Algebra 1

Course Overview

• Introduction to Algebra: Importance and Applications in Real Life
  

• Developing Problem-Solving and Critical Thinking Skills
  

• Building Mathematical Foundations for Advanced Courses
  

• Understanding Functions, Linear Equations, and Graphing

Basic Operations & Properties

• The Real Number System: Integers, Fractions, Decimals, and Rational Numbers
  

• Properties of Numbers: Commutative, Associative, Distributive Laws
  

• Order of Operations (PEMDAS)
  

• Evaluating Algebraic Expressions
  

• Simplifying Expressions Using Like Terms
  

• Introduction to Variables and Constants

Linear Equations & Inequalities

• Solving One-Step and Multi-Step Linear Equations
  

• Solving and Graphing Linear Inequalities
  

• Understanding the Solution Set and Interval Notation
  

• Solving Word Problems Involving Linear Equations
  

• Applications of Linear Equations: Distance, Rate, and Time Problems
  

• Systems of Linear Equations: Substitution and Elimination Methods

Functions & Graphing

• Introduction to Functions: Definition, Domain, and Range
  

• Graphing Linear Functions: Slope-Intercept Form, Point-Slope Form
  

• Identifying and Interpreting Slope and Y-Intercept
  

• Transformations of Functions: Shifting, Stretching, and Reflecting
  

• Graphing and Solving Absolute Value Equations
  

• Solving and Graphing Piecewise Functions

Polynomials

• Introduction to Polynomials: Terms, Degree, and Leading Coefficient
  

• Operations with Polynomials: Addition, Subtraction, Multiplication
  

• Factoring Polynomials: GCF, Difference of Squares, Trinomial Factoring
  

• Solving Polynomial Equations by Factoring
  

• The Zero Product Property and Its Applications
  

• Long Division and Synthetic Division of Polynomials

Rational Expressions & Equations

• Simplifying Rational Expressions
  

• Multiplying and Dividing Rational Expressions
  

• Solving Rational Equations
  

• Identifying and Avoiding Restrictions in Rational Expressions
  

• Applications of Rational Equations: Work, Speed, and Distance Problems

Radicals & Exponents

• Exponent Rules and Properties
  

• Simplifying Radical Expressions: Square Roots, Cube Roots
  

• Operations with Radicals: Addition, Subtraction, Multiplication, Division
  

• Solving Equations Involving Square Roots and Higher Powers
  

• The Pythagorean Theorem and Its Applications
  

Quadratic Equations

• Solving Quadratic Equations by Factoring
  

• Solving Quadratic Equations by Completing the Square
  

• The Quadratic Formula: Derivation and Application
  

• Graphing Quadratic Functions: Parabolas and Vertex Form
  

• Real-World Applications of Quadratic Equations
  

Statistics & Probability

• Mean, Median, Mode, and Range
  

• Introduction to Probability: Counting Principles, Events, Outcomes
  

• Using Probability in Real-World Applications: Games, Predictions
  

Assessment & Practice

• Regular Quizzes, Midterm, and Final Exam
  

• Problem Solving and Word Problem Applications
  

• Homework and Practice Worksheets
  

• Group Activities and Collaborative Problem Solving
  

Preparation for Algebra II

• Reviewing Key Concepts: Solving Systems, Graphing, Factoring

• Introducing More Complex Functions and Equations for Algebra II