Question 1

Factor the sum or difference of cubes. 27n3 + 8

Accepted Answer

A)  (3n - 2)3 
B)  (3n + 2)3 
C)  (3n + 2)(9n2 - 6n + 4) 
D)  (3n + 2)(9n2 + 6n + 4) 
E)  (3n - 2)(9n2 - 6n + 4) 
A)  (3n - 2)3 
B)  (3n + 2)3 
C)  (3n + 2)(9n2 - 6n + 4) 
D)  (3n + 2)(9n2 + 6n + 4) 
E)  (3n - 2)(9n2 - 6n + 4)

Question 2

Factor the trinomial. 9m2 + 9m + 2

Accepted Answer

A)  (9m - 2)(m - 1) 
B)  (9m + 2)(m + 1) 
C)  (3m - 2)(3m + 1) 
D)  (3m - 2)(3m - 1) 
E)  (3m + 2)(3m + 1) 
A)  (9m - 2)(m - 1) 
B)  (9m + 2)(m + 1) 
C)  (3m - 2)(3m + 1) 
D)  (3m - 2)(3m - 1) 
E)  (3m + 2)(3m + 1)

Question 3

Simplify the expression below.

Accepted Answer

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

Question 4

Perform the operation and write the result in standard form.

Accepted Answer

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

Question 5

Evaluate   when   and

Accepted Answer

A)  -800 
B)  40 
C)  2000 
D)  1600 
E)  -200 
A)  -800 
B)  40 
C)  2000 
D)  1600 
E)  -200

Question 6

Write the rational expression in simplest form.

Accepted Answer

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

Question 7

Write each number in the expression below in scientific notation.Perform the operation and write your answer in scientific notation.

Accepted Answer

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

Question 8

Multiply. (-x - 6)(-2x - 8)

Accepted Answer

A)  -3x - 14 
B)  -3x2 - 14 
C)  22x + 48 
D)  -3x2 - 17x - 14 
E)  2x2 + 20x + 48 
A)  -3x - 14 
B)  -3x2 - 14 
C)  22x + 48 
D)  -3x2 - 17x - 14 
E)  2x2 + 20x + 48

Question 9

Evaluate the expression for the given value of x.   x = 3

Accepted Answer

A)  12 
B)    
C)    
D)  81 
E)  -81 
A)  12 
B)    
C)    
D)  81 
E)  -81

Question 10

Write the rational expression in simplest form.

Accepted Answer

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

Question 11

Reduce the index of the radical.

Accepted Answer

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

Question 12

The number of committees consisting of exactly 3 people that can be formed from a group of n people is given by the polynomial   Find the number of committees consisting of exactly 3 people that can be formed from a group of   people. Round to the nearest whole number.

Accepted Answer

A)  6545 
B)  5445 
C)  5456 
D)  5638 
E)  6540 
A)  6545 
B)  5445 
C)  5456 
D)  5638 
E)  6540

Question 13

The length L of the hypotenuse of a right triangle is   where x and y are the lengths of the other two sides.Find the length of the hypotenuse when the other sides measure 1 unit and   units.

Accepted Answer

A)  1 unit 
B)    units 
C)    units 
D)    units 
E)    units 
A)  1 unit 
B)    units 
C)    units 
D)    units 
E)    units

Question 14

Use inequality notation to describe the set. u is positive

Accepted Answer

A)  u $\le$ $\infty$ 
B)  u  0 
A)  u $\le$ $\infty$ 
B)  u  0

Question 15

On an expressway, the recommended safe distance between cars in feet is given by   where v is the speed of the car in miles per hour.Find the safe distance when   miles per hour.Round your answer to the nearest tenth.

Accepted Answer

A)  44.7 feet 
B)  71.6 feet 
C)  62.6 feet 
D)  35.8 feet 
E)  107.4 feet 
A)  44.7 feet 
B)  71.6 feet 
C)  62.6 feet 
D)  35.8 feet 
E)  107.4 feet

Question 16

Use a calculator to approximate the number.(Round your answer to three decimal places.)

Accepted Answer

A)  2.924 
B)  75.000 
C)  5.000 
D)  8.333 
E)  28.000 
A)  2.924 
B)  75.000 
C)  5.000 
D)  8.333 
E)  28.000

Question 17

Factor by grouping. z3 + 4z2 + 8z + 32

Accepted Answer

A)  z2 + 8(z + 4) 
B)  (z2 + 8)2(z + 4) 
C)  (z2 + 8)(z + 4) 
D)  (z2 - 8)(z - 4) 
E)  (z2 + 8)(z + 4)2 
A)  z2 + 8(z + 4) 
B)  (z2 + 8)2(z + 4) 
C)  (z2 + 8)(z + 4) 
D)  (z2 - 8)(z - 4) 
E)  (z2 + 8)(z + 4)2

Question 18

Simplify the following radical expression.

Accepted Answer

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

Question 19

Simplify the expression.

Accepted Answer

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

Question 20

When food is placed in a refrigerator, the time required for the food to cool depends on the amount of food, the air circulation in the refrigerator, the original temperature of the food, and the temperature of the refrigerator.One model for the temperature of food that starts at   and is placed in a   refrigerator is     where   is the temperature (in degrees Fahrenheit) and   is the time (in hours).According to the model, after how many hours will the food reach a temperature of

Accepted Answer

A)  after 5 hours 
B)  after 2 hours 
C)  after 6 hours 
D)  after 3 hours 
E)  after 1 hour 
A)  after 5 hours 
B)  after 2 hours 
C)  after 6 hours 
D)  after 3 hours 
E)  after 1 hour

Factor the sum or difference of cubes. 27n³ + 8

Factor the trinomial. 9m² + 9m + 2

Simplify the expression below.

Perform the operation and write the result in standard form.

Evaluate when and

Write the rational expression in simplest form.

Write each number in the expression below in scientific notation.Perform the operation and write your answer in scientific notation.

Multiply. (-x - 6)(-2x - 8)

Evaluate the expression for the given value of x. x = 3

Write the rational expression in simplest form.

Reduce the index of the radical.

The number of committees consisting of exactly 3 people that can be formed from a group of n people is given by the polynomial Find the number of committees consisting of exactly 3 people that can be formed from a group of people. Round to the nearest whole number.

The length L of the hypotenuse of a right triangle is where x and y are the lengths of the other two sides.Find the length of the hypotenuse when the other sides measure 1 unit and units.

Use inequality notation to describe the set. u is positive

On an expressway, the recommended safe distance between cars in feet is given by where v is the speed of the car in miles per hour.Find the safe distance when miles per hour.Round your answer to the nearest tenth.

Use a calculator to approximate the number.(Round your answer to three decimal places.)

Factor by grouping. z³ + 4z² + 8z + 32

Simplify the following radical expression.

Simplify the expression.

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Exam 1: Fundamental Concepts of Algebra

Factor the sum or difference of cubes. 27n3 + 8

Factor the trinomial. 9m2 + 9m + 2

Simplify the expression below.

Perform the operation and write the result in standard form.

Evaluate when and

Write the rational expression in simplest form.

Write each number in the expression below in scientific notation.Perform the operation and write your answer in scientific notation.

Multiply. (-x - 6)(-2x - 8)

Evaluate the expression for the given value of x. x = 3

Write the rational expression in simplest form.

Reduce the index of the radical.

The number of committees consisting of exactly 3 people that can be formed from a group of n people is given by the polynomial Find the number of committees consisting of exactly 3 people that can be formed from a group of people. Round to the nearest whole number.

The length L of the hypotenuse of a right triangle is where x and y are the lengths of the other two sides.Find the length of the hypotenuse when the other sides measure 1 unit and units.

Use inequality notation to describe the set. u is positive

On an expressway, the recommended safe distance between cars in feet is given by where v is the speed of the car in miles per hour.Find the safe distance when miles per hour.Round your answer to the nearest tenth.

Use a calculator to approximate the number.(Round your answer to three decimal places.)

Factor by grouping. z3 + 4z2 + 8z + 32

Simplify the following radical expression.

Simplify the expression.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Series, and Probability

Filters

Factor the sum or difference of cubes. 27n³ + 8

Factor the trinomial. 9m² + 9m + 2

Factor by grouping. z³ + 4z² + 8z + 32