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 and 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 and 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 and 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 and 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 and 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 and Probability

  • Mean, Median, Mode, and Range

  • Introduction to Probability: Counting Principles, Events, Outcomes

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

Assessment and 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