Question 1

Use the summation properties to evaluate the series. The following rules may be needed: $$\begin{array} { l l l } 
\mathrm { n } & \mathrm { n } & \mathrm { n } \
\sum \mathrm { i } = \frac { \mathrm { n } ( \mathrm { n } + 1 ) } { 2 } ; & \sum \mathrm { i } ^ { 2 } = \frac { \mathrm { n } ( \mathrm { n } + 1 ) ( 2 \mathrm { n } + 1 ) } { 6 } ; & \sum \mathrm { i } ^ { 3 } = \frac { \mathrm { n } ^ { 2 } ( \mathrm { n } + 1 ) ^ { 2 } } { 4 } \
\mathrm { i } = 1 & \mathrm { i } = 1 & \mathrm { i } = 1
\end{array}$$
-$$\sum _ { i = 1 } ^ { 5 } \left( i ^ { 2 } + i - 1 \right)$$

Accepted Answer

A)  224 
B)  220 
C)  65 
D)  69 
A)  224 
B)  220 
C)  65 
D)  69

Question 2

Write out the first five terms of the sequence.
-$$a _ { n } = 2 ( 2 n - 3 )$$

Accepted Answer

A)  $- 6 , - 2,2,6,10$ 
B)  $- 2,2,6,10,14$ 
C)  $- 2 , - 4 , - 6 , - 8 , - 10$ 
D)  $- 1,1,3,5,7$ 
A)  $- 6 , - 2,2,6,10$ 
B)  $- 2,2,6,10,14$ 
C)  $- 2 , - 4 , - 6 , - 8 , - 10$ 
D)  $- 1,1,3,5,7$

Question 3

Write out the first five terms of the sequence.
-$$a _ { n } = \frac { n ^ { 2 } - 9 } { n ^ { 2 } + 9 }$$

Accepted Answer

A)  $- \frac { 4 } { 5 } , 1,0,1 , \frac { 17 } { 8 }$ 
B)  $1 , - \frac { 5 } { 13 } , 1 , \frac { 7 } { 25 } , 1$ 
C)  $1,1,1,1,1$ 
D)  $- \frac { 4 } { 5 } , - \frac { 5 } { 13 } , 0 , \frac { 7 } { 25 } , \frac { 8 } { 17 }$ 
A)  $- \frac { 4 } { 5 } , 1,0,1 , \frac { 17 } { 8 }$ 
B)  $1 , - \frac { 5 } { 13 } , 1 , \frac { 7 } { 25 } , 1$ 
C)  $1,1,1,1,1$ 
D)  $- \frac { 4 } { 5 } , - \frac { 5 } { 13 } , 0 , \frac { 7 } { 25 } , \frac { 8 } { 17 }$

Question 4

Decide whether the given sequence is finite or infinite.
-$a _ { 1 } = 2 , a _ { 2 } = 7 ;$ for $3 \leq n \leq 20 , a _ { n } = 8 \cdot a _ { n - 1 } + 3 \cdot a _ { n - 2 }$

Accepted Answer

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

Question 5

Solve the problem.
-What is the probability that the arrow will land on 4 or 5?

Accepted Answer

A)  4 
B)  $\frac { 5 } { 3 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 2 } { 5 }$ 
A)  4 
B)  $\frac { 5 } { 3 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 2 } { 5 }$

Question 6

Solve the problem.
-How many relay teams of 4 members can be chosen from a 7 member team to run in a relay race?

Accepted Answer

A)  210 
B)  840 
C)  22 
D)  28 
A)  210 
B)  840 
C)  22 
D)  28

Question 7

Find the common ratio r for the given infinite geometric sequence.
-$\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 } , \ldots$

Accepted Answer

A)  2 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  6 
A)  2 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  6

Question 8

Solve the problem.
-How many different 4-letter radio-station call letters can be made if the first letter must be K or W, repeats are allowed, but the call letters cannot end in an O?

Accepted Answer

A)  16,900 
B)  33,800 
C)  456,976 
D)  35,152 
A)  16,900 
B)  33,800 
C)  456,976 
D)  35,152

Question 9

Find the future value of the annuity.
-There are payments of $100 at the end of each year for 15 years at 2% interest compounded annually

Accepted Answer

A)  $1597.39 
B)  $659.74 
C)  $6729.34 
D)  $1729.34 
A)  $1597.39 
B)  $659.74 
C)  $6729.34 
D)  $1729.34

Question 10

Find the first six terms of the sequence.
-$$a _ { 1 } = - 1 , a _ { n } = 4 \cdot a _ { n - 1 }$$

Accepted Answer

A)  $- 1 , - 4,0,4,8,12$ 
B)  $- 4 , - 16 , - 64 , - 256 , - 1024 , - 4096$ 
C)  $- 1 , - 4 , - 16 , - 64 , - 256 , - 1024$ 
D)  $0,4 , - 4,0,4,8$ 
A)  $- 1 , - 4,0,4,8,12$ 
B)  $- 4 , - 16 , - 64 , - 256 , - 1024 , - 4096$ 
C)  $- 1 , - 4 , - 16 , - 64 , - 256 , - 1024$ 
D)  $0,4 , - 4,0,4,8$

Question 11

Provide an appropriate response.
-Let $f ( x ) = 3 \left( 2 ^ { x } \right)$, and consider the sequence $f ( 1 ) , f ( 2 ) , f ( 3 ) , \ldots$. Is this a geometric sequence, and if so, what is the common ratio?

Accepted Answer

A)  Yes; $x$ 
B)  Yes; 3 
C)  No 
D)  Yes; 2 
A)  Yes; $x$ 
B)  Yes; 3 
C)  No 
D)  Yes; 2

Question 12

Find the nth term of the geometric sequence.
-$$\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = \frac { 1 } { 4 } , \mathrm { n } = 5$$

Accepted Answer

A)  $\mathrm { a } _ { 5 } = \frac { 1 } { 128 }$ 
B)  $\mathrm { a } _ { 5 } = \frac { 1 } { 512 }$ 
C)  a5 $= \frac { 1 } { 2048 }$ 
D)  a5 $= \frac { 1 } { 64 }$ 
A)  $\mathrm { a } _ { 5 } = \frac { 1 } { 128 }$ 
B)  $\mathrm { a } _ { 5 } = \frac { 1 } { 512 }$ 
C)  a5 $= \frac { 1 } { 2048 }$ 
D)  a5 $= \frac { 1 } { 64 }$

Question 13

Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 46 \left( - \frac { 5 } { 7 } \right) ^ { i - 1 }$$

Accepted Answer

A)  Does not converge. 
B)  $- \frac { 115 } { 6 }$ 
C)  $\frac { 7 } { 12 }$ 
D)  $\frac { 161 } { 6 }$ 
A)  Does not converge. 
B)  $- \frac { 115 } { 6 }$ 
C)  $\frac { 7 } { 12 }$ 
D)  $\frac { 161 } { 6 }$

Question 14

Find the probability.
-A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Accepted Answer

A)  $\frac { 13 } { 6 }$ 
B)  $\frac { 2 } { 13 }$ 
C)  6 
D)  $\frac { 6 } { 13 }$ 
A)  $\frac { 13 } { 6 }$ 
B)  $\frac { 2 } { 13 }$ 
C)  6 
D)  $\frac { 6 } { 13 }$

Question 15

Solve the problem.
-The distribution of B.A. degrees conferred by a local college is listed below, by major.   What is the probability that a randomly selected degree is not in Mathematics?

Accepted Answer

A)  0.682 
B)  0.768 
C)  0.303 
D)  0.232 
A)  0.682 
B)  0.768 
C)  0.303 
D)  0.232

Question 16

Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 9 } { 4 } \right) ^ { i - 1 }$$

Accepted Answer

A)  $\frac { 12 } { 13 }$ 
B)  Does not converge. 
C)  $- \frac { 27 } { 13 }$ 
D)  $\frac { 4 } { 13 }$ 
A)  $\frac { 12 } { 13 }$ 
B)  Does not converge. 
C)  $- \frac { 27 } { 13 }$ 
D)  $\frac { 4 } { 13 }$

Question 17

Solve the problem.
-A lottery game has balls numbered 1 through 15. What is the probability of selecting an even numbered ball or a 7?

Accepted Answer

A)  $\frac { 7 } { 8 }$ 
B)  $\frac { 8 } { 15 }$ 
C)  $\frac { 7 } { 15 }$ 
D)  $\frac { 2 } { 5 }$ 
A)  $\frac { 7 } { 8 }$ 
B)  $\frac { 8 } { 15 }$ 
C)  $\frac { 7 } { 15 }$ 
D)  $\frac { 2 } { 5 }$

Question 18

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = \frac { 2 n } { n + 5 }$$

Accepted Answer

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

Question 19

Solve the problem.
-Suppose that a family has 5 children and that the probability of having a girl is 12 . What is the probability of having exactly two girls and three boys?

Accepted Answer

A)  0.0625 
B)  0.0312 
C)  0.3125 
D)  0.6252 
A)  0.0625 
B)  0.0312 
C)  0.3125 
D)  0.6252

Question 20

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).
-$$\text { a5 } = 1 , \mathrm {~d} = - 5 , \mathrm { n } = 5$$

Accepted Answer

A)  $0,21,16,11,6$ 
B)  $21,16,11,6,1$ 
C)  $- 21 , - 16 , - 11 , - 6 , - 1$ 
D)  $25,19,13,7,1$ 
A)  $0,21,16,11,6$ 
B)  $21,16,11,6,1$ 
C)  $- 21 , - 16 , - 11 , - 6 , - 1$ 
D)  $25,19,13,7,1$

Use the summation properties to evaluate the series. The following rules may be needed: =; =; = =1 =1 =1 - $\sum _ { i = 1 } ^ { 5 } \left( i ^ { 2 } + i - 1 \right)$

Write out the first five terms of the sequence. - $a _ { n } = 2 ( 2 n - 3 )$

Write out the first five terms of the sequence. - $a _ { n } = \frac { n ^ { 2 } - 9 } { n ^ { 2 } + 9 }$

Decide whether the given sequence is finite or infinite. - $a _ { 1 } = 2 , a _ { 2 } = 7 ;$ for $3 \leq n \leq 20 , a _ { n } = 8 \cdot a _ { n - 1 } + 3 \cdot a _ { n - 2 }$

Solve the problem. -What is the probability that the arrow will land on 4 or 5?

Solve the problem. -How many relay teams of 4 members can be chosen from a 7 member team to run in a relay race?

Find the common ratio r for the given infinite geometric sequence. - $\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 } , \ldots$

Solve the problem. -How many different 4-letter radio-station call letters can be made if the first letter must be K or W, repeats are allowed, but the call letters cannot end in an O?

Find the future value of the annuity. -There are payments of $100 at the end of each year for 15 years at 2% interest compounded annually

Find the first six terms of the sequence. - $a _ { 1 } = - 1 , a _ { n } = 4 \cdot a _ { n - 1 }$

Provide an appropriate response. -Let $f ( x ) = 3 \left( 2 ^ { x } \right)$ , and consider the sequence $f ( 1 ) , f ( 2 ) , f ( 3 ) , \ldots$ . Is this a geometric sequence, and if so, what is the common ratio?

Find the nth term of the geometric sequence. - $\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = \frac { 1 } { 4 } , \mathrm { n } = 5$

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 46 \left( - \frac { 5 } { 7 } \right) ^ { i - 1 }$

Find the probability. -A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Solve the problem. -The distribution of B.A. degrees conferred by a local college is listed below, by major. What is the probability that a randomly selected degree is not in Mathematics?

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 9 } { 4 } \right) ^ { i - 1 }$

Solve the problem. -A lottery game has balls numbered 1 through 15. What is the probability of selecting an even numbered ball or a 7?

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = \frac { 2 n } { n + 5 }$

Solve the problem. -Suppose that a family has 5 children and that the probability of having a girl is 12 . What is the probability of having exactly two girls and three boys?

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\text { a5 } = 1 , \mathrm {~d} = - 5 , \mathrm { n } = 5$

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

Review of Basic Concepts

Filters

Exam 11: Further Topics in Algebra

Use the summation properties to evaluate the series. The following rules may be needed: =; =; = =1 =1 =1 - ∑i=15(i2+i−1)\sum _ { i = 1 } ^ { 5 } \left( i ^ { 2 } + i - 1 \right)∑i=15​(i2+i−1)

Write out the first five terms of the sequence. - an=2(2n−3)a _ { n } = 2 ( 2 n - 3 )an​=2(2n−3)

Write out the first five terms of the sequence. - an=n2−9n2+9a _ { n } = \frac { n ^ { 2 } - 9 } { n ^ { 2 } + 9 }an​=n2+9n2−9​

Decide whether the given sequence is finite or infinite. - a1=2,a2=7;a _ { 1 } = 2 , a _ { 2 } = 7 ;a1​=2,a2​=7; for 3≤n≤20,an=8⋅an−1+3⋅an−23 \leq n \leq 20 , a _ { n } = 8 \cdot a _ { n - 1 } + 3 \cdot a _ { n - 2 }3≤n≤20,an​=8⋅an−1​+3⋅an−2​