Prerequisites

Question 1

Variable

Answer 1

A letter used to represent various numbers

Question 2

Algebraic Expression

Answer 2

A combination of variables and numbers using the operations of addition, subtraction, multiplication, or division, as well as powers or roots

Question 3

Exponential Notation

Answer 3

Question 4

Evaluating an Algebraic Expression

Answer 4

To find the value of the expression for a given value of the variable

Question 5

The Order of Operations Agreement

Answer 5

Question 6

Equation

Answer 6

Formed when and equal sign is placed between two algebraic expressions

Question 7

Formula

Answer 7

An equation that uses variables to express a relationship between two or more quantities

Question 8

Mathematical Modeling

Answer 8

The process of finding formulas to describe real-world phenomena

Question 9

Mathematical Model

Answer 9

Formulas, together with the meaning assigned to the variables

Question 10

Model Breakdown

Answer 10

When a mathematical model gives an estimate that is not a good approximation or is extended to include values of teh variable that do not make sense

Question 11

Set

Answer 11

A collection of objects whose contents can be clearly determined

Question 12

Elements

Answer 12

The objects in a set

Question 13

Roster Method

Answer 13

The braces, { }, indicate that we are representing a set. Uses commas to separate the elements of the set

Question 14

Set-Builder Notation

Answer 14

The elements of the set are described but not listed.

{x | x is a counting number less than 6}

Read as: “x” –” | “ such that – “x is a counting number less than 6”

Question 15

Intersection of Sets

Answer 15

Question 16

Union of Sets

Answer 16

Question 17

Natural Numbers

Answer 17

Question 18

Whole Numbers

Answer 18

Question 19

Integers

Answer 19

Question 20

Rational Numbers

Answer 20

Question 21

Irrational Numbers

Answer 21

Question 22

Real Numbers

Answer 22

The set of numbers that are either reational or irrational

{x | x is rational or irrational}

Question 23

Real Number Line

Answer 23

A graph used to represent the set of real numbers

Question 24

Origin

Answer 24

An arbitrary point labeled as 0 on a number line

Question 25

Unit Distance

Answer 25

The distance from 0 to 1 on a number line

Question 26

Positive Numbers

Answer 26

Numbers to the right of 0 on the real number line

Question 27

Negative Numbers

Answer 27

Numbers to the left of 0 on the real number line

Question 28

Graphed

Answer 28

On a real number line, placing a dot at the correct location for each number

Question 29

Inequality Symbols

Answer 29

\< and \>

Question 30

Absolute Value

Answer 30

Question 31

Properties of Absolute Value

Answer 31

Question 32

Distance between Two Points on the Real Number Line

Answer 32

If a and b are any two points on a real number line, then the distance between a and b is given by | a - b | or | b - a | , where | a - b | = | b - a |.

Question 33

Commutative Property of Addition

Answer 33

Question 34

Commutative Property of Multiplication

Answer 34

Question 35

Associative Property of Addition

Answer 35

Question 36

Associative Property of Multiplication

Answer 36

Question 37

Distributive Property of Multiplication over Addition

Answer 37

Question 38

Identity Property of Addition

Answer 38

Question 39

Identity Property of Multiplication

Answer 39

Question 40

Inverse Property of Addition

Answer 40

Question 41

Inverse Property of Multiplication

Answer 41

Question 42

Subtraction

Answer 42

Question 43

Division

Answer 43

Question 44

Terms

Answer 44

The parts of an algebraic expression that are separated by addition

Question 45

Coefficient

Answer 45

The numerical part of a term. Example: 7x The coefficient is: 7

Question 46

Factors

Answer 46

The parts of each term that are multiplied. The factors of the term 7x are 7 and x.

Question 47

Like Terms

Answer 47

Terms that have exactly the same variable factors. Example - 3x and 7x are like terms

Question 48

Simplified

Answer 48

When the parentheses have been removed and like terms ahve been combined in an algebraic equation

Question 49

Properties of Negatives

Answer 49

Question 50

The Product Rule

Answer 50

Question 51

The Quotient Rule

Answer 51

Question 52

The Zero Exponent Rule

Answer 52

Question 53

The Negative Exponent Rule

Answer 53

Question 54

Negative Exponents in Numerators and Denominators

Answer 54

Question 55

The Power Rule (Powers to Powers)

Answer 55

Question 56

Product to Powers

Answer 56

Question 57

Quotients to Powers

Answer 57

Question 58

Simplifying Exponential Expressions

Answer 58

Question 59

Scientific Notation

Answer 59

Question 60

Converting from Decimal to Scientific Notation

Answer 60

Question 61

Principal Square Root

Answer 61

Question 62

Simplifying the square root of a squared term

Answer 62

Question 63

The Product Rule for Square Roots

Answer 63

Question 64

The Quotient Rule for Square Roots

Answer 64

Question 65

Multiplying Conjugates

Answer 65

Question 66

Principal nth Root of a Real Number

Answer 66

Question 67

Finding nth Roots of Perfect nth Powers

Answer 67

Question 68

The Product and Quotient Rules for nth Roots

Answer 68

Question 69

Definition of a^(1/n)

Answer 69

Question 70

Definition of a^(m/n)

Answer 70

Question 71

Polynomial

Answer 71

A single term or the sum of two or more terms containing vairalbes with whole-number exponents

Question 72

Standard form of a Polynomial

Answer 72

Writing the terms of a polynomial in the order of descending powers fo the variable

Question 73

The Degree of axⁿ

Answer 73

Question 74

Monomial

Answer 74

A simplified polynomial that has exactly one term

Question 75

Binomial

Answer 75

A simplified polynomial that has two terms

Question 76

Trinomial

Answer 76

A simplified polynomial with three terms

Question 77

Degree of a Polynomial

Answer 77

The greatest degree of all terms of the polynomial. Example - 4x² + 3x is a binomial with a degree of 2

Question 78

Definition of a Polynomial in x

Answer 78

Question 79

Multiplying Polynomials When Neither Is a Monomial

Answer 79

Multiply each term of one polynomial by each term of the other polynomial. Then combine like terms.

Question 80

FOIL Method

Answer 80

Used when multiplying two binomials. Represents the order of First, Outer, Inner, Last.

Question 81

The Product of the Sum and Difference of Two Terms

Answer 81

Question 82

The Square of a Binomial Sum

Answer 82

Question 83

The Square of a Binomial Difference

Answer 83

Question 84

Sum and Difference of Two Terms

Answer 84

Question 85

Squaring a Binomial

Answer 85

Question 86

Cubing a Binomial

Answer 86

Question 87

Greatest Common Factor (GCF)

Answer 87

An expression of the highest degree that divides each term of the polynomial. The distributive property in reverse direction ab + ac = a(b + c)

Question 88

Factoring Trinomials

Answer 88

Question 89

The Difference of Two Squares

Answer 89

Question 90

Factoring Perfect Square Trinomials

Answer 90

Question 91

Factoring the Sum or Difference of Two Cubes

Answer 91

Question 92

A Strategy for Factoring a Polynomial

Answer 92

Question 93

Rational Expression

Answer 93

The quotient of two polynomials Example - ( x - 2 ) / 4, 4 / ( x - 2 ), x / ( x² - 1 )

Question 94

Simplifying Rational Expressions

Answer 94

1. Factor the numerator and the denominator completely. 2. Divide both the numerator and the denominator byany common factors.

Question 95

Multiplying Rational Expressions

Answer 95

1. Factor all numerators and denominators completely. 2. Divide numerators and denominators by common factors. 3. Multiply the remaining factors in the numerators and multiply the remaining factors in the denominators.

Question 96

Finding the Least Common Denominator

Answer 96

1. Factor each denominator completely. 2. List the factors of the first denominator. 3. Add to the list in step 2 any factors of the second denominator that do not appear in the list. 4. Form the product of each different factor fom the list in step 3. This product is the least common denominator.

Question 97

Adding and Subtracting Rational Expressions That Have Different Denominators

Answer 97

1. Find the LCD of the rational expressions. 2. Rewrite each rational expression as an equivalent expression whose denominator is the LCD. To do so, multiply the numerator and the denominator of each rational expression by any factor(s) needed to convert the denominator into the LCD. 3. Add or subtract numerators, placing the resulting expression over the LCD. 4. If possible, simplify the resulting rational expression.