Question 1

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

Question 2

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

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

Question 3

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

Accepted Answer

A) 3 
B) 15 
C) 720 
D) 360 
E) 6 
A) 3 
B) 15 
C) 720 
D) 360 
E) 6

Question 4

Use the binomial theorem to expand and simplify.

Accepted Answer

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

Question 5

Use the binomial theorem to expand and simplify.

Accepted Answer

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

Question 6

A single card is drawn from a deck. Find the probability that the card is either red or a two.

Accepted Answer

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

Question 7

Find the sum of the arithmetic sequence   that satisfies the stated conditions.

Accepted Answer

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

Question 8

If eleven 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) 17,160 
B) 6 
C) 1,320 
D) 11,880 
E) 132 
A) 17,160 
B) 6 
C) 1,320 
D) 11,880 
E) 132

Question 9

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

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

Question 10

Use the principle of mathematical induction to find the factor of the expression.   Hint:

Accepted Answer

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

Question 11

Find the number of terms in the arithmetic sequence with the given conditions.   ,

Accepted Answer

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

Question 12

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 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

Evaluate the expression. 6!0!

Accepted Answer

A) 120 
B) 720 
C) 40,320 
D) 0 
E) 1 
A) 120 
B) 720 
C) 40,320 
D) 0 
E) 1

Question 15

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)

Question 16

Find the number.

Accepted Answer

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

Question 17

Find the number of terms in the arithmetic sequence with the given conditions.   ,

Accepted Answer

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

Question 18

Use the binomial theorem to expand and simplify.

Accepted Answer

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

Question 19

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 20

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)

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.

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.)

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

Use the binomial theorem to expand and simplify.

Use the binomial theorem to expand and simplify.

A single card is drawn from a deck. Find the probability that the card is either red or a two.

Find the sum of the arithmetic sequence that satisfies the stated conditions.

If eleven 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.

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.)

Use the principle of mathematical induction to find the factor of the expression. Hint:

Find the number of terms in the arithmetic sequence with the given conditions. ,

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

Find the third term of the recursively defined infinite sequence.

Evaluate the expression. 6!0!

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.

Find the number.

Find the number of terms in the arithmetic sequence with the given conditions. ,

Use the binomial theorem to expand and simplify.

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

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

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

Exam 10: Sequences, Series and Probability

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.

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.)

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

Use the binomial theorem to expand and simplify.

Use the binomial theorem to expand and simplify.

A single card is drawn from a deck. Find the probability that the card is either red or a two.

Find the sum of the arithmetic sequence that satisfies the stated conditions.

If eleven 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.

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.)

Use the principle of mathematical induction to find the factor of the expression. Hint:

Find the number of terms in the arithmetic sequence with the given conditions. ,

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

Find the third term of the recursively defined infinite sequence.

Evaluate the expression. 6!0!

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.

Find the number.

Find the number of terms in the arithmetic sequence with the given conditions. ,

Use the binomial theorem to expand and simplify.

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

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

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