Question 1

Decide whether the given sequence is finite or infinite.
-$$a _ { 1 } = 8 ; \text { for } 2 \leq n \leq 40 , a _ { n } = 5 \cdot a _ { n - 1 } + 5$$

Accepted Answer

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

Question 2

Solve the problem.
-In how many ways can 11 people be chosen and arranged in a straight line, if there are 12 people from whom to choose?

Accepted Answer

A)  132 
B)  12 
C)  479,001,600 
D)  24 
A)  132 
B)  12 
C)  479,001,600 
D)  24

Question 3

Solve the problem.
-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)  $0.5000$ 
B)  $0.8125$ 
C)  $0.9688$ 
D)  $0.3125$ 
A)  $0.5000$ 
B)  $0.8125$ 
C)  $0.9688$ 
D)  $0.3125$

Question 4

Provide an appropriate response.
-Consider the arrangements of the letters in the word ALGEBRA. Is this a combination, a permutation, or neither?

Accepted Answer

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

Question 5

Provide an appropriate response.
-Convert the decimal $.868686 \ldots$ to a fraction by writing it as the infinite series
$$\frac { 86 } { 100 } + \frac { 86 } { 100 ^ { 2 } } + \frac { 86 } { 100 ^ { 3 } } + \ldots$$

Accepted Answer

A)  $0.87878788$ 
B)  $0.87$ 
C)  $\frac { 86 } { 99 }$ 
D)  $0.85$ 
A)  $0.87878788$ 
B)  $0.87$ 
C)  $\frac { 86 } { 99 }$ 
D)  $0.85$

Question 6

Find the first six terms of the sequence.
-$$a _ { 1 } = 5 , a _ { n } = a _ { n } - 1 + 7$$

Accepted Answer

A)  $5,12,19,26,33,40$ 
B)  $12,19,26,33,40,47$ 
C)  $5,7,14,21,28,35$ 
D)  $0,7,14,21,28,35$ 
A)  $5,12,19,26,33,40$ 
B)  $12,19,26,33,40,47$ 
C)  $5,7,14,21,28,35$ 
D)  $0,7,14,21,28,35$

Question 7

Write out the first five terms of the sequence.
-$$a _ { n } = 4 n - 3$$

Accepted Answer

A)  $1,5,9,13,17$ 
B)  $- 1 , - 5 , - 9 , - 13 , - 17$ 
C)  $7,11,15,19,23$ 
D)  $1,2,3,4,5$ 
A)  $1,5,9,13,17$ 
B)  $- 1 , - 5 , - 9 , - 13 , - 17$ 
C)  $7,11,15,19,23$ 
D)  $1,2,3,4,5$

Question 8

Solve the problem.
-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)  $0.03125$ 
C)  $0.31255$ 
D)  $0.15625$ 
A)  $0.06252$ 
B)  $0.03125$ 
C)  $0.31255$ 
D)  $0.15625$

Decide whether the given sequence is finite or infinite. - $a _ { 1 } = 8 ; \text { for } 2 \leq n \leq 40 , a _ { n } = 5 \cdot a _ { n - 1 } + 5$

Solve the problem. -In how many ways can 11 people be chosen and arranged in a straight line, if there are 12 people from whom to choose?

Solve the problem. -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?

Provide an appropriate response. -Consider the arrangements of the letters in the word ALGEBRA. Is this a combination, a permutation, or neither?

Provide an appropriate response. -Convert the decimal $.868686 \ldots$ to a fraction by writing it as the infinite series $\frac { 86 } { 100 } + \frac { 86 } { 100 ^ { 2 } } + \frac { 86 } { 100 ^ { 3 } } + \ldots$

Find the first six terms of the sequence. - $a _ { 1 } = 5 , a _ { n } = a _ { n } - 1 + 7$

Write out the first five terms of the sequence. - $a _ { n } = 4 n - 3$

Solve the problem. -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?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Filters

Exam 12: Further Topics in Algebra

Decide whether the given sequence is finite or infinite. - a1=8; for 2≤n≤40,an=5⋅an−1+5a _ { 1 } = 8 ; \text { for } 2 \leq n \leq 40 , a _ { n } = 5 \cdot a _ { n - 1 } + 5a1​=8; for 2≤n≤40,an​=5⋅an−1​+5