Question 1

Six cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all six cards are clubs.

Accepted Answer

A) 1,716 
B) 5,089,630 
C) 24 
D) 28,276 
E) 720 
A) 1,716 
B) 5,089,630 
C) 24 
D) 28,276 
E) 720 A

Question 2

In how many ways can a student answer a 32-question true-false test if the student randomly marks 6 of the questions true and 26 of the questions false?

Accepted Answer

A) 347,373,600 
B) 28,048,800 
C) 201,376 
D) 906,192 
E) 225,792,840 
A) 347,373,600 
B) 28,048,800 
C) 201,376 
D) 906,192 
E) 225,792,840 D

Question 3

Find the sum.

Accepted Answer

A) 30 
B) 8 
C) 18 
D) 20 
E) 12 
A) 30 
B) 8 
C) 18 
D) 20 
E) 12 D

Question 4

Write the given series in summation notation.

Accepted Answer

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

Question 5

Suppose that $500,000 of counterfeit money is currently in circulation and that each time the counterfeit money is used, 35% of it is detected and removed from circulation. How much counterfeit money, to the nearest thousand dollars, is used in transactions before all of it is removed from circulation?

Accepted Answer

A) $769,000 
B) $1,346,000 
C) $1,154,000 
D) $705,000 
E) $1,410,000 
A) $769,000 
B) $1,346,000 
C) $1,154,000 
D) $705,000 
E) $1,410,000

Question 6

Thirty people enter a tennis tournament. How many different first-round matches are possible if each player can be matched with any other player?

Accepted Answer

A) 105 
B) 435 
C) 155,117,520 
D) 32,768 
E) 870 
A) 105 
B) 435 
C) 155,117,520 
D) 32,768 
E) 870

Question 7

Write the rational number   as the quotient of two integers in simplest form.

Accepted Answer

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

Question 8

Sometimes a city will argue that having a professional sports franchise in the city will contribute to economic growth. The rationale for this statement is based on the multiplier effect. Suppose a city estimates that a professional sports franchise will create $45 million of additional income and that a person receiving a portion of this money will spend 80% and save 20%. Assuming the multiplier effect model is accurate, what is the net effect of the $45 million? Round to the nearest hundred thousand.

Accepted Answer

A) $450.0 million 
B) $225.0 million 
C) $281.3 million 
D) $262.5 million 
E) $356.3 million 
A) $450.0 million 
B) $225.0 million 
C) $281.3 million 
D) $262.5 million 
E) $356.3 million

Question 9

A six-digit binary number is a sequence of six digits, each consisting of 0 or 1. For instance, 101010 and 011011 are six-digit binary numbers. How many six-digit binary numbers are possible?

Accepted Answer

A) 32 
B) 256 
C) 128 
D) 16 
E) 64 
A) 32 
B) 256 
C) 128 
D) 16 
E) 64

Question 10

Find the n th term of the geometric sequence. 5, -10, 20,...

Accepted Answer

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

Question 11

A car holds seven passengers, four in the front seat and three in the back seat. How many different seating arrangements of seven people are possible if two people refuses to sit in front and one person refuses to sit in back?

Accepted Answer

A) 24 
B) 2,520 
C) 864 
D) 6 
E) 1,260 
A) 24 
B) 2,520 
C) 864 
D) 6 
E) 1,260

Question 12

Write the given series in summation notation.

Accepted Answer

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

Question 13

Evaluate the series.

Accepted Answer

A) 25 
B) 95 
C) 0 
D) 1225 
E) 775 
A) 25 
B) 95 
C) 0 
D) 1225 
E) 775

Question 14

Find the sum of the finite geometric series.

Accepted Answer

A) -600 
B) -5460 
C) -195 
D) -147615 
E) -15 
A) -600 
B) -5460 
C) -195 
D) -147615 
E) -15

Question 15

Simplify the factorial expression.

Accepted Answer

A)    
B) 11,880 
C) 110 
D) 990 
E) 7920 
A)    
B) 11,880 
C) 110 
D) 990 
E) 7920

Question 16

As a test for extrasensory perception (ESP), eight cards, four black and four white, are shuffled, and then a person looks at each card. In another room, the ESP subject attempts to guess whether the card is black or white. The ESP subject must guess black four times and white four times. If the ESP subject has no extrasensory perception, what is the probability that the subject will correctly name six of the eight cards? Round to the nearest thousandth.

Accepted Answer

A) 0.014 
B) 0.229 
C) 0.450 
D) 0.667 
E) 0.039 
A) 0.014 
B) 0.229 
C) 0.450 
D) 0.667 
E) 0.039

Question 17

Evaluate the factorial expression.

Accepted Answer

A) 3432 
B) 1 
C) 2002 
D) 14 
E) 1001 
A) 3432 
B) 1 
C) 2002 
D) 14 
E) 1001

Question 18

Twelve persons are arranged in a line. What is the probability that three specific people are standing next to each other?

Accepted Answer

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

Question 19

Use mathematical induction to prove the formula for every positive integer n . Show all your work.

Accepted Answer

1)When n = 1, @#IMG-DLM& . The formula i

Question 20

Find the n th partial sum of the arithmetic sequence.

Accepted Answer

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

Six cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all six cards are clubs.

In how many ways can a student answer a 32-question true-false test if the student randomly marks 6 of the questions true and 26 of the questions false?

Find the sum.

Write the given series in summation notation.

Thirty people enter a tennis tournament. How many different first-round matches are possible if each player can be matched with any other player?

Write the rational number as the quotient of two integers in simplest form.

A six-digit binary number is a sequence of six digits, each consisting of 0 or 1. For instance, 101010 and 011011 are six-digit binary numbers. How many six-digit binary numbers are possible?

Find the n th term of the geometric sequence. 5, -10, 20,...

A car holds seven passengers, four in the front seat and three in the back seat. How many different seating arrangements of seven people are possible if two people refuses to sit in front and one person refuses to sit in back?

Write the given series in summation notation.

Evaluate the series.

Find the sum of the finite geometric series.

Simplify the factorial expression.

Evaluate the factorial expression.

Twelve persons are arranged in a line. What is the probability that three specific people are standing next to each other?

Use mathematical induction to prove the formula for every positive integer n . Show all your work.

Find the n th partial sum of the arithmetic sequence.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Preliminary Concepts

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Exam 11: Sequences, Series, and Probability

Six cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all six cards are clubs.

In how many ways can a student answer a 32-question true-false test if the student randomly marks 6 of the questions true and 26 of the questions false?

Find the sum.

Write the given series in summation notation.

Thirty people enter a tennis tournament. How many different first-round matches are possible if each player can be matched with any other player?

Write the rational number as the quotient of two integers in simplest form.

A six-digit binary number is a sequence of six digits, each consisting of 0 or 1. For instance, 101010 and 011011 are six-digit binary numbers. How many six-digit binary numbers are possible?

Find the n th term of the geometric sequence. 5, -10, 20,...

A car holds seven passengers, four in the front seat and three in the back seat. How many different seating arrangements of seven people are possible if two people refuses to sit in front and one person refuses to sit in back?

Write the given series in summation notation.

Evaluate the series.

Find the sum of the finite geometric series.

Simplify the factorial expression.

Evaluate the factorial expression.

Twelve persons are arranged in a line. What is the probability that three specific people are standing next to each other?

Use mathematical induction to prove the formula for every positive integer n . Show all your work.

Find the n th partial sum of the arithmetic sequence.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Preliminary Concepts

Filters