Question 1

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = ( 18 + n ) ^ { 1 / n }$$

Accepted Answer

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

Question 2

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { i = 3 } ^ { 6 } ( i - 8 ) ^ { - 1 }$$

Accepted Answer

A)  $2.27$ 
B)  $- 14$ 
C)  $- 3.95$ 
D)  $- 1.28$ 
A)  $2.27$ 
B)  $- 14$ 
C)  $- 3.95$ 
D)  $- 1.28$

Question 3

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

Question 4

Solve the problem.
-A bag contains 7 apples and 5 oranges. If you select 6 pieces of fruit without looking, how many ways can you get 6 apples?

Accepted Answer

A)  35 
B)  7 
C)  12 
D)  14 
A)  35 
B)  7 
C)  12 
D)  14

Question 5

Solve the problem.
-An ordinary die is tossed. What are the odds in favor of the die showing a 4?

Accepted Answer

A)  2 to 3 
B) 1 to 6 
C) 1 to 4 
D) 1 to 5 
A)  2 to 3 
B) 1 to 6 
C) 1 to 4 
D) 1 to 5

Question 6

Use the formula for SS1U1B1nS1U1B0 to find the sum of the first five terms of the geometric sequence.
-$3,9,27,81 , \ldots$

Accepted Answer

A)  360 
B)  353 
C)  363 
D)  365 
A)  360 
B)  353 
C)  363 
D)  365

Question 7

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$\mathrm { a } _ { \mathrm { n } } = 59 \mathrm { e } ^ { \mathrm { n } }$$

Accepted Answer

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

Question 8

Find the nth term of the geometric sequence.
-$$a _ { 1 } = 1856 , r = \frac { 1 } { 4 } , n = 4$$

Accepted Answer

A)  $\mathrm { a } _ { 4 } = \frac { 1 } { 29 }$ 
B)  $a _ { 4 } = - 29$ 
C)  $\mathrm { a } _ { 4 } = 29$ 
D)  $\mathrm { a } _ { 4 } = - \frac { 1 } { 29 }$ 
A)  $\mathrm { a } _ { 4 } = \frac { 1 } { 29 }$ 
B)  $a _ { 4 } = - 29$ 
C)  $\mathrm { a } _ { 4 } = 29$ 
D)  $\mathrm { a } _ { 4 } = - \frac { 1 } { 29 }$

Question 9

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$\mathrm { a } _ { 12 } = 109 , \mathrm { a } _ { 68 } = 557$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 448 , \mathrm {~d} = 21$ 
B)  $\mathrm { a } _ { 1 } = 21 , \mathrm {~d} = 448$ 
C)  $\mathrm { a } _ { 1 } = 21 , \mathrm {~d} = 8$ 
D)  $\mathrm { a } _ { 1 } = 448 , \mathrm {~d} = 8$ 
A)  $\mathrm { a } _ { 1 } = 448 , \mathrm {~d} = 21$ 
B)  $\mathrm { a } _ { 1 } = 21 , \mathrm {~d} = 448$ 
C)  $\mathrm { a } _ { 1 } = 21 , \mathrm {~d} = 8$ 
D)  $\mathrm { a } _ { 1 } = 448 , \mathrm {~d} = 8$

Question 10

Solve the problem.
-How many ways can a class president, a class secretary, and a class treasurer be chosen from a group of 8 candidates?

Accepted Answer

A)  21 
B)  1680 
C)  336 
D)  24 
A)  21 
B)  1680 
C)  336 
D)  24

Question 11

Find the future value of the annuity.
-There are payments of $1000 at the end of each year for 7 years at 3% interest compounded annually

Accepted Answer

A)  $7662.46 
B)  $6468.41 
C)  $40,995.80 
D)  $3980.17 
A)  $7662.46 
B)  $6468.41 
C)  $40,995.80 
D)  $3980.17

Question 12

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

Accepted Answer

A)  $- 714$ 
B)  168 
C)  $- 2856$ 
D)  $- 8568$ 
A)  $- 714$ 
B)  168 
C)  $- 2856$ 
D)  $- 8568$

Question 13

Solve the problem.
-Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 5, 7, or 3?

Accepted Answer

A)  $\frac { 1 } { 10 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 3 } { 10 }$ 
A)  $\frac { 1 } { 10 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 3 } { 10 }$

Question 14

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 at least three boys?

Accepted Answer

A)  0.1563 
B)  0.4688 
C)  0.3125 
D)  0.5000 
A)  0.1563 
B)  0.4688 
C)  0.3125 
D)  0.5000

Question 15

Solve the problem.
-A man earned $\$ 3500$ the first year he worked. If he received a raise of $\$ 500$ at the end of each year, what was his salary during the 15 th year?

Accepted Answer

A)  $\$ 11,000$ 
B)  $\$ 7000$ 
C)  $\$ 10,500$ 
D)  None of these 
A)  $\$ 11,000$ 
B)  $\$ 7000$ 
C)  $\$ 10,500$ 
D)  None of these

Question 16

Find aS1U1B1nS1U1B0 and aS1U1B16S1U1B0 for the following arithmetic sequence.
-$2,6,10,14,18 , \ldots$

Accepted Answer

A)  $\mathrm { a } _ { \mathrm { n } } = \mathrm { n } + 4 ; \mathrm { a } _ { 6 } = 10$ 
B)  $a _ { n } = 4 n - 2 ; a _ { 6 } = 22$ 
C)  $a _ { n } = 2 n - 4 ; a _ { 6 } = 8$ 
D)  $\mathrm { a } _ { \mathrm { n } } = 2 ( 4 ) ^ { \mathrm { n } - 1 } ; \mathrm { a } _ { 6 } = 32,768$ 
A)  $\mathrm { a } _ { \mathrm { n } } = \mathrm { n } + 4 ; \mathrm { a } _ { 6 } = 10$ 
B)  $a _ { n } = 4 n - 2 ; a _ { 6 } = 22$ 
C)  $a _ { n } = 2 n - 4 ; a _ { 6 } = 8$ 
D)  $\mathrm { a } _ { \mathrm { n } } = 2 ( 4 ) ^ { \mathrm { n } - 1 } ; \mathrm { a } _ { 6 } = 32,768$

Question 17

Solve the problem.
-A stack of poles has 40 poles in the bottom row, 39 poles in the next row, and so on, with 10 poles in the top row. How many poles are there in the stack?

Accepted Answer

A)  785 
B)  765 
C)  775 
D)  695 
A)  785 
B)  765 
C)  775 
D)  695

Question 18

Evaluate the sum using the given information.
-$x _ { 1 } = 1 , x _ { 2 } = - 3 , x _ { 3 } = 2$, and $x _ { 4 } = 3$
$$\sum _ { i = 1 } ^ { 4 } \left( - x _ { i } ^ { 2 } - 4 \right)$$

Accepted Answer

A)  7 
B)  $- 27$ 
C)  $- 39$ 
D)  $- 46$ 
A)  7 
B)  $- 27$ 
C)  $- 39$ 
D)  $- 46$

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.
-$$a _ { n } = 3.9 n + 8.96$$

Accepted Answer

A)  $212.08$ 
B)  $47.96$ 
C)  $304.1$ 
D)  $256.14$ 
A)  $212.08$ 
B)  $47.96$ 
C)  $304.1$ 
D)  $256.14$

Question 20

Solve the problem.
-If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 0.04, what are the odds against a direct hit?

Accepted Answer

A)  24 to 1 
B) 25 to 1 
C) 1 to 25 
D)  23 to 1 
A)  24 to 1 
B) 25 to 1 
C) 1 to 25 
D)  23 to 1

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = ( 18 + n ) ^ { 1 / n }$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 3 } ^ { 6 } ( i - 8 ) ^ { - 1 }$

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. -A bag contains 7 apples and 5 oranges. If you select 6 pieces of fruit without looking, how many ways can you get 6 apples?

Solve the problem. -An ordinary die is tossed. What are the odds in favor of the die showing a 4?

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $3,9,27,81 , \ldots$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $\mathrm { a } _ { \mathrm { n } } = 59 \mathrm { e } ^ { \mathrm { n } }$

Find the nth term of the geometric sequence. - $a _ { 1 } = 1856 , r = \frac { 1 } { 4 } , n = 4$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { a } _ { 12 } = 109 , \mathrm { a } _ { 68 } = 557$

Solve the problem. -How many ways can a class president, a class secretary, and a class treasurer be chosen from a group of 8 candidates?

Find the future value of the annuity. -There are payments of $1000 at the end of each year for 7 years at 3% interest compounded annually

Use the summation properties to evaluate the series. The following rules may be needed: =; =; = =1 =1 =1 - $\sum _ { i = 1 } ^ { 6 } \left( - 3 i ^ { 2 } - i ^ { 3 } \right)$

Solve the problem. -Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 5, 7, or 3?

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 at least three boys?

Solve the problem. -A man earned $\$ 3500$ the first year he worked. If he received a raise of $\$ 500$ at the end of each year, what was his salary during the 15 th year?

Find a_n and a₆ for the following arithmetic sequence. - $2,6,10,14,18 , \ldots$

Solve the problem. -A stack of poles has 40 poles in the bottom row, 39 poles in the next row, and so on, with 10 poles in the top row. How many poles are there in the stack?

Evaluate the sum using the given information. - $x _ { 1 } = 1 , x _ { 2 } = - 3 , x _ { 3 } = 2$ , and $x _ { 4 } = 3$ $\sum _ { i = 1 } ^ { 4 } \left( - x _ { i } ^ { 2 } - 4 \right)$

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. - $a _ { n } = 3.9 n + 8.96$

Solve the problem. -If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 0.04, what are the odds against a direct hit?

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

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - an=(18+n)1/na _ { n } = ( 18 + n ) ^ { 1 / n }an​=(18+n)1/n

Evaluate the sum. Round to two decimal places, if necessary. - ∑i=36(i−8)−1\sum _ { i = 3 } ^ { 6 } ( i - 8 ) ^ { - 1 }∑i=36​(i−8)−1