ALGEBRA

Sets of Real Numbers

Properties of Real Numbers

Properties of Equality

Properties of Fractions

Division Properties of Zero

Real Number Line

Interval

Absolute Value

Distance between Two Points on the Number Line

Definition of Positive Integer Exponents

Definition of b⁰

Definition of b⁻ⁿ

Properties of Exponents

Definition of ⁿ√a

Properties of Radicals

General Form of a Polynomial

Factoring Polynomials

Order of Operations

Adding and Subtracting Polynomials

Multiplying Polynomials

Dividing Polynomials

Rational Expressions

Complex Fractions

Definition of a Complex Number

Definition of a Linear Equation

Addition and Multiplication Properties of Equality

Systems of Linear Equations

Determinants

Quadratic Equations

Properties of Inequalities

Arithmetic Sequence

Arithmetic Series

Geometric Sequences

Geometric Series

Binomial Theorem

The Cartesian Coordinate System

Linear Functions

Forms of Linear Equations

Quadratic Functions

Basic Operation of Functions

Exponential Functions

Natural Exponential Function

Logarithmic Functions

GEOMETRY

Definition of an Angle

Unit Measurement of Angles

Types of Angles

Thales’ Theorem

Oblique Triangle

Geocenter of a Triangle

Orthocenter

Similarity of Triangles

The Law of Cosines

The Law of Sines

Right Triangle

Ratio of the Sides of a Right Triangle

Pythagorean Theorem

Equilateral Triangles

Isosceles Triangle

Square

Rectangle

Parallelogram

Rhombus

Trapezoid

Kite

Regular Polygons

Circle

Sector of a Circle

Segment of a Circle

Annulus (Circular Ring)

Ellipse

Cube

Cuboid

Right Prism

Pyramid

Frustum of Pyramid

Cone

Frustum of Cone

Cylinder

Hollow Cylinder

Sliced Cylinder

Sphere

Spherical Cap

Sector of a Sphere

Zone of a Sphere

Torus

Ellipsoid

Barrel

TRIGONOMETRY

Circular and Angular Measures

Trigonometric Circle

Basic Formulas

Trigonometric Ratios for Right Angled Triangles

Sum and Difference of Functions of Angles

Sum and Difference of Angles

Double Angle Formulas

Half Angle Formulas

Functions of Important Angles

Solving Trigonometric Equations

Verifying Trigonometric Identities

Graphs of the Sine and Cosine Functions

Graphs of the Tangent and Cotangent Functions

ANALYTICAL GEOMETRY

Distance between Two Points

Point of Division

Inclination and Slope of a Line

Parallel and Perpendicular Lines

Angle between Two Intersection Lines

Triangle

Equations for a Straight Line

Distance from a Line to a Point

Circles

Ellipses

Parabolas

Hyperbolas

Polar Coordinates

Cartesian Coordinates

Distance between Two Points

Angle between Two Lines

Every Plane

Line Perpendicular to Plane

Parallel and Perpendicular Planes

Distance of a Point from a Plane

Normal Form

Intercept Form

Angle Between Two Planes

The Straight Line in Space

Equations of a Line

Relative Directions of a Line and Plane

The Sphere

The Ellipsoid

Hyperboloid

Elliptic Paraboloid

Hyperbolic Paraboloid

Cylindrical Surface

MATHEMATICS OF FINANCE

Simple Interest

Compound Interest

Annuities

Amortization of Loans

Sinking Fund Payment

CALCULUS

Limits

Rule for Limits

Slope of Tangent Line

Definition of the Derivative

Basic Derivatives

Increasing and Decreasing Function y=f(x)

Maximum and Minimum Function y=f(x)

Solving Applied Problems

Integration

Basic Integration Rules

Integration by Substitution

Basic Integrals

Arc Length

Finding an Area and a Volume

Finding the Area between Two Curves

STATISTICS

Definition of Set and Notation

Terms and Symbols

Venn Diagrams

Operations on Sets

De Morgan’s Laws

Counting the Elements in a Set

Permutations

Combinations

Probability Terminology

Basic Probability Principles

Random Variable

Mean Value or Expected Value

Variance

Standard Deviation

Normal Distribution

Binomial Distribution

Poisson Distribution

Exponential Distribution

General Reliability Definitions

Exponential Distribution Used as Reliability Function

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