a relay race?

Accepted Answer

A)  24 
B)  360 
C)  120 
D)  18 
A)  24 
B)  360 
C)  120 
D)  18

Question 17

How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?

Accepted Answer

A)  1,000,000 
B)  46,656 
C)  999,999 
D)  720 
A)  1,000,000 
B)  46,656 
C)  999,999 
D)  720

Question 18

Graph the parabola.
-$x=-5(y-5)^{2}+1$

Accepted Answer

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

Question 19

Write the indicated term of the binomial expansion.
-$( 2 x + 8 ) ^ { 3 } ; \quad 3$ rd term

Accepted Answer

A)  64 
B)  $768 x$ 
C)  $384 x$ 
D)  $96 x ^ { 2 }$ 
A)  64 
B)  $768 x$ 
C)  $384 x$ 
D)  $96 x ^ { 2 }$

Question 20

A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) none are queens?
b) all are queens?

Accepted Answer

A)  a) $0.07487$
b) 0 
B)  a) 0
b) $0.07487$ 
C)  a) $0.65884$ 
b) 0 
D)  a) 0 b) 
$0.65884$ 
A)  a) $0.07487$
b) 0 
B)  a) 0
b) $0.07487$ 
C)  a) $0.65884$ 
b) 0 
D)  a) 0 b) 
$0.65884$

Graph the hyperbola. - $16 x^{2}-9 y^{2}=144$ $Graph the hyperbola. - 16 x^{2}-9 y^{2}=144$

In how many ways can a class president and a class secretary be chosen from a group of 4 candidates?

Find the eccentricity $e$ of the ellipse. - $x ^ { 2 } + 2 y ^ { 2 } = 6$

Evaluate the series, if it converges. - $\sum _ { k = 1 } ^ { \infty } \left( \frac { 3 } { 8 } \right) ^ { k }$

Choose the equation that matches the graph. -

Match the equation of the ellipse with the appropriate description. - $\frac { x ^ { 2 } } { 9 } = 1 - \frac { y ^ { 2 } } { 25 }$

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

Evaluate the expression. - $9 C 5$

Graph the hyperbola. - $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 4 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 4 } = 1$

Bruce agrees to go to work for Jim at a rate of 1¢ for the first day, 2¢ for the second day, 4¢ for the third day, 8¢ for the fourth day, and so on. What will Bruce's daily pay be on day 14, and how much total wages will he have Earned at the end of that day?

Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 5 shirts chosen from the 8 shirts in his closet. In how many ways can this be done?

A bag contains 8 apples and 6 oranges. If you select 7 pieces of fruit without looking, how many ways can you get exactly 6 apples?

Write the binomial expansion of the expression. - $\left( 2 x ^ { 2 } - y \right) ^ { 5 }$

Provide an appropriate response. -What is the common ratio in the geometric sequence $\left. a _ { n } = \log \left[ 2 ^ { \left( 9 ^ { n } - 1 \right.} \right) \right]$ ?

How many relay teams of 4 members can be chosen from a 6 member team to run in a relay race?

How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?

Graph the parabola. - $x=-5(y-5)^{2}+1$ $Graph the parabola. - x=-5(y-5)^{2}+1$

Write the indicated term of the binomial expansion. - $( 2 x + 8 ) ^ { 3 } ; \quad 3$ rd term

A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) none are queens? b) all are queens?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

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

Graph the hyperbola. - 16x2−9y2=14416 x^{2}-9 y^{2}=14416x2−9y2=144

In how many ways can a class president and a class secretary be chosen from a group of 4 candidates?

Find the eccentricity e e e of the ellipse. - x2+2y2=6x ^ { 2 } + 2 y ^ { 2 } = 6x2+2y2=6

Evaluate the series, if it converges. - ∑k=1∞(38)k\sum _ { k = 1 } ^ { \infty } \left( \frac { 3 } { 8 } \right) ^ { k }∑k=1∞​(83​)k

Choose the equation that matches the graph. -

Match the equation of the ellipse with the appropriate description. - x29=1−y225\frac { x ^ { 2 } } { 9 } = 1 - \frac { y ^ { 2 } } { 25 }9x2​=1−25y2​

Find the center, foci, and asymptotes of the hyperbola. - y29−x216=1\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 19y2​−16x2​=1

Evaluate the expression. - 9C59 C 59C5

Graph the hyperbola. - y264−x24=1\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 4 } = 164y2​−4x2​=1

Bruce agrees to go to work for Jim at a rate of 1¢ for the first day, 2¢ for the second day, 4¢ for the third day, 8¢ for the fourth day, and so on. What will Bruce's daily pay be on day 14, and how much total wages will he have Earned at the end of that day?

Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 5 shirts chosen from the 8 shirts in his closet. In how many ways can this be done?

A bag contains 8 apples and 6 oranges. If you select 7 pieces of fruit without looking, how many ways can you get exactly 6 apples?

Write the binomial expansion of the expression. - (2x2−y)5\left( 2 x ^ { 2 } - y \right) ^ { 5 }(2x2−y)5

Provide an appropriate response. -What is the common ratio in the geometric sequence an=log⁡[2(9n−1)]\left. a _ { n } = \log \left[ 2 ^ { \left( 9 ^ { n } - 1 \right.} \right) \right]an​=log[2(9n−1)] ?

How many relay teams of 4 members can be chosen from a 6 member team to run in a relay race?

How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?

Graph the parabola. - x=−5(y−5)2+1x=-5(y-5)^{2}+1x=−5(y−5)2+1

Write the indicated term of the binomial expansion. - (2x+8)3;3( 2 x + 8 ) ^ { 3 } ; \quad 3(2x+8)3;3 rd term

A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) none are queens? b) all are queens?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Graph the hyperbola. - $16 x^{2}-9 y^{2}=144$ $Graph the hyperbola. - 16 x^{2}-9 y^{2}=144$

Find the eccentricity $e$ of the ellipse. - $x ^ { 2 } + 2 y ^ { 2 } = 6$

Evaluate the series, if it converges. - $\sum _ { k = 1 } ^ { \infty } \left( \frac { 3 } { 8 } \right) ^ { k }$

Match the equation of the ellipse with the appropriate description. - $\frac { x ^ { 2 } } { 9 } = 1 - \frac { y ^ { 2 } } { 25 }$

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

Evaluate the expression. - $9 C 5$

Graph the hyperbola. - $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 4 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 4 } = 1$

Write the binomial expansion of the expression. - $\left( 2 x ^ { 2 } - y \right) ^ { 5 }$

Provide an appropriate response. -What is the common ratio in the geometric sequence $\left. a _ { n } = \log \left[ 2 ^ { \left( 9 ^ { n } - 1 \right.} \right) \right]$ ?

Graph the parabola. - $x=-5(y-5)^{2}+1$ $Graph the parabola. - x=-5(y-5)^{2}+1$

Write the indicated term of the binomial expansion. - $( 2 x + 8 ) ^ { 3 } ; \quad 3$ rd term