Question 1

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

Accepted Answer

A) 70 
B) 60 
C) 12 
D) 56 
E) 45 
A) 70 
B) 60 
C) 12 
D) 56 
E) 45 B

Question 2

A pile of logs has 34 logs in the bottom layer, 32 in the second layer, 30 in the third, and so on. The top layer contains 12 logs. Find the total number of logs in the pile.

Accepted Answer

A) 276 logs 
B) 270 logs 
C) 552 logs 
D) 274 logs 
E) 272 logs 
A) 276 logs 
B) 270 logs 
C) 552 logs 
D) 274 logs 
E) 272 logs A

Question 3

Find the number.

Accepted Answer

A) 9 
B) 5 
C) 3 
D) 7 
E) 5,040 
A) 9 
B) 5 
C) 3 
D) 7 
E) 5,040 D

Question 4

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

Accepted Answer

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

Question 5

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 66 matches?

Accepted Answer

A) 24 
B) 66 
C) 10 
D) 12 
E) 11 
A) 24 
B) 66 
C) 10 
D) 12 
E) 11

Question 6

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

Accepted Answer

A) 24 
B) 2 
C) 12 
D) 6 
E) 4 
A) 24 
B) 2 
C) 12 
D) 6 
E) 4

Question 7

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 55 matches?

Accepted Answer

A) 22 
B) 11 
C) 10 
D) 14 
E) 55 
A) 22 
B) 11 
C) 10 
D) 14 
E) 55

Question 8

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

Question 9

Find the third term of the sequence:   is the number of decimal places in   .

Accepted Answer

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

Question 10

Use the binomial theorem to expand and simplify.

Accepted Answer

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

Question 11

A rubber ball is dropped from a height of 60 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) 300 ft 
B) 480 ft 
C) 240 ft 
D) 60 ft 
E) 180 ft 
A) 300 ft 
B) 480 ft 
C) 240 ft 
D) 60 ft 
E) 180 ft

Question 12

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

Accepted Answer

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

Question 13

Find the third term of the recursively defined infinite sequence.

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

If seven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Accepted Answer

A) 42 
B) 210 
C) 6 
D) 1,680 
E) 840 
A) 42 
B) 210 
C) 6 
D) 1,680 
E) 840

Question 16

A bicycle rider coasts downhill, traveling 7 feet the first second. In each succeeding second, the rider travels 4 feet farther than in the preceding second. If the rider reaches the bottom of the hill in 8 seconds, find the total distance traveled.

Accepted Answer

A) 164 feet 
B) 172 feet 
C) 160 feet 
D) 152 feet 
E) 168 feet 
A) 164 feet 
B) 172 feet 
C) 160 feet 
D) 152 feet 
E) 168 feet

Question 17

Find the nth term and the fifth term of the geometric sequence.

Accepted Answer

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

Question 18

A contest will have five cash prizes totaling $13,000, and there will be a $500 difference between successive prizes. Find the first prize.

Accepted Answer

A) $4,100 
B) $3,100 
C) $3,600 
D) $5,100 
E) $6,100 
A) $4,100 
B) $3,100 
C) $3,600 
D) $5,100 
E) $6,100

Question 19

Find the nth term and the fifth term of the geometric sequence.

Accepted Answer

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

Question 20

A man is 52 years old and a woman is 34 years old. The probability that the man will be alive in 10 years is 0.78, whereas the probability that the woman will be alive 10 years from now is 0.88. 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

Accepted Answer

A)    
B)   
now. 
C)    
D)    
E)    
A)    
B)   
now. 
C)    
D)    
E)

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

A pile of logs has 34 logs in the bottom layer, 32 in the second layer, 30 in the third, and so on. The top layer contains 12 logs. Find the total number of logs in the pile.

Find the number.

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

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 66 matches?

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

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 55 matches?

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 third term of the sequence: is the number of decimal places in .

Use the binomial theorem to expand and simplify.

A rubber ball is dropped from a height of 60 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 principle of mathematical induction to find the equivalent expression for every positive integer n.

Find the third term of the recursively defined infinite sequence.

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

If seven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

A bicycle rider coasts downhill, traveling 7 feet the first second. In each succeeding second, the rider travels 4 feet farther than in the preceding second. If the rider reaches the bottom of the hill in 8 seconds, find the total distance traveled.

Find the nth term and the fifth term of the geometric sequence.

A contest will have five cash prizes totaling $13,000, and there will be a $500 difference between successive prizes. Find the first prize.

Find the nth term and the fifth term of the geometric 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

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

A pile of logs has 34 logs in the bottom layer, 32 in the second layer, 30 in the third, and so on. The top layer contains 12 logs. Find the total number of logs in the pile.

Find the number.

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

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 66 matches?

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

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 55 matches?

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 third term of the sequence: is the number of decimal places in .

Use the binomial theorem to expand and simplify.

A rubber ball is dropped from a height of 60 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 principle of mathematical induction to find the equivalent expression for every positive integer n.

Find the third term of the recursively defined infinite sequence.

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

If seven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

A bicycle rider coasts downhill, traveling 7 feet the first second. In each succeeding second, the rider travels 4 feet farther than in the preceding second. If the rider reaches the bottom of the hill in 8 seconds, find the total distance traveled.

Find the nth term and the fifth term of the geometric sequence.

A contest will have five cash prizes totaling $13,000, and there will be a $500 difference between successive prizes. Find the first prize.

Find the nth term and the fifth term of the geometric 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