Question 1

In how many ways can you answer the questions on an exam that consists of 6 multiple choice questions, each of which has 3 answer choices?

Accepted Answer

A)  1569 
B)  499 
C)  216 
D)  729 
A)  1569 
B)  499 
C)  216 
D)  729 D

Question 2

Express the rational number as a fraction of integers.
-$6.93939393 \ldots$

Accepted Answer

A)  $\frac { 229 } { 99 }$ 
B)  $\frac { 229 } { 30 }$ 
C)  $\frac { 229 } { 11 }$ 
D)  $\frac { 229 } { 33 }$ 
A)  $\frac { 229 } { 99 }$ 
B)  $\frac { 229 } { 30 }$ 
C)  $\frac { 229 } { 11 }$ 
D)  $\frac { 229 } { 33 }$ D

Question 3

Evaluate.
-$\left( \begin{array} { l } 236 \ 236 \end{array} \right)$

Accepted Answer

A)  118 
B)  472 
C)  0 
D)  1 
A)  118 
B)  472 
C)  0 
D)  1 D

Question 4

Write the sum using summation notation, assuming the suggested pattern continues.
-$$2 - 4 + 8 - 16 + \ldots$$

Accepted Answer

A)  $\sum _ { n = 0 } ^ { \infty } 2 \cdot 2 ^ { n + 1 }$ 
B)  $\sum _ { n = 0 } ^ { \infty } 2 ( - 2 ) ^ { n + 1 }$ 
C)  $\sum _ { n = 0 } ^ { \infty } 2 \cdot 2 ^ { n }$ 
D)  $\sum _ { n = 0 } ^ { \infty } 2 ( - 2 ) ^ { n }$ 
A)  $\sum _ { n = 0 } ^ { \infty } 2 \cdot 2 ^ { n + 1 }$ 
B)  $\sum _ { n = 0 } ^ { \infty } 2 ( - 2 ) ^ { n + 1 }$ 
C)  $\sum _ { n = 0 } ^ { \infty } 2 \cdot 2 ^ { n }$ 
D)  $\sum _ { n = 0 } ^ { \infty } 2 ( - 2 ) ^ { n }$

Question 5

Determine whether the sequence converges or diverges. If it converges, give the limit.
-$$\frac { 1 } { 4096 } , \frac { 1 } { 1024 } , \frac { 1 } { 256 } , \frac { 1 } { 64 } , \ldots$$

Accepted Answer

A)  Converges; $\frac { 1 } { 5120 }$ 
B)  Diverges 
C)  Converges; 0 
D)  Converges; $\frac { 2 } { 3 }$ 
A)  Converges; $\frac { 1 } { 5120 }$ 
B)  Diverges 
C)  Converges; 0 
D)  Converges; $\frac { 2 } { 3 }$

Question 6

Find the first six terms of the sequence.
-$$a _ { 1 } = - 5 , a _ { n } = a _ { n - 1 } + 8$$

Accepted Answer

A)  $- 5,3,11,19,27,35$ 
B)  $0,8,16,24,32,40$ 
C)  $- 5,8,16,24,32,40$ 
D)  $3,11,19,27,35,43$ 
A)  $- 5,3,11,19,27,35$ 
B)  $0,8,16,24,32,40$ 
C)  $- 5,8,16,24,32,40$ 
D)  $3,11,19,27,35,43$

Question 7

The code for some garage door openers consists of 15 electrical switches that can be set to "+" , "0" , or "-" by the owner. With this type of opener, how many different codes are possible?

Accepted Answer

A)  14,350,167 
B)  14,347,707 
C)  14,348,907 
D)  14,348,659 
A)  14,350,167 
B)  14,347,707 
C)  14,348,907 
D)  14,348,659

Question 8

Find the sum of the arithmetic sequence.
-$$32,37,42,47 , \ldots , 87$$

Accepted Answer

A)  92 
B)  714 
C) 684 
D)  694 
A)  92 
B)  714 
C) 684 
D)  694

Question 9

Find the first six terms of the sequence.
-$$a _ { 1 } = 5 , a _ { 2 } = 5 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$$

Accepted Answer

A)  $5,5,10,10,15,15$ 
B)  $5,5,25,125,3125,390,625$ 
C)  $5,5,10,15,25,40$ 
D)  $5,5,10,15,20,25$ 
A)  $5,5,10,10,15,15$ 
B)  $5,5,25,125,3125,390,625$ 
C)  $5,5,10,15,25,40$ 
D)  $5,5,10,15,20,25$

Question 10

Solve.
-A certain species of tree grows an average of $2.2 \mathrm {~cm}$ per week. Write an explicit rule for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 7 meters tall.

Accepted Answer

A)  $h _ { n } = 700 + 2.2 n$ 
B)  $h _ { n } = 7 + 2.2 n$ 
C)  $h _ { n } = 7000 + 2.2 n$ 
D)  $h _ { n } = 700 + 220 n$ 
A)  $h _ { n } = 700 + 2.2 n$ 
B)  $h _ { n } = 7 + 2.2 n$ 
C)  $h _ { n } = 7000 + 2.2 n$ 
D)  $h _ { n } = 700 + 220 n$

Question 11

State an explicit rule for the nth term of the recursively-defined sequence.
-$$a _ { n } = 8 \cdot a _ { n - 1 } ; a _ { 1 } = 2$$

Accepted Answer

A)  $a _ { n } = 2 \cdot 8 ^ { n - 1 }$ 
B)  $a _ { n } = 2 \cdot 8 ^ { n }$ 
C)  $a _ { n } = 8 \cdot 2 ^ { n }$ 
D)  $a _ { n } = 8 \cdot 2 ^ { n - 1 }$ 
A)  $a _ { n } = 2 \cdot 8 ^ { n - 1 }$ 
B)  $a _ { n } = 2 \cdot 8 ^ { n }$ 
C)  $a _ { n } = 8 \cdot 2 ^ { n }$ 
D)  $a _ { n } = 8 \cdot 2 ^ { n - 1 }$

Question 12

Construct a graph for the first ten terms of the sequence.
-$$a _ { n } = \sqrt { n + 2 } - \sqrt { n + 1 }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 13

Expand the binomial.
-$( \sqrt { x } + \sqrt { 5 } ) ^ { 4 }$

Accepted Answer

A)  $x ^ { 2 } + 4 x \sqrt { 5 x } + 30 x + 20 \sqrt { 5 x } + 25$ 
B)  $x ^ { 2 } + 25$ 
C)  $x ^ { 2 } + 4 x \sqrt { 5 x } + 6 x + 4 \sqrt { 5 x } + 5$ 
D)  $x ^ { 2 } + 4 x \sqrt { 5 x } + 11 x + 9 \sqrt { 5 x } + 25$ 
A)  $x ^ { 2 } + 4 x \sqrt { 5 x } + 30 x + 20 \sqrt { 5 x } + 25$ 
B)  $x ^ { 2 } + 25$ 
C)  $x ^ { 2 } + 4 x \sqrt { 5 x } + 6 x + 4 \sqrt { 5 x } + 5$ 
D)  $x ^ { 2 } + 4 x \sqrt { 5 x } + 11 x + 9 \sqrt { 5 x } + 25$

Question 14

Solve.
-The population of a town was 27,200 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Accepted Answer

A)  22,700 
B)  4500 
C)  23,000 
D)  22,400 
A)  22,700 
B)  4500 
C)  23,000 
D)  22,400

Question 15

Find the first six terms of the sequence.
-$$a _ { 1 } = 5 , a _ { 2 } = 6 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$$

Accepted Answer

A)  $5,6,11,17,28,45$ 
B)  $5,6,11,12,17,17$ 
C)  $5,6,30,180,5400,972,000$ 
D)  $5,6,10,15,20,25$ 
A)  $5,6,11,17,28,45$ 
B)  $5,6,11,12,17,17$ 
C)  $5,6,30,180,5400,972,000$ 
D)  $5,6,10,15,20,25$

Question 16

Tell whether permutations or combinations are being described.
-4 cards are selected from a deck of 52 to form a hand for a certain card game.

Accepted Answer

A)  Permutations 
B)  Combinations 
A)  Permutations 
B)  Combinations

Question 17

Find the sum of the arithmetic sequence.
-4, 8, 16, 32, 64

Accepted Answer

A)  125 
B)  124 
C)  126 
D)  114 
A)  125 
B)  124 
C)  126 
D)  114

Question 18

State an explicit rule for the nth term of the recursively-defined sequence.
-$$a _ { n } = \left( \frac { 1 } { 7 } \right) \cdot a _ { n - 1 } ; a _ { 1 } = 1$$

Accepted Answer

A)  $a _ { n } = 1 \cdot \left( \frac { 1 } { 7 } \right) ^ { n }$ 
B)  $a _ { n } = 7 \cdot \left( \frac { 1 } { 1 } \right) ^ { n }$ 
C)  $ a _ { n } = 7 \cdot \left( \frac { 1 } { 1 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 1 \cdot \left( \frac { 1 } { 7 } \right) ^ { n - 1 }$ 
A)  $a _ { n } = 1 \cdot \left( \frac { 1 } { 7 } \right) ^ { n }$ 
B)  $a _ { n } = 7 \cdot \left( \frac { 1 } { 1 } \right) ^ { n }$ 
C)  $ a _ { n } = 7 \cdot \left( \frac { 1 } { 1 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 1 \cdot \left( \frac { 1 } { 7 } \right) ^ { n - 1 }$

Question 19

Find an explicit rule for the nth term of the arithmetic sequence.
-$$a _ { 18 } = - 47 , a _ { 19 } = 8$$

Accepted Answer

A)  $a _ { n } = - 982 - 55 ( n - 1 )$ 
B)  $a _ { n } = - 982 - 55 ( n + 1 )$ 
C)  $a _ { n } = - 982 + 55 ( n + 1 )$ 
D)  $a _ { n } = - 982 + 55 ( n - 1 )$ 
A)  $a _ { n } = - 982 - 55 ( n - 1 )$ 
B)  $a _ { n } = - 982 - 55 ( n + 1 )$ 
C)  $a _ { n } = - 982 + 55 ( n + 1 )$ 
D)  $a _ { n } = - 982 + 55 ( n - 1 )$

Question 20

In how many ways can you answer the questions on an exam that consists of 20 true-false questions?

Accepted Answer

A)  1,048,656 
B)  1,048,576 
C)  1,048,696 
D)  1,048,512 
A)  1,048,656 
B)  1,048,576 
C)  1,048,696 
D)  1,048,512

In how many ways can you answer the questions on an exam that consists of 6 multiple choice questions, each of which has 3 answer choices?

Express the rational number as a fraction of integers. - $6.93939393 \ldots$

Evaluate. - $\left( \begin{array} { l } 236 \\ 236 \end{array} \right)$

Write the sum using summation notation, assuming the suggested pattern continues. - $2 - 4 + 8 - 16 + \ldots$

Determine whether the sequence converges or diverges. If it converges, give the limit. - $\frac { 1 } { 4096 } , \frac { 1 } { 1024 } , \frac { 1 } { 256 } , \frac { 1 } { 64 } , \ldots$

Find the first six terms of the sequence. - $a _ { 1 } = - 5 , a _ { n } = a _ { n - 1 } + 8$

The code for some garage door openers consists of 15 electrical switches that can be set to "+" , "0" , or "-" by the owner. With this type of opener, how many different codes are possible?

Find the sum of the arithmetic sequence. - $32,37,42,47 , \ldots , 87$

Find the first six terms of the sequence. - $a _ { 1 } = 5 , a _ { 2 } = 5 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Solve. -A certain species of tree grows an average of $2.2 \mathrm {~cm}$ per week. Write an explicit rule for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 7 meters tall.

State an explicit rule for the nth term of the recursively-defined sequence. - $a _ { n } = 8 \cdot a _ { n - 1 } ; a _ { 1 } = 2$

Construct a graph for the first ten terms of the sequence. - $a _ { n } = \sqrt { n + 2 } - \sqrt { n + 1 }$ $Construct a graph for the first ten terms of the sequence. - a _ { n } = \sqrt { n + 2 } - \sqrt { n + 1 }$

Expand the binomial. - $( \sqrt { x } + \sqrt { 5 } ) ^ { 4 }$

Solve. -The population of a town was 27,200 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Find the first six terms of the sequence. - $a _ { 1 } = 5 , a _ { 2 } = 6 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Tell whether permutations or combinations are being described. -4 cards are selected from a deck of 52 to form a hand for a certain card game.

Find the sum of the arithmetic sequence. -4, 8, 16, 32, 64

State an explicit rule for the nth term of the recursively-defined sequence. - $a _ { n } = \left( \frac { 1 } { 7 } \right) \cdot a _ { n - 1 } ; a _ { 1 } = 1$

Find an explicit rule for the nth term of the arithmetic sequence. - $a _ { 18 } = - 47 , a _ { 19 } = 8$

In how many ways can you answer the questions on an exam that consists of 20 true-false questions?

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 9: Discrete Mathematics

In how many ways can you answer the questions on an exam that consists of 6 multiple choice questions, each of which has 3 answer choices?

Express the rational number as a fraction of integers. - 6.93939393…6.93939393 \ldots6.93939393…

Evaluate. - (236236)\left( \begin{array} { l } 236 \\ 236 \end{array} \right)(236236​)

Write the sum using summation notation, assuming the suggested pattern continues. - 2−4+8−16+…2 - 4 + 8 - 16 + \ldots2−4+8−16+…

Determine whether the sequence converges or diverges. If it converges, give the limit. - 14096,11024,1256,164,…\frac { 1 } { 4096 } , \frac { 1 } { 1024 } , \frac { 1 } { 256 } , \frac { 1 } { 64 } , \ldots40961​,10241​,2561​,641​,…

Find the first six terms of the sequence. - a1=−5,an=an−1+8a _ { 1 } = - 5 , a _ { n } = a _ { n - 1 } + 8a1​=−5,an​=an−1​+8

The code for some garage door openers consists of 15 electrical switches that can be set to "+" , "0" , or "-" by the owner. With this type of opener, how many different codes are possible?

Find the sum of the arithmetic sequence. - 32,37,42,47,…,8732,37,42,47 , \ldots , 8732,37,42,47,…,87

Find the first six terms of the sequence. - a1=5,a2=5; for n≥3,an=an−1+an−2a _ { 1 } = 5 , a _ { 2 } = 5 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }a1​=5,a2​=5; for n≥3,an​=an−1​+an−2​

Solve. -A certain species of tree grows an average of 2.2 cm2.2 \mathrm {~cm}2.2 cm per week. Write an explicit rule for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 7 meters tall.

State an explicit rule for the nth term of the recursively-defined sequence. - an=8⋅an−1;a1=2a _ { n } = 8 \cdot a _ { n - 1 } ; a _ { 1 } = 2an​=8⋅an−1​;a1​=2

Construct a graph for the first ten terms of the sequence. - an=n+2−n+1a _ { n } = \sqrt { n + 2 } - \sqrt { n + 1 }an​=n+2​−n+1​

Expand the binomial. - (x+5)4( \sqrt { x } + \sqrt { 5 } ) ^ { 4 }(x​+5​)4

Solve. -The population of a town was 27,200 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Find the first six terms of the sequence. - a1=5,a2=6; for n≥3,an=an−1+an−2a _ { 1 } = 5 , a _ { 2 } = 6 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }a1​=5,a2​=6; for n≥3,an​=an−1​+an−2​

Tell whether permutations or combinations are being described. -4 cards are selected from a deck of 52 to form a hand for a certain card game.

Find the sum of the arithmetic sequence. -4, 8, 16, 32, 64

State an explicit rule for the nth term of the recursively-defined sequence. - an=(17)⋅an−1;a1=1a _ { n } = \left( \frac { 1 } { 7 } \right) \cdot a _ { n - 1 } ; a _ { 1 } = 1an​=(71​)⋅an−1​;a1​=1

Find an explicit rule for the nth term of the arithmetic sequence. - a18=−47,a19=8a _ { 18 } = - 47 , a _ { 19 } = 8a18​=−47,a19​=8

In how many ways can you answer the questions on an exam that consists of 20 true-false questions?

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Express the rational number as a fraction of integers. - $6.93939393 \ldots$

Evaluate. - $\left( \begin{array} { l } 236 \\ 236 \end{array} \right)$

Write the sum using summation notation, assuming the suggested pattern continues. - $2 - 4 + 8 - 16 + \ldots$

Determine whether the sequence converges or diverges. If it converges, give the limit. - $\frac { 1 } { 4096 } , \frac { 1 } { 1024 } , \frac { 1 } { 256 } , \frac { 1 } { 64 } , \ldots$

Find the first six terms of the sequence. - $a _ { 1 } = - 5 , a _ { n } = a _ { n - 1 } + 8$

Find the sum of the arithmetic sequence. - $32,37,42,47 , \ldots , 87$

Find the first six terms of the sequence. - $a _ { 1 } = 5 , a _ { 2 } = 5 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Solve. -A certain species of tree grows an average of $2.2 \mathrm {~cm}$ per week. Write an explicit rule for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 7 meters tall.

State an explicit rule for the nth term of the recursively-defined sequence. - $a _ { n } = 8 \cdot a _ { n - 1 } ; a _ { 1 } = 2$

Construct a graph for the first ten terms of the sequence. - $a _ { n } = \sqrt { n + 2 } - \sqrt { n + 1 }$ $Construct a graph for the first ten terms of the sequence. - a _ { n } = \sqrt { n + 2 } - \sqrt { n + 1 }$

Expand the binomial. - $( \sqrt { x } + \sqrt { 5 } ) ^ { 4 }$

Find the first six terms of the sequence. - $a _ { 1 } = 5 , a _ { 2 } = 6 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

State an explicit rule for the nth term of the recursively-defined sequence. - $a _ { n } = \left( \frac { 1 } { 7 } \right) \cdot a _ { n - 1 } ; a _ { 1 } = 1$

Find an explicit rule for the nth term of the arithmetic sequence. - $a _ { 18 } = - 47 , a _ { 19 } = 8$