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MAC 1105 Fall 2019 > Chapter P > Flashcards

Chapter P Flashcards

1
Q

Multiplying Conjugates

A
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2
Q

Difference of Two Squares

A
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3
Q

variable

A

a letter used to represent various Numbers

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4
Q

Special Products

A
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5
Q

Simplifying Exponential Expressions

A
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6
Q

Finding the Least Common Denominator

A
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7
Q

Adding and Subtracting Rational Expressions That Have Different Denominators

A
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8
Q

Factoring the Sum or Difference of Two Cubes

A
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9
Q

Finding nth Roots of Perfect nth Powers

A
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10
Q

Associative Property of Addition

A

Changing grouping when adding does not affect he sum.

(a + b) + c = a + (b + c)

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11
Q

Power Rule

A
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12
Q

Product to Powers

A
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13
Q

Simplifying Rational Expressions

A
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14
Q

Factoring Perfect Square Trinomials

A
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15
Q

Quotient to Powers

A
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16
Q

evaluating an algebraic expression

A

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

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17
Q

Definition of a1/n

A
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18
Q

Negative Exponents in Numerators and Denominators

A
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19
Q

Polynomial in x

A
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20
Q
A
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21
Q

set

A

a collection of objects whose contents can be clearly determined

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22
Q

Principal nth Root of a Real Number

A
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23
Q

Definition of am/n

A
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24
Q

Quotient Rule

A
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25
Q

Product and Quotient Rules for nth Roots

A
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26
Q

roster method

A

the use of braces { } and commas to separate the elements of the set

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27
Q

Union of Sets

A

the set of elements that are membersof set A or of set B or of both sets. expressed as AUB

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28
Q

Properties of Negatives

A
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29
Q

Zero Exponent Rule

A
30
Q

mathematical models

A

modeling formulas together with the meaning assigned to the variables

31
Q

Converting from Decimal to Scientific Notation

A
32
Q

Exponential Notation

A

a counting number raised to the nth power from a base number

33
Q

Strategy for Factoring a Polynomial

A
34
Q

Degree of axn

A
35
Q

Important Subsets of the Real Numbers

A
36
Q

Order of Operations Agreement

A

Parenthesis - innermost to outermost Exponents Multiplications and divisions as they occur from left to right Additions and subtractions as they occur from left to right

37
Q

Absolute Value

A
38
Q

Absolute Value Properties

A

1

39
Q

Product Rule

A
40
Q

Subtraction and Division

A
41
Q

Negative Exponent Rule

A
42
Q

set-builder notation

A

the elements of the set are described but not listed (x,y)

43
Q

Distance Between Two Points on a Number Line

A

|a - b| = |b-a|

44
Q

elements

A

the objects in a set

45
Q

equation

A

an equal sign is placed between two algebraic expressions

46
Q

Multiplying Polynomials When Neither is a Monomial

A
47
Q

Strategy for Factoring ax2 + bx + c

A
48
Q

Properties of the Real Numbers

A

1

49
Q

Product of the Sum and Difference of Two Terms

A
50
Q

Irrational Numbers

A

the set of irrational numbers is the set of all numbers whose decimal representations are neither terminating nor repeating. Irrational numbers cannot be expressed as a quotient of integers.
Example:

51
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

52
Q

Whole Numbers

A

{0,1,2,3,4,5, … }
The set of whole numbers includes 0 and the natural numbers
Example: 0,2,3,5,17

53
Q

Natural Numbers

A

{1,2,3,4,5,…} These are the numbers that we use for counting.
Example: 2,3,5,17

54
Q

Using FOIL to Multiply Binomials

A
55
Q

Product Rule for Square Roots

A
56
Q

formula

A

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

57
Q

Scientific Notation

A
58
Q

Real Numbers

A

the set of numbers that are either reational or irrational

59
Q

Intersection of Sets

A

the set of elements common to both sets A and B. expressed as

60
Q

commutative property of multiplication

A

changing order when multiplying does not affect the product (ab = ba)
Example: x · 6 = 6x

61
Q

mathematical model breakdown

A

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

62
Q

mathematical modeling

A

the process of finding formulas to describe real-world phenomena

63
Q

Square of a Binomial Sum

A
64
Q

Quotient Rule for Square Roots

A
65
Q

commutative property of addition

A

changing order when addeing does not affect the sum (a + b = b + a)
Example: 13+7=7+13

66
Q

Rational Numbers

A

{a/b | a and b are integers and b<>0}
The set of rational numbers is the set of all numbers that can be expressed as a quotient of two integers, with the denominator not 0. Rational numbers can be expressed as terminating or repeating decimals.

Example: -17=(-17/1),-5=(-5/1),-3,-2,0,2,3,5,17,
(2/5)=0.4,(-2/3)=-0.6666

67
Q

Square of a Binomial Difference

A
68
Q

Integers

A

{…,-5,-4,-3,-2,-1,0,1,2,3,4,5,…}
The set of integers includes the negatives of the natural numbers and the whole numbers.
Example: -17,-5,-3,-2,0,2,3,5,17

69
Q

Multiplying Rational Expressions

A
70
Q

Principal Square Root

A

MAC 1105 Fall 2019 (7 decks)

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