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