Question 1

Evaluate the expression.
-P(8, 0)

Accepted Answer

A)  0.5 
B)  1 
C)  80,640 
D)  40,320 
A)  0.5 
B)  1 
C)  80,640 
D)  40,320

Question 2

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

Accepted Answer

A)  429 
B)  $- 441$ 
C)  1770 
D)  $- 876$ 
A)  429 
B)  $- 441$ 
C)  1770 
D)  $- 876$

Question 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.

Accepted Answer

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

Question 4

It can be shown that $( 1 + x ) ^ { n } = 1 + n x + \frac { n ( n - 1 ) } { 2 ! } x ^ { 2 } + \frac { n ( n - 1 ) ( n - 2 ) } { 3 ! } x ^ { 3 } \ldots$ is true for any real number n (not just positive
integer values) and any real number x, where $| x | < 1$ Use this series to approximate the given number to the nearest
thousandth.
-$$\left( 5 ^ { 2 } \right) ^ { n } = 5 ^ { 2 n }$$

Accepted Answer

Answers will vary. One possible proof fo

Question 5

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

Accepted Answer

A)  110 
B)  400 
C)  100 
D)  40 
A)  110 
B)  400 
C)  100 
D)  40

Question 6

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$7 ^ { n } > 7 ^ { n - 1 }$$

Accepted Answer

Answers will vary. One possible proof fo

Question 7

Solve the problem.
-A baseball manager has 10 players of the same ability. How many 9 player starting lineups can he create?

Accepted Answer

A)  362,880 
B)  10 
C)  3,628,800 
D)  90 
A)  362,880 
B)  10 
C)  3,628,800 
D)  90

Question 8

List the elements in the sample space of the experiment.
-A group of 19 people are assigned numbers 1 through 19. List the sample space of the event choosing a person with a number 5 or less.

Accepted Answer

A)  {19} 
B)  {1} 
C)  {1, 2, 3, 4} 
D)  {1, 2, 3, 4, 5} 
A)  {19} 
B)  {1} 
C)  {1, 2, 3, 4} 
D)  {1, 2, 3, 4, 5}

Question 9

Use the formula for SS1U1B1nS1U1B0 to find the sum of the first five terms of the geometric sequence.
-$4 , - 16,64 , - 256 , \ldots$

Accepted Answer

A)  1364 
B)  $- 1364$ 
C)  $- 820$ 
D)  820 
A)  1364 
B)  $- 1364$ 
C)  $- 820$ 
D)  820

Question 10

Solve the problem.
-A box contains 4 slips of paper, on each of which is written the number 1, 2, 3, or 4, respectively. A slip is drawn, and the number on it is noted. That slip is put aside, and another slip is drawn and
The number on it noted. What is the probability that
a) the sum of the two numbers is 5?
b) the first number drawn is a 2 and the second number is not 5?
c) the sum of the two numbers is not 10?

Accepted Answer

A)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 }$ c) 0 
B)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 1 
C)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 }$ c) 1 
D)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 0 
A)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 }$ c) 0 
B)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 1 
C)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 }$ c) 1 
D)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 0

Question 11

Solve the problem.
-Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 } \text {. What is the }$ probability of having at least four girls?

Accepted Answer

A)  0.3125 
B)  0.1563 
C)  0.0313 
D)  0.1875 
A)  0.3125 
B)  0.1563 
C)  0.0313 
D)  0.1875

Question 12

Evaluate the sum using the given information.
-$x _ { 1 } = 2 , x _ { 2 } = - 2 , x _ { 3 } = - 4 , x _ { 4 } = - 3$, and $\Delta x = - 0.9 ; f ( x ) = \frac { 5 } { 2 x + 1 }$
4
$\sum _ { i = 1 } f \left( x _ { i } \right) \Delta x$ (Round to the nearest tenth, if necessary.)

Accepted Answer

A)  $0.9$ 
B)  $2.1$ 
C)  $- 0.9$ 
D)  $1.8$ 
A)  $0.9$ 
B)  $2.1$ 
C)  $- 0.9$ 
D)  $1.8$

Question 13

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { \mathrm { k } = 1 } ^ { 4 } ( - 1 ) ^ { \mathrm { k } \cdot 9 \mathrm { k } }$$

Accepted Answer

A)  6561 
B)  90 
C)  18 
D)  $- 90$ 
A)  6561 
B)  90 
C)  18 
D)  $- 90$

Question 14

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { \mathrm { k } = 2 } ^ { 5 } \frac { \left( \mathrm { k } ^ { 2 } - 3 \right) } { 2 }$$

Accepted Answer

A)  21 
B)  12 
C)  42 
D)  23 
A)  21 
B)  12 
C)  42 
D)  23

Question 15

Write the binomial expansion of the expression.
-$$\left( \frac { 1 } { 3 } x + 2 \right) ^ { 3 }$$

Accepted Answer

A)  $\frac { 1 } { 27 } x ^ { 6 } + \frac { 4 } { 9 } x ^ { 3 } + 8$ 
B)  $\frac { 1 } { 9 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } + 4 x + 8$ 
C)  $\frac { 1 } { 27 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } + 4 x + 8$ 
D)  $\frac { 1 } { 9 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } + 8$ 
A)  $\frac { 1 } { 27 } x ^ { 6 } + \frac { 4 } { 9 } x ^ { 3 } + 8$ 
B)  $\frac { 1 } { 9 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } + 4 x + 8$ 
C)  $\frac { 1 } { 27 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } + 4 x + 8$ 
D)  $\frac { 1 } { 9 } x ^ { 3 } + \frac { 2 } { 3 } x ^ { 2 } + 8$

Question 16

Find aS1U1B1nS1U1B0 and aS1U1B16S1U1B0 for the following arithmetic sequence.
-$$- 4,4,12,20,28 , \ldots$$

Accepted Answer

A)  $\mathrm { a } _ { \mathrm { n } } = 12 \mathrm { n } - 8 ; \mathrm { a } _ { 6 } = 64$ 
B)  $\mathrm { a } _ { \mathrm { n } } = - 4 ( 8 ) ^ { \mathrm { n } - 1 } ; \mathrm { a } _ { 6 } = - 32$ 
C)  $a _ { n } = 4 ( 2 n - 3 ) ; a _ { 6 } = 36$ 
D)  $a _ { n } = 8 n - 3 ; a _ { 6 } = 45$ 
A)  $\mathrm { a } _ { \mathrm { n } } = 12 \mathrm { n } - 8 ; \mathrm { a } _ { 6 } = 64$ 
B)  $\mathrm { a } _ { \mathrm { n } } = - 4 ( 8 ) ^ { \mathrm { n } - 1 } ; \mathrm { a } _ { 6 } = - 32$ 
C)  $a _ { n } = 4 ( 2 n - 3 ) ; a _ { 6 } = 36$ 
D)  $a _ { n } = 8 n - 3 ; a _ { 6 } = 45$

Question 17

Use a calculator to evaluate the expression.
-${ } _ { 14 } \mathrm { C } _ { 8 }$

Accepted Answer

A)  6006 
B)  3003 
C)  $1.211 \times 10 ^ { 8 }$ 
D)  $15,135,120$ 
A)  6006 
B)  3003 
C)  $1.211 \times 10 ^ { 8 }$ 
D)  $15,135,120$

Question 18

Solve the problem.
-A ball is dropped from a height of $5.0 \mathrm {~m}$. On each upward bounce the ball returns to $\frac { 2 } { 5 }$ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Accepted Answer

A)  $12.9 \mathrm {~m}$ 
B)  $12.6 \mathrm {~m}$ 
C)  $8.3 \mathrm {~m}$ 
D)  $11.6 \mathrm {~m}$ 
A)  $12.9 \mathrm {~m}$ 
B)  $12.6 \mathrm {~m}$ 
C)  $8.3 \mathrm {~m}$ 
D)  $11.6 \mathrm {~m}$

Question 19

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { i = 3 } ^ { 6 } ( 3 i - 4 )$$

Accepted Answer

A)  38 
B)  42 
C)  23 
D)  33 
A)  38 
B)  42 
C)  23 
D)  33

Question 20

Write the indicated term of the binomial expansion.
-$( 5 x + 4 ) ^ { 5 } ; \quad 5$ th term

Accepted Answer

A)  $8000 x ^ { 2 }$ 
B)  $1600 x$ 
C)  5120 
D)  $6400 \mathrm { x }$ 
A)  $8000 x ^ { 2 }$ 
B)  $1600 x$ 
C)  5120 
D)  $6400 \mathrm { x }$

Evaluate the expression. -P(8, 0)

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

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.

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

Use mathematical induction to prove that the statement is true for every positive integer n. - $7 ^ { n } > 7 ^ { n - 1 }$

Solve the problem. -A baseball manager has 10 players of the same ability. How many 9 player starting lineups can he create?

List the elements in the sample space of the experiment. -A group of 19 people are assigned numbers 1 through 19. List the sample space of the event choosing a person with a number 5 or less.

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $4 , - 16,64 , - 256 , \ldots$

Solve the problem. -Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 } \text {. What is the }$ probability of having at least four girls?

Evaluate the sum using the given information. - $x _ { 1 } = 2 , x _ { 2 } = - 2 , x _ { 3 } = - 4 , x _ { 4 } = - 3$ , and $\Delta x = - 0.9 ; f ( x ) = \frac { 5 } { 2 x + 1 }$ 4 $\sum _ { i = 1 } f \left( x _ { i } \right) \Delta x$ (Round to the nearest tenth, if necessary.)

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 4 } ( - 1 ) ^ { \mathrm { k } \cdot 9 \mathrm { k } }$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 2 } ^ { 5 } \frac { \left( \mathrm { k } ^ { 2 } - 3 \right) } { 2 }$

Write the binomial expansion of the expression. - $\left( \frac { 1 } { 3 } x + 2 \right) ^ { 3 }$

Find a_n and a₆ for the following arithmetic sequence. - $- 4,4,12,20,28 , \ldots$

Use a calculator to evaluate the expression. - ${ } _ { 14 } \mathrm { C } _ { 8 }$

Solve the problem. -A ball is dropped from a height of $5.0 \mathrm {~m}$ . On each upward bounce the ball returns to $\frac { 2 } { 5 }$ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 3 } ^ { 6 } ( 3 i - 4 )$

Write the indicated term of the binomial expansion. - $( 5 x + 4 ) ^ { 5 } ; \quad 5$ th term

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

Evaluate the expression. -P(8, 0)

Use the summation properties to evaluate the series. The following rules may be needed: =; =; = =1 =1 =1 - ∑i=16(1−2i3)\sum _ { i = 1 } ^ { 6 } \left( 1 - 2 i ^ { 3 } \right)∑i=16​(1−2i3)