Question 1

Write out the first five terms of the sequence.
-$$a _ { n } = ( - 1 ) ^ { n - 1 } ( 7 n - 8 )$$

Accepted Answer

A)  $1,6 , - 13 , - 20 , - 27$ 
B)  $- 1,6,13,20,27$ 
C)  $- 1 , - 22,13 , - 20,43$ 
D)  $- 1 , - 6,13 , - 20,27$ 
A)  $1,6 , - 13 , - 20 , - 27$ 
B)  $- 1,6,13,20,27$ 
C)  $- 1 , - 22,13 , - 20,43$ 
D)  $- 1 , - 6,13 , - 20,27$

Question 2

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

Accepted Answer

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

Question 3

Use a graphing calculator to evaluate the series.
-$$\sum _ { k = 2 } ^ { 12 } \left( k ^ { 2 } - 6 k + 7 \right)$$

Accepted Answer

A)  1010 
B)  110 
C)  1164 
D)  264 
A)  1010 
B)  110 
C)  1164 
D)  264

Question 4

Solve the problem.
-A 5-card hand is dealt from a deck of 52 cards. What is the probability that
a) all are from the same suit?
b) all are hearts?
c) exactly 2 are spades?

Accepted Answer

A)  a) $0.000495$
b) $0.00198$
c) $0.003516$ 
B)  a) $0.00198$
b) $0.000495$
c) $0.003516$ 
C)  a) $0.000495$
b) $0.00198$
c) $0.00003$ 
D)  a) $0.00198$
b) $0.000495$
c) $0.27428$ 
A)  a) $0.000495$
b) $0.00198$
c) $0.003516$ 
B)  a) $0.00198$
b) $0.000495$
c) $0.003516$ 
C)  a) $0.000495$
b) $0.00198$
c) $0.00003$ 
D)  a) $0.00198$
b) $0.000495$
c) $0.27428$

Question 5

Solve the problem.
-One digit from the number 3,565,885 is written on each of seven cards. What is the probability of drawing a card that shows 3,5 , or 6 ?

Accepted Answer

A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  $\frac { 3 } { 7 }$ 
A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  $\frac { 3 } { 7 }$

Question 6

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.
-$$a _ { n } = \sqrt { 5 } n + \sqrt { 3 }$$

Accepted Answer

A)  $140.304$ 
B)  $117.944$ 
C)  $116.212$ 
D)  $166.633$ 
A)  $140.304$ 
B)  $117.944$ 
C)  $116.212$ 
D)  $166.633$

Question 7

Solve the problem.
-How many ways can a president, vice-president, and secretary be chosen from a club with 12 members? Assume that no member can hold more than one office.

Accepted Answer

A)  36 
B)  220 
C)  1320 
D)  6 
A)  36 
B)  220 
C)  1320 
D)  6

Question 8

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { \mathrm { k } = 1 } ^ { 4 } 4 ^ { \mathrm { k } }$$

Accepted Answer

A)  1024 
B)  16 
C)  256 
D)  340 
A)  1024 
B)  16 
C)  256 
D)  340

Question 9

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.
-Find the sum of all the integers from 56 to 97.

Accepted Answer

A)  3157 
B)  3213 
C)  3116 
D)  3060 
A)  3157 
B)  3213 
C)  3116 
D)  3060

Question 10

Solve the problem.
-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) $0.65884$ 
C)  a) $0.65884$ b) 0 
D)  a) 0 b) $0.07487$ 
A)  a) $0.07487$ b) 0 
B)  a) 0 b) $0.65884$ 
C)  a) $0.65884$ b) 0 
D)  a) 0 b) $0.07487$

Question 11

Use mathematical induction to prove that the statement is true for every positive integer n.
-$0.23^ n < 0.23 ^ { n - 1 }$

Accepted Answer

Answers will vary. One possible proof fo

Question 12

Evaluate the series, if it converges.
-$$3 - \frac { 6 } { 5 } + \frac { 12 } { 25 } - \frac { 24 } { 125 } + \ldots$$

Accepted Answer

A)  $- \frac { 6 } { 7 }$ 
B)  $\frac { 15 } { 7 }$ 
C)  Does not converge 
D)  $\frac { 5 } { 7 }$ 
A)  $- \frac { 6 } { 7 }$ 
B)  $\frac { 15 } { 7 }$ 
C)  Does not converge 
D)  $\frac { 5 } { 7 }$

Question 13

Provide an appropriate response.
-Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither?

Accepted Answer

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

Question 14

Provide an appropriate response.
-Consider the selections of seven apples from a barrel of 75 apples. Is this a combination, a permutation, or neither?

Accepted Answer

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

Question 15

Provide an appropriate response.
-Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

Accepted Answer

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

Question 16

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

Accepted Answer

A)  $\frac { 1 } { 2 } , \frac { 3 } { 4 } , \frac { 5 } { 6 } , \frac { 7 } { 8 } , \frac { 9 } { 10 }$ 
B)  $\frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 1 } { 3 } , \frac { 7 } { 24 } , \frac { 9 } { 35 }$ 
C)  $1 , \frac { 5 } { 8 } , \frac { 7 } { 15 } , \frac { 3 } { 8 } , \frac { 11 } { 35 }$ 
D)  $\frac { 1 } { 3 } , \frac { 1 } { 2 } , \frac { 5 } { 11 } , \frac { 7 } { 18 } , \frac { 1 } { 3 }$ 
A)  $\frac { 1 } { 2 } , \frac { 3 } { 4 } , \frac { 5 } { 6 } , \frac { 7 } { 8 } , \frac { 9 } { 10 }$ 
B)  $\frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 1 } { 3 } , \frac { 7 } { 24 } , \frac { 9 } { 35 }$ 
C)  $1 , \frac { 5 } { 8 } , \frac { 7 } { 15 } , \frac { 3 } { 8 } , \frac { 11 } { 35 }$ 
D)  $\frac { 1 } { 3 } , \frac { 1 } { 2 } , \frac { 5 } { 11 } , \frac { 7 } { 18 } , \frac { 1 } { 3 }$

Question 17

Solve the problem.
-100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected,
Find the probability that the person does not work full time.   1. Public transportation: 6 full time, 8 part time
2) Bicycle: 3 full time, 3 part time
3) Drive alone: 31 full time, 32 part time
4) Car pool: 7 full time, 10 part time

Accepted Answer

A)  0.32 
B)  0.47 
C)  0.50 
D)  0.53 
A)  0.32 
B)  0.47 
C)  0.50 
D)  0.53

Question 18

Use the formula for $$\mathrm { S } _ { \mathbf { n } }$$ to find the sum of the first five terms of the geometric sequence.
-$3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \ldots$

Accepted Answer

A)  $\frac { 1023 } { 256 }$ 
B)  $\frac { 5 } { 128 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  1023 
A)  $\frac { 1023 } { 256 }$ 
B)  $\frac { 5 } { 128 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  1023

Question 19

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 stack of poles has 39 poles in the bottom row, 38 poles in the next row, and so on, with 6 poles in the top row. How many poles are there in the stack?

Accepted Answer

A)  765 
B)  759 
C)  690 
D)  771 
A)  765 
B)  759 
C)  690 
D)  771

Question 20

Solve the problem.
-How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 10 members? Assume that no member can hold more than one office.

Accepted Answer

A)  24 
B)  40 
C)  5040 
D)  210 
A)  24 
B)  40 
C)  5040 
D)  210

Write out the first five terms of the sequence. - $a _ { n } = ( - 1 ) ^ { n - 1 } ( 7 n - 8 )$

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

Use a graphing calculator to evaluate the series. - $\sum _ { k = 2 } ^ { 12 } \left( k ^ { 2 } - 6 k + 7 \right)$

Solve the problem. -A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) all are from the same suit? b) all are hearts? c) exactly 2 are spades?

Solve the problem. -One digit from the number 3,565,885 is written on each of seven cards. What is the probability of drawing a card that shows 3,5 , or 6 ?

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. - $a _ { n } = \sqrt { 5 } n + \sqrt { 3 }$

Solve the problem. -How many ways can a president, vice-president, and secretary be chosen from a club with 12 members? Assume that no member can hold more than one office.

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 4 } 4 ^ { \mathrm { k } }$

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. -Find the sum of all the integers from 56 to 97.

Solve the problem. -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?

Use mathematical induction to prove that the statement is true for every positive integer n. - $0.23^ n < 0.23 ^ { n - 1 }$

Evaluate the series, if it converges. - $3 - \frac { 6 } { 5 } + \frac { 12 } { 25 } - \frac { 24 } { 125 } + \ldots$

Provide an appropriate response. -Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither?

Provide an appropriate response. -Consider the selections of seven apples from a barrel of 75 apples. Is this a combination, a permutation, or neither?

Provide an appropriate response. -Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

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

Use the formula for $\mathrm { S } _ { \mathbf { n } }$ to find the sum of the first five terms of the geometric sequence. - $3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \ldots$

Solve the problem. -How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 10 members? Assume that no member can hold more than one office.

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

Write out the first five terms of the sequence. - an=(−1)n−1(7n−8)a _ { n } = ( - 1 ) ^ { n - 1 } ( 7 n - 8 )an​=(−1)n−1(7n−8)

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

Use a graphing calculator to evaluate the series. - ∑k=212(k2−6k+7)\sum _ { k = 2 } ^ { 12 } \left( k ^ { 2 } - 6 k + 7 \right)∑k=212​(k2−6k+7)