Algebra I - Definitions I

Front 1

Distributive Property of multiplication over addition

Back 1

a(b+c) = ab + bc

Front 2

Axioms

Back 2

Defining rules of algebra; self-evident or universally recognized truth.

Front 3

Commutative Property for Addition

Back 3

a+b = b+a

Front 4

Commutative Property for Multiplication

Back 4

ab = ba

Front 5

Associative Property for Addition

Back 5

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

Front 6

Assoctiative Property for Multiplication

Back 6

(ab)c = a(bc)

Front 7

The power Rule

Back 7

When a base is raised to an exponent and then that expression is raised to another exponent, the result equals the base to the product of the two exponents.

Front 8

Set

Back 8

A collection of objects.

Front 9

Universal Set

Back 9

Represented by U, the Universal Set contains everything.

Front 10

Empty Set

Back 10

Represented by Ø or {}, the Empty Set or Null Set contains nothing.

Front 11

Union

Back 11

the combination of two or more sets to get their Union. AUB is the combination of set A and set B

Front 12

Natural Numbers

Back 12

Also called Counting Numbers, Natural Numbers are the whole numbers that we use for counting. They're represented by the set N= {1,2,3...}

Front 13

Whole Numbers

Back 13

Natural numbers plus 0. They are represented by the set W = {0,1,2,3...}

Front 14

Integers

Back 14

Whole numbers that are either positive or negative. 0 is included in this set. They are represented by the set I = {...-2,-1,0,1,2...}. Another symbol commonly used for the set of integers is Z.

Front 15

Rational Numbers

Back 15

Rational numbers are made up of ratios.

A ration can be written as a fraction. Any number whose decimal either repeats or terminates is a rational number. Since integers can also be written as ratios with a denominator of 1, they are also rational numbers. The set of Rational numbers is represented by Q. (ex. 1/3 = .333..., and 3/8 = .375 are rational numbers) Q = {p/q | p, q Є I, q ≠ 0}

Front 16

Numerator

Back 16

The top part of a fraction.

Front 17

Denominator

Back 17

The bottom part of a fraction.

Front 18

Irrational Numbers

Back 18

Nubers that are not rational. The can never be fully written as a ratio or decimal. They are decimals that do not repeat or end. For example, the square root of 2 (1.41421356...) is an irrational number because the decimal part neither repeats nor ends.

Front 19

Real Numbers

Back 19

The set of rational numbers and the set of irrational numbers combined.

Front 20

Number Line

Back 20

The number line is such that every point on it corresponds to a real number.

A set of numbers can be represented on a number line. A solid cirle indicates that the point is included in the set. A hollow circle indicates that the point is excluded from the set.

Front 21

The reciprocal of non-zero number x

Back 21

1/x

Front 22

The reciprocal of zero

Back 22

The reciprocal of zero is not defined because division by zero is not defined.

Front 23

Absolute Value

Back 23

The absolute value (or modulus, or magnitude) |a| of a real number a is the numerical value of a without regard to its sign.Represented as |x| = x if x ≥ 0 and |x| = -x if x < 0

Front 24

Distributive Property of Multiplication Over Subtraction

Back 24

a(b-c) = ab - ac

Front 25

Subtraction and Division are not...

Back 25

commutative: a - b ≠ b - a, and a ÷ b ≠ b ÷ a

Front 26

To add numbers of the same sign...

Back 26

add the numbers and retain the sign. 5 + 3 = 8, (-5) + (-3) = -8

Front 27

Additive Identity

Back 27

Zero is called the additive identity because zero added to any real number equals the number itself. a + 0 = a. Zero subtracted from any real number is the number itself. a-0 = a

Front 28

Additive Inverse

Back 28

The additive inverse of any number x is -x.

Front 29

Multiplication of two real numbers with the same sign equals:

Back 29

a positive number

Front 30

Multiplication of two real numbers with opposite signs equals:

Back 30

A negative number

Front 31

Division of two real numbers with the same sign equals

Back 31

a positive number

Front 32

Division of two real numbers with opposite signs equals

Back 32

a negative number

Front 33

Exponents

Back 33

Exponents are a notation to indicate repeated multiplication of a number by itself. For example, a x a x a...n times = a^n.

Front 34

Linear equation

Back 34

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. A linear equation is a polynomial of degree 1.

Front 35

Relation

Back 35

Any set of ordered pairs

Front 36

Domain (of the relation)

Back 36

The set of all first components of ordered pairs

Front 37

Range (of the relation)

Back 37

The set of all second components of ordered pairs

Front 38

The definition of a linear equation with one variable.

Back 38

A linear equation in one variable x is an equation that can be written in the form ax + b = 0, where a and b are real numbers and a ≠ (is not equal to) 0.

Front 39

Identity Equation

Back 39

An equation that is true for all real numbers for which both sides (of the equation) are defined. For example,

x + 3 = x + 2 + 1

Front 40

Conditional Equation

Back 40

An equation that is not an identity equation, but that is true for at least one real number. For example,

2x + 3 = 17

The equation is not an identity, and it is only true if x is 7.

Front 41

Inconsistent Equation

Back 41

An equation that is not true for even one real number. For example,

x = x + 7

There is no number that is equal to itself plus 7.The equation has no solution, which is visualized as an empty set; { } or Ø

Front 42

Function

Back 42

Functions are methods of explaining relationships and can be represented as a rule, a graph, a table, or in words.

Front 43

Evaluate

Back 43

Simplify or Answer

Front 44

Subsitutue

Back 44

To replace a variable with a value

Front 45

Slope

Back 45

Change in y over change in x