Algebra II

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Algebra II release 25.63

FULL VERSION
CONTENTS

Rectangular Coordinate System
- Rectangular Coordinates of a Point
- The Distance Formula
- Circles
- The Midpoint Formula
Functions and Graphs
- Basic Definitions and Notations
- Graphs of Functions
- Composite Functions
- Inverse Functions
- Graphic Solution of Equations
- Graphic Solution of Inequalities
Linear Equations and Inequalities in One Variable
- Solving Linear Equations
- Solving Linear Inequalities
- Solving Equations Involving Absolute Values
- Solving Inequalities Involving Absolute Values
Systems of Linear Equations and Inequalities
- Systems of Two Linear Equations in Two Variables
  - Basic Concepts
  - Solutions Using Graphing
  - Solutions Using Substitution
  - Solutions Using Elimination
- Determinants and Cramer's Rule
  - Determinants of Order 2
  - Determinants of Order 3
    - Definition and Properties of Determinants
    - Minors and Cofactors
    - The Expansion Theorem
  - Systems of Two Linear Equations in Two Unknowns. Cramer's Rule
  - Systems of Three Linear Equations in Three Unknowns. Cramer's Rule
- Linear Inequalities in Two Variables
- Systems of Linear Inequalities in Two Variables
Operations with Polynomials
- Addition of Polynomials
- Subtraction of Polynomials
- Multiplication of Polynomials
- Division of Polynomials
Factoring Polynomials
- Greatest Common Factor
- Difference of Squares
- Sum or Difference of Cubes
- Factoring trinomials with a=1
- Trinomials of the Form ax2 + bx + c
- Square Trinomials
- Solving Equations by Factoring
Roots of Polynomial Equations
- The Remainder Theorem
- The Factor Theorem
- Descartes' Rule of Signs
- Rational Zeros
Rational Expressions
- Simplifying Rational Expressions
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Finding the Least Common Denominator
- Adding and Subtracting Rational Expressions
  - Rational Expressions with the Same Denominators
  - Rational Expressions with Different Denominators
- Graphing Rational Functions
  - Vertical Asymptotes for the Graph of Rational Functions
  - Horizontal Asymptotes for the Graph of Rational Functions
  - Oblique Asymptotes for the Graph of Rational Functions
- Solving Rational Equations
Exponents and Radicals
- Square Roots
  - Basic Definitions
  - Approximate Square Roots
  - Equations Involving Radicals
- nth Roots
- Fractional Exponents
Complex Numbers
- Basic Definitions and Graphical Representation of Complex Numbers
- Operations with Complex Numbers
  - Conjugate Complex Numbers
  - Addition
  - Subtraction
  - Multiplication
  - Division
Quadratic Functions
- Completing the Square
- Factoring Trinomials by Completing the Square
- Graphs of Quadratic Functions
- Maximum and Minimum Problems
- Solving Quadratic Equations
  - Solving Quadratic Equations by Completing the Square
  - Solving Quadratic Equations by General Formula
  - The Sum and the Product of the Roots
  - Complex Roots of a Quadratic Equation
- Graphic Solution of Quadratic Inequalities
Conic Sections
- The Parabola
- The Ellipse
- The Hyperbola
Exponential and Logarithmic Functions
- Graphs of Functions
  - Exponential Function
  - Logarithmic Function
  - Exponential and Logarithmic Functions
- Properties of Logarithms
- Solving Exponential and Logarithmic Equations
  - Solving Exponential Equations
  - Solving Logarithmic Equations
- Applications
  - Compound Interest
  - Exponential Growth or Decay
Sequences and Series
- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Infinite Geometric Series
Miscellaneous
- Binomial Theorem
  - Factorial Notation
  - Binomial Expansions
  - Pascal's Triangle
- Counting Principles
  - Permutations
    - Permutations of n Elements
    - Permutations of n Elements Taken r at a Time
    - Distinguishable Permutations
  - Combinations
  - Fundamental Counting Principles