Question 1

Find the first six terms of the sequence.
-$a _ { 1 } = 1$, $a _ { 2 } = - 1 ;$ for $n \geq 3 , a _ { n } = a _ { n - 1 } - a _ { n - 2 }$

Accepted Answer

A)  $1 , - 1 , - 2 , - 1,1,2$ 
B)  $1 , - 1,0 , - 1 , - 4 , - 5$ 
C)  $1 , - 1,2,1,5 , - 8$ 
D)  $1 , - 1 , - 3 , - 5 , - 7 , - 9$ 
A)  $1 , - 1 , - 2 , - 1,1,2$ 
B)  $1 , - 1,0 , - 1 , - 4 , - 5$ 
C)  $1 , - 1,2,1,5 , - 8$ 
D)  $1 , - 1 , - 3 , - 5 , - 7 , - 9$

Question 2

Solve the problem.
-A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 7 different flags available, how many possible signals can be flown?

Accepted Answer

A)  21 
B)  35 
C)  343 
D)  210 
A)  21 
B)  35 
C)  343 
D)  210

Question 3

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).
-$$\mathrm { a } _ { 1 } = 2 , \mathrm {~d} = 1 , \mathrm { n } = 6$$

Accepted Answer

A)  $0,2,3,4,5,6$ 
B)  $2,2,2,2,2,2$ 
C)  $2,3,4,5,6,8$ 
D)  $2,3,4,5,6,7$ 
A)  $0,2,3,4,5,6$ 
B)  $2,2,2,2,2,2$ 
C)  $2,3,4,5,6,8$ 
D)  $2,3,4,5,6,7$

Question 4

Solve the problem.
-Three noncollinear points determine a triangle. How many triangles can be formed with 7 noncollinear points?

Accepted Answer

A)  35 
B)  21 
C)  210 
D)  840 
A)  35 
B)  21 
C)  210 
D)  840

Question 5

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$S _ { 19 } = - 418 , \text { a } 19 = - 49$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 5 , \mathrm {~d} = - 5.16$ 
B)  $a _ { 1 } = 5 , d = - 3$ 
C)  $\mathrm { a } _ { 1 } = 887 , \mathrm {~d} = - 5.16$ 
D)  $\mathrm { a } _ { 1 } = 887 , \mathrm {~d} = - 3$ 
A)  $\mathrm { a } _ { 1 } = 5 , \mathrm {~d} = - 5.16$ 
B)  $a _ { 1 } = 5 , d = - 3$ 
C)  $\mathrm { a } _ { 1 } = 887 , \mathrm {~d} = - 5.16$ 
D)  $\mathrm { a } _ { 1 } = 887 , \mathrm {~d} = - 3$

Question 6

Write the series using summation notation.
-$$1 + \frac { 1 } { 2 ^ { 8 } } + \frac { 1 } { 3 ^ { 8 } } + \frac { 1 } { 4 ^ { 8 } } + \frac { 1 } { 5 ^ { 8 } }$$

Accepted Answer

A)  $\sum _ { \mathrm { k } = 2 } ^ { 6 } \frac { 1 } { \mathrm { k } ^ { 8 } }$ 
B)  $\sum _ { k = 0 } ^ { 5 } \frac { 1 } { \mathrm { k } ^ { 8 } }$ 
C)  $\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 1 } { \mathrm { k } ^ { 8 } }$ 
D)  $\sum _ { k = 1 } ^ { \infty } \mathrm { k } ^ { 8 }$ 
A)  $\sum _ { \mathrm { k } = 2 } ^ { 6 } \frac { 1 } { \mathrm { k } ^ { 8 } }$ 
B)  $\sum _ { k = 0 } ^ { 5 } \frac { 1 } { \mathrm { k } ^ { 8 } }$ 
C)  $\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 1 } { \mathrm { k } ^ { 8 } }$ 
D)  $\sum _ { k = 1 } ^ { \infty } \mathrm { k } ^ { 8 }$

Question 7

Evaluate the expression.
-P(13, 6)

Accepted Answer

A)  8,648,640 
B)  1,235,520 
C)  617,760 
D)  10,080 
A)  8,648,640 
B)  1,235,520 
C)  617,760 
D)  10,080

Question 8

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

Accepted Answer

A)  16 
B)  22 
C)  20 
D)  21 
A)  16 
B)  22 
C)  20 
D)  21

Question 9

Solve the problem.
-How many different three-digit numbers can be written using digits from the set {4, 5, 6, 7, 8} without any repeating digits?

Accepted Answer

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

Question 10

Solve the problem.
-In how many ways can a group of 8 students be selected from 9 students?

Accepted Answer

A)  72 
B)  1 
C)  8 
D)  9 
A)  72 
B)  1 
C)  8 
D)  9

Question 11

Solve the problem.
-In how many ways can 7 people line up for play tickets?

Accepted Answer

A)  823,543 
B)  5040 
C)  7 
D)  1 
A)  823,543 
B)  5040 
C)  7 
D)  1

Question 12

Solve the problem.
-How many ways can a committee of 6 be selected from a club with 10 members?

Accepted Answer

A)  1,000,000 
B)  60 
C)  210 
D)  151,200 
A)  1,000,000 
B)  60 
C)  210 
D)  151,200

Question 13

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)  $a _ { n } = n + 2$ 
D)  $a _ { n } = 4 - n$ 
A)  $a _ { n } = n + 3$ 
B)  $a _ { n } = n - 4$ 
C)  $a _ { n } = n + 2$ 
D)  $a _ { n } = 4 - n$

Question 14

Use mathematical induction to prove that the statement is true for every positive integer n.
-$n ! > 3 n , \text { for } n \geq 4$

Accepted Answer

Answers will vary. One possible proof fo

Question 15

Decide whether the given sequence is finite or infinite.
-$\mathrm { a } _ { 1 } = 5 , \mathrm { a } _ { 2 } = 6 ;$ for $\mathrm { n } \geq 3 , \mathrm { a } _ { \mathrm { n } } = 5 \cdot \mathrm { a } _ { \mathrm { n } - 1 } + 6 \cdot \mathrm { a } _ { \mathrm { n } - 2 }$

Accepted Answer

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

Question 16

Solve the problem.
-Suppose that an insect population density, in thousands, during year $\mathrm { n }$ can be modeled by the recursively defined sequence: $a _ { 1 } = 1 ; a _ { n } = 2.79 a _ { n - 1 } - 0.15 a _ { n - 1 } ^ { 2 }$ for $n > 1$.
Use technology to graph the sequence for $n = 1,2,3 , \ldots , 20$. Describe what happens to the population density function.

Accepted Answer

A)  The insect population stabilizes near $8.73$ thousand. 
B)  The insect population stabilizes near $12.86$ thousand. 
C)  The insect population increases every year. 
D)  The insect population stabilizes near $11.93$ thousand. 
A)  The insect population stabilizes near $8.73$ thousand. 
B)  The insect population stabilizes near $12.86$ thousand. 
C)  The insect population increases every year. 
D)  The insect population stabilizes near $11.93$ thousand.

Question 17

What is the sum of the exponents on x and y in each term in a binomial expansion?

Accepted Answer

The answer of What is the sum of the exponents...

Question 18

Decide whether the given sequence is finite or infinite.
-$$\mathrm { a } _ { 1 } = 10 ; \text { for } \mathrm { n } \geq 2 , \mathrm { a } _ { \mathrm { n } } = 9 \cdot \mathrm { a } _ { \mathrm { n } - 1 }$$

Accepted Answer

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

Question 19

Solve the problem.
-There are 6 women running in a race. How many first, second, and third place possibilities can occur?

Accepted Answer

A)  216 
B)  18 
C)  20 
D)  120 
A)  216 
B)  18 
C)  20 
D)  120

Question 20

Use a calculator to evaluate the expression.
-${ } _ { 32 } \mathrm { C } _ { 4 }$

Accepted Answer

A)  215,760 
B)  35,960 
C)  143,840 
D)  863,040 
A)  215,760 
B)  35,960 
C)  143,840 
D)  863,040

Find the first six terms of the sequence. - $a _ { 1 } = 1$ , $a _ { 2 } = - 1 ;$ for $n \geq 3 , a _ { n } = a _ { n - 1 } - a _ { n - 2 }$

Solve the problem. -A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 7 different flags available, how many possible signals can be flown?

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\mathrm { a } _ { 1 } = 2 , \mathrm {~d} = 1 , \mathrm { n } = 6$

Solve the problem. -Three noncollinear points determine a triangle. How many triangles can be formed with 7 noncollinear points?

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $S _ { 19 } = - 418 , \text { a } 19 = - 49$

Write the series using summation notation. - $1 + \frac { 1 } { 2 ^ { 8 } } + \frac { 1 } { 3 ^ { 8 } } + \frac { 1 } { 4 ^ { 8 } } + \frac { 1 } { 5 ^ { 8 } }$

Evaluate the expression. -P(13, 6)

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

Solve the problem. -How many different three-digit numbers can be written using digits from the set {4, 5, 6, 7, 8} without any repeating digits?

Solve the problem. -In how many ways can a group of 8 students be selected from 9 students?

Solve the problem. -In how many ways can 7 people line up for play tickets?

Solve the problem. -How many ways can a committee of 6 be selected from a club with 10 members?

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

Use mathematical induction to prove that the statement is true for every positive integer n. - $n ! > 3 n , \text { for } n \geq 4$

Decide whether the given sequence is finite or infinite. - $\mathrm { a } _ { 1 } = 5 , \mathrm { a } _ { 2 } = 6 ;$ for $\mathrm { n } \geq 3 , \mathrm { a } _ { \mathrm { n } } = 5 \cdot \mathrm { a } _ { \mathrm { n } - 1 } + 6 \cdot \mathrm { a } _ { \mathrm { n } - 2 }$

What is the sum of the exponents on x and y in each term in a binomial expansion?

Decide whether the given sequence is finite or infinite. - $\mathrm { a } _ { 1 } = 10 ; \text { for } \mathrm { n } \geq 2 , \mathrm { a } _ { \mathrm { n } } = 9 \cdot \mathrm { a } _ { \mathrm { n } - 1 }$

Solve the problem. -There are 6 women running in a race. How many first, second, and third place possibilities can occur?

Use a calculator to evaluate the expression. - ${ } _ { 32 } \mathrm { C } _ { 4 }$

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 the first six terms of the sequence. - a1=1a _ { 1 } = 1a1​=1 , a2=−1;a _ { 2 } = - 1 ;a2​=−1; for n≥3,an=an−1−an−2n \geq 3 , a _ { n } = a _ { n - 1 } - a _ { n - 2 }n≥3,an​=an−1​−an−2​

Solve the problem. -A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 7 different flags available, how many possible signals can be flown?

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - a1=2, d=1,n=6\mathrm { a } _ { 1 } = 2 , \mathrm {~d} = 1 , \mathrm { n } = 6a1​=2, d=1,n=6

Solve the problem. -Three noncollinear points determine a triangle. How many triangles can be formed with 7 noncollinear points?

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - S19=−418, a 19=−49S _ { 19 } = - 418 , \text { a } 19 = - 49S19​=−418, a 19=−49

Write the series using summation notation. - 1+128+138+148+1581 + \frac { 1 } { 2 ^ { 8 } } + \frac { 1 } { 3 ^ { 8 } } + \frac { 1 } { 4 ^ { 8 } } + \frac { 1 } { 5 ^ { 8 } }1+281​+381​+481​+581​

Evaluate the expression. -P(13, 6)

Evaluate the sum. Round to two decimal places, if necessary. - ∑k=25(3k−5)\sum _ { k = 2 } ^ { 5 } ( 3 k - 5 )∑k=25​(3k−5)

Solve the problem. -How many different three-digit numbers can be written using digits from the set {4, 5, 6, 7, 8} without any repeating digits?

Solve the problem. -In how many ways can a group of 8 students be selected from 9 students?

Solve the problem. -In how many ways can 7 people line up for play tickets?

Solve the problem. -How many ways can a committee of 6 be selected from a club with 10 members?

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

Use mathematical induction to prove that the statement is true for every positive integer n. - n!>3n, for n≥4n ! > 3 n , \text { for } n \geq 4n!>3n, for n≥4

What is the sum of the exponents on x and y in each term in a binomial expansion?

Decide whether the given sequence is finite or infinite. - a1=10; for n≥2,an=9⋅an−1\mathrm { a } _ { 1 } = 10 ; \text { for } \mathrm { n } \geq 2 , \mathrm { a } _ { \mathrm { n } } = 9 \cdot \mathrm { a } _ { \mathrm { n } - 1 }a1​=10; for n≥2,an​=9⋅an−1​

Solve the problem. -There are 6 women running in a race. How many first, second, and third place possibilities can occur?

Use a calculator to evaluate the expression. - 32C4{ } _ { 32 } \mathrm { C } _ { 4 }32​C4​

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

Find the first six terms of the sequence. - $a _ { 1 } = 1$ , $a _ { 2 } = - 1 ;$ for $n \geq 3 , a _ { n } = a _ { n - 1 } - a _ { n - 2 }$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\mathrm { a } _ { 1 } = 2 , \mathrm {~d} = 1 , \mathrm { n } = 6$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $S _ { 19 } = - 418 , \text { a } 19 = - 49$

Write the series using summation notation. - $1 + \frac { 1 } { 2 ^ { 8 } } + \frac { 1 } { 3 ^ { 8 } } + \frac { 1 } { 4 ^ { 8 } } + \frac { 1 } { 5 ^ { 8 } }$

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

Use mathematical induction to prove that the statement is true for every positive integer n. - $n ! > 3 n , \text { for } n \geq 4$

Decide whether the given sequence is finite or infinite. - $\mathrm { a } _ { 1 } = 10 ; \text { for } \mathrm { n } \geq 2 , \mathrm { a } _ { \mathrm { n } } = 9 \cdot \mathrm { a } _ { \mathrm { n } - 1 }$

Use a calculator to evaluate the expression. - ${ } _ { 32 } \mathrm { C } _ { 4 }$