Question 1

Find a general term an for the geometric sequence.
-$\frac { 1 } { 6 } , 1,6 , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 6 } ( 6 ) ^ { n - 1 }$ 
B)  $a _ { n } = \left( \frac { 1 } { 6 } \right) ^ { n - 1 } + \frac { 5 } { 6 }$ 
C)  $a _ { n } = \frac { 1 } { 6 } + \frac { 5 } { 6 } ( n - 1 )$ 
D)  $a _ { n } = \frac { 1 } { 6 } + 6 ( n - 1 )$ 
A)  $a _ { n } = \frac { 1 } { 6 } ( 6 ) ^ { n - 1 }$ 
B)  $a _ { n } = \left( \frac { 1 } { 6 } \right) ^ { n - 1 } + \frac { 5 } { 6 }$ 
C)  $a _ { n } = \frac { 1 } { 6 } + \frac { 5 } { 6 } ( n - 1 )$ 
D)  $a _ { n } = \frac { 1 } { 6 } + 6 ( n - 1 )$

Question 2

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

Accepted Answer

A)  36 
B)  60 
C)  68 
D)  84 
A)  36 
B)  60 
C)  68 
D)  84

Question 3

Solve the problem.
-How many 4-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)  9999 
B)  256 
C)  10,000 
D)  24 
A)  9999 
B)  256 
C)  10,000 
D)  24

Question 4

Solve the problem.
-License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed?

Accepted Answer

A)  100,000 
B)  1,757,600 
C)  175,760 
D)  11,881,376 
A)  100,000 
B)  1,757,600 
C)  175,760 
D)  11,881,376

Question 5

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

Accepted Answer

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

Question 6

Solve the problem.
-The beginning population of a town was 32,900 . If the population decreased by 250 people per year, how many people lived in the town 15 years later?

Accepted Answer

A)  29,150 
B)  3750 
C)  28,900 
D)  29,400 
A)  29,150 
B)  3750 
C)  28,900 
D)  29,400

Question 7

Solve the problem.
-If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.01, what are the odds against an earthquake?

Accepted Answer

A)  100 to 1 
B) 98 to 1 
C) 1 to 100 
D)  99 to 1 
A)  100 to 1 
B) 98 to 1 
C) 1 to 100 
D)  99 to 1

Question 8

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth.
-$\sum _ { \mathrm { k } = 1 } ^ { 6 } ( 1.41 ) ^ { \mathrm { k } }$

Accepted Answer

A)  $14.317$ 
B)  $15.727$ 
C)  $23.585$ 
D)  $22.175$ 
A)  $14.317$ 
B)  $15.727$ 
C)  $23.585$ 
D)  $22.175$

Question 9

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = 8 \text {, a5 } = 512$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 2 , \mathrm { r } = 0.25$ 
B)  $\mathrm { a } _ { 1 } = 2 , \mathrm { r } = 4$ 
C)  $\mathrm { a } _ { 1 } = 512 , \mathrm { r } = 0.25$ 
D)  $\mathrm { a } _ { 1 } = 8 , \mathrm { r } = 4$ 
A)  $\mathrm { a } _ { 1 } = 2 , \mathrm { r } = 0.25$ 
B)  $\mathrm { a } _ { 1 } = 2 , \mathrm { r } = 4$ 
C)  $\mathrm { a } _ { 1 } = 512 , \mathrm { r } = 0.25$ 
D)  $\mathrm { a } _ { 1 } = 8 , \mathrm { r } = 4$

Question 10

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-$$a _ { n } = \sqrt { 8 } n + \sqrt { 5 }$$

Accepted Answer

A)  $211.273$ 
B)  $149.640$ 
C)  $172.860$ 
D)  $177.924$ 
A)  $211.273$ 
B)  $149.640$ 
C)  $172.860$ 
D)  $177.924$

Question 11

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-

Accepted Answer

A)  $a _ { n } = n - 3$ 
B)  $a _ { n } = n + 4$ 
C)  $a _ { n } = n - 4$ 
D)  $a _ { n } = n + 3$ 
A)  $a _ { n } = n - 3$ 
B)  $a _ { n } = n + 4$ 
C)  $a _ { n } = n - 4$ 
D)  $a _ { n } = n + 3$

Question 12

Write out the first five terms of the sequence.
-$$a _ { n } = 2 n - 1$$

Accepted Answer

A)  $1,2,3,4,5$ 
B)  $3,5,7,9,11$ 
C)  $- 1 , - 3 , - 5 , - 7 , - 9$ 
D)  $1,3,5,7,9$ 
A)  $1,2,3,4,5$ 
B)  $3,5,7,9,11$ 
C)  $- 1 , - 3 , - 5 , - 7 , - 9$ 
D)  $1,3,5,7,9$

Question 13

Use the formula for SS1U1B1nS1U1B0 to find the sum of the first five terms of the geometric sequence.
-$\mathrm { a } _ { 1 } = 7.099 , \mathrm { r } = 3.687$ (Round to the nearest hundredth)

Accepted Answer

A)  $253.20$ 
B)  $485.59$ 
C)  $1797.45$ 
D)  $- 1309.94$ 
A)  $253.20$ 
B)  $485.59$ 
C)  $1797.45$ 
D)  $- 1309.94$

Question 14

Find the probability.
-A bag contains 9 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 5 } { 16 }$ 
C)  $\frac { 9 } { 16 }$ 
D)  $\frac { 2 } { 11 }$ 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 5 } { 16 }$ 
C)  $\frac { 9 } { 16 }$ 
D)  $\frac { 2 } { 11 }$

Question 15

Find the sum of the geometric series.
-$$\sum _ { \mathrm { k } = 1 } ^ { 5 } 4 ( - 3 ) ^ { \mathrm { k } }$$

Accepted Answer

A)  $- 2460$ 
B)  $- 732$ 
C)  69 
D)  240 
A)  $- 2460$ 
B)  $- 732$ 
C)  69 
D)  240

Question 16

Find a general term an for the geometric sequence.
-$$a _ { 1 } = \frac { 1 } { 9 } , r = - 5$$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 9 } - \frac { 2 } { 15 } ( n - 1 )$ 
B)  $a _ { n } = \left( \frac { 1 } { 9 } \right) ^ { 11 - 1 } - \frac { 2 } { 15 }$ 
C)  $a _ { n } = \frac { 1 } { 9 } \cdot ( - 5 ) ^ { n - 1 }$ 
D)  $a _ { n } = \frac { 1 } { 9 } - \frac { 1 } { 5 } ( n - 1 )$ 
A)  $a _ { n } = \frac { 1 } { 9 } - \frac { 2 } { 15 } ( n - 1 )$ 
B)  $a _ { n } = \left( \frac { 1 } { 9 } \right) ^ { 11 - 1 } - \frac { 2 } { 15 }$ 
C)  $a _ { n } = \frac { 1 } { 9 } \cdot ( - 5 ) ^ { n - 1 }$ 
D)  $a _ { n } = \frac { 1 } { 9 } - \frac { 1 } { 5 } ( n - 1 )$

Question 17

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

Accepted Answer

A)  $- 80$ 
B)  $- 50$ 
C)  40 
D)  $- 70$ 
A)  $- 80$ 
B)  $- 50$ 
C)  40 
D)  $- 70$

Question 18

Solve the problem.
-How many different three-digit numbers can be written using digits from the set {3, 4, 5, 6, 7} without any repeating digits?

Accepted Answer

A)  120 
B)  20 
C)  10 
D)  60 
A)  120 
B)  20 
C)  10 
D)  60

Question 19

Find the sum of the geometric series.
-$\sum _ { \mathrm { i } = 1 } ^ { 5 } 3 ( 2 ) ^ { \mathrm { i } }$

Accepted Answer

A)  255 
B)  42 
C)  22 
D)  186 
A)  255 
B)  42 
C)  22 
D)  186

Question 20

Find the sum of the first n terms of the following arithmetic sequence.
-$$a _ { 1 } = 1 , d = - 1 ; \quad n = 6$$

Accepted Answer

A)  6 
B)  -7 
C)  $- 5$ 
D)  $- 9$ 
A)  6 
B)  -7 
C)  $- 5$ 
D)  $- 9$

Find a general term an for the geometric sequence. - $\frac { 1 } { 6 } , 1,6 , \ldots$

Use the summation properties to evaluate the series. The following rules may be needed: =; =; = =1 =1 =1 - $\sum _ { \mathrm { i } = 1 } ^ { 6 } ( 4 \mathrm { i } - 4 )$

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

Solve the problem. -License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed?

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

Solve the problem. -The beginning population of a town was 32,900 . If the population decreased by 250 people per year, how many people lived in the town 15 years later?

Solve the problem. -If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.01, what are the odds against an earthquake?

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth. - $\sum _ { \mathrm { k } = 1 } ^ { 6 } ( 1.41 ) ^ { \mathrm { k } }$

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = 8 \text {, a5 } = 512$

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. - $a _ { n } = \sqrt { 8 } n + \sqrt { 5 }$

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Write out the first five terms of the sequence. - $a _ { n } = 2 n - 1$

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $\mathrm { a } _ { 1 } = 7.099 , \mathrm { r } = 3.687$ (Round to the nearest hundredth)

Find the probability. -A bag contains 9 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Find the sum of the geometric series. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } 4 ( - 3 ) ^ { \mathrm { k } }$

Find a general term an for the geometric sequence. - $a _ { 1 } = \frac { 1 } { 9 } , r = - 5$

Use the summation properties to evaluate the series. The following rules may be needed: =; =; = =1 =1 =1 - $\sum _ { i = 1 } ^ { 4 } \left( - 2 i ^ { 2 } + i \right)$

Solve the problem. -How many different three-digit numbers can be written using digits from the set {3, 4, 5, 6, 7} without any repeating digits?

Find the sum of the geometric series. - $\sum _ { \mathrm { i } = 1 } ^ { 5 } 3 ( 2 ) ^ { \mathrm { i } }$

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 1 } = 1 , d = - 1 ; \quad n = 6$

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

Find a general term an for the geometric sequence. - 16,1,6,…\frac { 1 } { 6 } , 1,6 , \ldots61​,1,6,…

Use the summation properties to evaluate the series. The following rules may be needed: =; =; = =1 =1 =1 - ∑i=16(4i−4)\sum _ { \mathrm { i } = 1 } ^ { 6 } ( 4 \mathrm { i } - 4 )∑i=16​(4i−4)