Question 1

Find the sum.

Accepted Answer

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E)    
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E)

Question 2

Find the fourth partial sum for the given sequence.

Accepted Answer

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D)    
E)

Question 3

A contest will have five cash prizes totaling $11,000, and there will be a $400 difference between successive prizes. Find the first prize.

Accepted Answer

A) $3,800 
B) $3,000 
C) $2,200 
D) $5,000 
E) $3,400 
A) $3,800 
B) $3,000 
C) $2,200 
D) $5,000 
E) $3,400

Question 4

Without expanding completely, find the term in the expansion of the expression that contains   .

Accepted Answer

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D)    
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E)

Question 5

Find the sum.

Accepted Answer

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D)    
E)    
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B)    
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D)    
E)

Question 6

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

Accepted Answer

A) 977,407,200 
B) 8,145,060 
C) 720 
D) 45 
E) 6 
A) 977,407,200 
B) 8,145,060 
C) 720 
D) 45 
E) 6

Question 7

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 49. Find the total number of selections possible if a player selects only even numbers.

Accepted Answer

A) 134,596 
B) 144 
C) 6,991,908 
D) 60,410,085,120 
E) 96,909,120 
A) 134,596 
B) 144 
C) 6,991,908 
D) 60,410,085,120 
E) 96,909,120

Question 8

Find the fourth term of the recursively defined infinite sequence.

Accepted Answer

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Question 9

A man is 50 years old and a woman is 41 years old. The probability that the man will be alive in 10 years is 0.71, whereas the probability that the woman will be alive 10 years from now is 0.86. Assume that their life expectancies are unrelated. 
A. Find the probability that they will both be alive 10 years from now.
B. Find the probability that neither one will be alive 10 years from now.
C. Find the probability that at least one of the two will be alive 10 years from now.

Accepted Answer

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

Question 10

Express the sum in terms of n.   (Hint: Use the theorem on sums to write the sum as   . Next, use the following formulas   and the theorem on the sum of a constant.)

Accepted Answer

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

Question 11

Find the smallest positive integer j for which the statement is true.

Accepted Answer

A) 19 
B) 256 
C) 16 
D) 12 
E) 15 
A) 19 
B) 256 
C) 16 
D) 12 
E) 15

Question 12

Consider any nine points such that no three are collinear. How many lines are determined?

Accepted Answer

A) 36 
B) 362,880 
C) 4 
D) 181,440 
E) 9 
A) 36 
B) 362,880 
C) 4 
D) 181,440 
E) 9

Question 13

Evaluate the expression.

Accepted Answer

A) 1 
B) 20 
C) 6 
D) 120 
E) 5 
A) 1 
B) 20 
C) 6 
D) 120 
E) 5

Question 14

A girl has three skirts, ten blouses and five sweaters. How many different skirt-blouse-sweater combinations can she wear?

Accepted Answer

A) 160 
B) 18 
C) 120 
D) 146 
E) 150 
A) 160 
B) 18 
C) 120 
D) 146 
E) 150

Question 15

During 1990, smoking caused 418,890 deaths in the United States. Of these deaths, cardiovascular disease accounted for 179,820, cancer for 151,322, and respiratory diseases such as emphysema for 84,475. Find the probability that a smoking-related death was the result of either cancer or cardiovascular disease.

Accepted Answer

A) 0.813 
B) 0.209 
C) 0.791 
D) 0.803 
E) 0.786 
A) 0.813 
B) 0.209 
C) 0.791 
D) 0.803 
E) 0.786

Question 16

A rubber ball is dropped from a height of 45 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.

Accepted Answer

A) 45 ft 
B) 315 ft 
C) 225 ft 
D) 270 ft 
E) 180 ft 
A) 45 ft 
B) 315 ft 
C) 225 ft 
D) 270 ft 
E) 180 ft

Question 17

Use the binomial theorem to expand and simplify.

Accepted Answer

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B)    
C)    
D)    
E)    
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E)

Question 18

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Accepted Answer

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

Question 19

Express the sum in terms of n.   (Hint: Use the theorem on sums to write the sum as   . Next, use the following formulas   and the theorem on the sum of a constant.)

Accepted Answer

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

Question 20

Bode's sequence, defined by   can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

Accepted Answer

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

Find the sum.

Find the fourth partial sum for the given sequence.

A contest will have five cash prizes totaling $11,000, and there will be a $400 difference between successive prizes. Find the first prize.

Without expanding completely, find the term in the expansion of the expression that contains .

Find the sum.

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 49. Find the total number of selections possible if a player selects only even numbers.

Find the fourth term of the recursively defined infinite sequence.

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

Find the smallest positive integer j for which the statement is true.

Consider any nine points such that no three are collinear. How many lines are determined?

Evaluate the expression.

A girl has three skirts, ten blouses and five sweaters. How many different skirt-blouse-sweater combinations can she wear?

A rubber ball is dropped from a height of 45 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.

Use the binomial theorem to expand and simplify.

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Topics From Analytic Geometry

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Exam 10: Sequences, Series and Probability

Find the sum.

Find the fourth partial sum for the given sequence.

A contest will have five cash prizes totaling $11,000, and there will be a $400 difference between successive prizes. Find the first prize.

Without expanding completely, find the term in the expansion of the expression that contains .

Find the sum.

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 49. Find the total number of selections possible if a player selects only even numbers.

Find the fourth term of the recursively defined infinite sequence.

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

Find the smallest positive integer j for which the statement is true.

Consider any nine points such that no three are collinear. How many lines are determined?

Evaluate the expression.

A girl has three skirts, ten blouses and five sweaters. How many different skirt-blouse-sweater combinations can she wear?

A rubber ball is dropped from a height of 45 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.

Use the binomial theorem to expand and simplify.

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Topics From Analytic Geometry

Filters