MAT 1033 Vocab

Equal Symbol

"is equal to" A sign = indicating mathematical or logical equivalence

Real Numbers

- 18, 0, -1/2, 47/10, Pie, Square root

Negative Integers

- 20, -13, -1

Integers

-10,0,8

Non integers Rational Numbers

-14/5 , 9/10, 30/13

Zero

0

Algebraic Expression

A collection of numbers, variables, operation symbols, and grouping symbols.

Set

A collection of objects, each of which is called a member or element.

Exponential Expression

A mathematical expression consisting of a constant (especially e) reasoned to some power.

Term

A number or the product of a number and variables raised to powers.

To the right of

A number that is larger than the current number next to it (On the number line)

To the left of

A number that is smaller than the current number next to it (On the number line)

Real Number

A quantity that can be expressed as an infinite decimal expansion

All real numbers

A set notation that have solutions (Possibly the def).

Exponential Notation

A short-hand notation for repeated multiplication of the same factor

Variable

A symbol used to represent an unknown number.

Solution of an inequality

A value of the variable that makes the inequality a true statement.

The Absolute value

Absolute value of a real number a, denoted by |a|, is the distance between a and 0 on a number line.

Equivalent equations

Algebraic equations that have identical solutions or roots.

Equation

An Expression equal to another expression Expression = Expression

Multiplicative Inverses

An element of a mathematical set that when multiplied by a given element yields the identity elements B × 1/b = 1

Linear Equations

An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression.

Formula

An equation that describes a known relationship among quantities.

Linear Inequality in One Variable

An inequality that can be written in the form Ax + b < c

Member

An object that belongs to a set

Numerical Coeffiecient

Any constant term that is in front of one or more variables in a mathematical expression.

Element

Any one of the distinct objects that belong to that set.

Area of a rectangle formula

Area of a rectangle = length × width A = LW

Solution

Deciding which values of the variable make the equation a true statement.

Solving

Deciding which values of the variable make the equation a true statement.

Distance formula

Distance = rate × time D = RT

Identity

Equality relating one mathematical expression A to another mathematical expression B

Consecutive Even Integers

Even integers that follow each other and they differ by 2. If x is an even integer, then x + 2, X + 4 and x+ 6 are consecutive even integers.

Order Property for Real Numbers

For any two real numbers a and b, a is less than b if a is to the left of b on a number line.

Grouping Symbols

Grouping symbols are used to show what should be done first in a math expression. Ex: Parentheses (), Brackets[ ], Braces{ }

Number line

Horizontal straight lines in which the integers are placed in equal intervals.

Solving Equations of the Form |x| = a

If a is a positive number, then |X| = a is equivalent to x = a or x = - a |x| = a

Multiplication Property of Inequality (Negative)

If a, b, and c are real numbers and c is negative, then a < b and ac > bc are equivalent inequalities a < b and ac > bc

Multiplication Property of Inequality (Positive)

If a, b, and c are real numbers, and c is positive, then A< b and a +c < b + c Are equivalent inequalities A < b and a+c < b+c

Addition Property of Inequality

If a, b, and c are real numbers, then A<b and a + c < b + c Are equivalent inequalities A<b and a +c < b + c

Simple inequalities

Inequalities containing one inequality symbol

Consecutive Integers

Integers that follow each other in a patterned order, usually just one number after the other, like 1,2,3.... Let x be an Integer x, x + 1, x + 2

Positive Integers

Integers to the Right of 0

Negative Integers

Integers to the left of 0

Linear inequality in two variables

Is an inequality that can be written in one of the forms Ax + By < C, Ax + By > C Ax + By ≤ C Ax + By ≥ C

Symbol ">"

Is greater than

Symbol "<"

Is less than

Symbol "="

Means "is equal to."

"-'

Means the opposite of

Multiplication Property of Equality

Multiplying both sides of an equation by the same non-zero does not change the solution of the equation.

Consecutive Odd Integers

Odd integers that follow each other and they differ by 2.

Perimeter of a triangle Formula

Perimeter of a triangle = side a + side b + side c P = a + b + c

Graphing

Picturing the solutions of an inequality on a number line

Irrational Numbers

Pie, Square root

Identity Properties

Property that applies to a group of numbers in the form of a set

Simple interest formula

Simple interest = principle × rate × time I = PRT

Order of Operations

Simplify expressions using the order below. If Grouping symbols such as parentheses are preset, simplify expressions within those first, starting with the innermost set. If fraction bars are present, simplify the numerator and the denominator separately. Steps 1. Evaluate exponential expressions 2. Perform multiplications or divisions in order from left to right. 3. Perform additions or subtractions in order from left to right.

Combing like terms

Simplifying the sum or difference of like terms.

Unlike Terms

Terms with different variables that don't have the same powers.

Like Terms

Terms with the same variables raised to the same powers.

Natural Numbers or Positive Integers

The Set of Natural Numbers is (1,2,3,4,5,6...)

Subtract the same number from both sides (possibly a vocab

The equality still holds true

Addition property of equality

The first property of equality that help us write simpler equivalent expressions

Intersection of Two sets

The intersection of two sets, A and B is the set of all elements common to both sets A intersect B is denoted by A n B A n B

Additive Inverses

The number needed to bring a negative number to zero. A + (-a) = 0

Exponent

The number of times the base is used as a factor

Addends

The numbers or terms added together to form the sum.

Graph

The picture used to show the solutions of inequalities

Solving

The process of finding the solution of an equation

Multiplication

The process or skill of multiplying

Commutative property of Multiplication

The product in a multiplication problem remains the same regardless of the order of the factors. A × b = b × a

Base

The repeated factor

Rational Numbers

The set of all numbers that can be expressed as a quotient of integers with denominator not zero. {a/b| a and b are integers and b " to" 0 }

Irrational Numbers

The set of irrational numbers is the set of all non-rational numbers that correspond to points on the number line.

Real Numbers

The set of real numbers is the set of all numbers that correspond to points on a number line.

Whole

The set of whole numbers is (0,1,2,3,4,5,6....)

Intersection

The solution set of a compound inequality formed by the word and.

Mathematical Statement

The statement might be true or it might be false.

Divide both sides of the equation by the same (Possibly a vocab tern)

The two sides remain equal If a, b, and c are real numbers and c ¹ 0, then A = b and ac = b c Are equivalent equations.

Union of Two sets

The union of two sets, A and B, is the set of elements that belong to either of the sets. A union B is denoted by A U B A U B

Commutative property of addition

This property states that numbers can be added together in any order without changing the resulting sum. A + b = b + A

Associative Property of Multiplication

This property states that when performing addition, how numbers are grouped will not change the resulting sum. (a × b) × c = a ×(b × c)

Evaluate an Algebraic Expression

To evaluate an algebraic expression means to finds its numerical value once we know the values of the variables.

Evaluate

To find the Value of

Distributive property of multiplication over addition

To write a product as a sum or a sum as a product. A(b + c) = ab + ac

Complementary

Two Angles that have a sum of 90 degrees

Supplementary

Two angles whose sum is 180 degrees

Compound Inequalities

Two inequalities joined by the word and or or

Compound Inequalities

Two inequality symbols in one

Adding Inverses

Two numbers that are same distance from 0 but lie on opposite sides of 0.

Opposites

Two numbers that are same distance from 0 but lie on opposite sides of 0.

opposite or additive inverse

Two numbers that are the same distance from 0 but lie on opposite sides of 0 are called opposites or additive inverses of each other.

Interval Notation

Used to write solution sets of inequalities

Volume of a rectangular formula

Volume of rectangular solid = length × width × height V = LWH

Identities for Addition

When 0 is added to any real number, the result is the same real number. In other words, the identity of the real number is not changed. A + 0 = a and 0 + a = a

Identities for Multiplication

When a real number is multiplied by 1, the result is the same real number. In other words, the identity of the real number is not changed. A × 1 = a and 1 × a = a

Associative property of Addition

When multiplying three or more numbers, the way the numbers are grouped will not change the result. (a + b) + c = a + (b + c)

Inequality Symbols

When the statement is false nor true

Solution

value or a set of values that can satisfy an equation or equations

Absolute Value Equations

|X| = a ( If a is positive, then solve X = a or X = -a, If a is 0, solve X = 0, If a is negative, the equation |X| = a has no solution.) |X| = |Y| Solve X = Y or X = - Y