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College Algebra - MAC 1105 > Prerequisites > Flashcards

Prerequisites Flashcards

1
Q

Variable

A

A letter used to represent various numbers

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2
Q

Algebraic Expression

A

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

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3
Q

Exponential Notation

A
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4
Q

Evaluating an Algebraic Expression

A

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

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5
Q

The Order of Operations Agreement

A
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6
Q

Equation

A

Formed when and equal sign is placed between two algebraic expressions

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7
Q

Formula

A

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

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8
Q

Mathematical Modeling

A

The process of finding formulas to describe real-world phenomena

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9
Q

Mathematical Model

A

Formulas, together with the meaning assigned to the variables

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10
Q

Model Breakdown

A

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

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11
Q

Set

A

A collection of objects whose contents can be clearly determined

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12
Q

Elements

A

The objects in a set

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13
Q

Roster Method

A

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

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14
Q

Set-Builder Notation

A

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”

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15
Q

Intersection of Sets

A
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16
Q

Union of Sets

A
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17
Q

Natural Numbers

A
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18
Q

Whole Numbers

A
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19
Q

Integers

A
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20
Q

Rational Numbers

A
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21
Q

Irrational Numbers

A
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22
Q

Real Numbers

A

The set of numbers that are either reational or irrational

{x | x is rational or irrational}

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23
Q

Real Number Line

A

A graph used to represent the set of real numbers

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24
Q

Origin

A

An arbitrary point labeled as 0 on a number line

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25
Q

Unit Distance

A

The distance from 0 to 1 on a number line

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26
Q

Positive Numbers

A

Numbers to the right of 0 on the real number line

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27
Q

Negative Numbers

A

Numbers to the left of 0 on the real number line

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28
Q

Graphed

A

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

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29
Q

Inequality Symbols

A

< and >

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30
Q

Absolute Value

A
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31
Q

Properties of Absolute Value

A
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32
Q

Distance between Two Points on the Real Number Line

A

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 |.

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33
Q

Commutative Property of Addition

A
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34
Q

Commutative Property of Multiplication

A
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35
Q

Associative Property of Addition

A
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36
Q

Associative Property of Multiplication

A
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37
Q

Distributive Property of Multiplication over Addition

A
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38
Q

Identity Property of Addition

A
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39
Q

Identity Property of Multiplication

A
40
Q

Inverse Property of Addition

A
41
Q

Inverse Property of Multiplication

A
42
Q

Subtraction

A
43
Q

Division

A
44
Q

Terms

A

The parts of an algebraic expression that are separated by addition

45
Q

Coefficient

A

The numerical part of a term.

Example: 7x

The coefficient is: 7

46
Q

Factors

A

The parts of each term that are multiplied.

The factors of the term 7x are 7 and x.

47
Q

Like Terms

A

Terms that have exactly the same variable factors.

Example - 3x and 7x are like terms

48
Q

Simplified

A

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

49
Q

Properties of Negatives

A
50
Q

The Product Rule

A
51
Q

The Quotient Rule

A
52
Q

The Zero Exponent Rule

A
53
Q

The Negative Exponent Rule

A
54
Q

Negative Exponents in Numerators and Denominators

A
55
Q

The Power Rule (Powers to Powers)

A
56
Q

Product to Powers

A
57
Q

Quotients to Powers

A
58
Q

Simplifying Exponential Expressions

A
59
Q

Scientific Notation

A
60
Q

Converting from Decimal to Scientific Notation

A
61
Q

Principal Square Root

A
62
Q

Simplifying the square root of a squared term

A
63
Q

The Product Rule for Square Roots

A
64
Q

The Quotient Rule for Square Roots

A
65
Q

Multiplying Conjugates

A
66
Q

Principal nth Root of a Real Number

A
67
Q

Finding nth Roots of Perfect nth Powers

A
68
Q

The Product and Quotient Rules for nth Roots

A
69
Q

Definition of a^(1/n)

A
70
Q

Definition of a^(m/n)

A
71
Q

Polynomial

A

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

72
Q

Standard form of a Polynomial

A

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

73
Q

The Degree of axn

A
74
Q

Monomial

A

A simplified polynomial that has exactly one term

75
Q

Binomial

A

A simplified polynomial that has two terms

76
Q

Trinomial

A

A simplified polynomial with three terms

77
Q

Degree of a Polynomial

A

The greatest degree of all terms of the polynomial.

Example - 4x2 + 3x is a binomial with a degree of 2

78
Q

Definition of a Polynomial in x

A
79
Q

Multiplying Polynomials When Neither Is a Monomial

A

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

80
Q

FOIL Method

A

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

81
Q

The Product of the Sum and Difference of Two Terms

A
82
Q

The Square of a Binomial Sum

A
83
Q

The Square of a Binomial Difference

A
84
Q

Sum and Difference of Two Terms

A
85
Q

Squaring a Binomial

A
86
Q

Cubing a Binomial

A
87
Q

Greatest Common Factor (GCF)

A

An expression of the highest degree that divides each term of the polynomial. The distributive property in reverse direction

ab + ac = a(b + c)

88
Q

Factoring Trinomials

A
89
Q

The Difference of Two Squares

A
90
Q

Factoring Perfect Square Trinomials

A
91
Q

Factoring the Sum or Difference of Two Cubes

A
92
Q

A Strategy for Factoring a Polynomial

A
93
Q

Rational Expression

A

The quotient of two polynomials

Example - ( x - 2 ) / 4, 4 / ( x - 2 ), x / ( x2 - 1 )

94
Q

Simplifying Rational Expressions

A
  1. Factor the numerator and the denominator completely.
  2. Divide both the numerator and the denominator byany common factors.
95
Q

Multiplying Rational Expressions

A
  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.
96
Q

Finding the Least Common Denominator

A
  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.
97
Q

Adding and Subtracting Rational Expressions That Have Different Denominators

A
  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.

College Algebra - MAC 1105 (6 decks)

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