College Algebra Complete Crash Course Packet

Master College Algebra with Confidence—From the Basics to Advanced Applications!

Are you struggling with algebra concepts or looking for a powerful review before exams? This College Algebra Crash Course Packet is your all-in-one solution—perfect for high schoolers, college students, homeschool learners, or adult learners preparing for placement exams.

Whether you're learning from scratch or refreshing your skills, this packet will guide you through every essential topic—step by step—with clear notes, worked examples, practice problems, and cheat sheets.

🧠 What’s Inside: 12 Core Units + Supplemental Materials

1. Foundations of Algebra

• Real number system explained
• Mastering PEMDAS (order of operations)
• Properties of equality
• How to evaluate algebraic expressions
• Simplifying and factoring basics

2. Linear Equations and Inequalities

• Solving single-variable linear equations
• Inequalities & compound inequalities
• Absolute value equations and inequalities
• Application-based word problems

3. Graphs and Functions

• Cartesian plane & plotting points
• Graphs of linear and nonlinear equations
• Introduction to functions
• Domain, range, and function notation

4. Linear Functions

• Understanding slope and rate of change
• Graphing linear functions step-by-step
• Writing equations: point-slope, slope-intercept, standard form
• Parallel & perpendicular lines
• Applications in real-world modeling

5. Systems of Equations and Inequalities

• Solving systems: graphing, substitution, elimination
• Modeling with systems of equations
• Graphing and analyzing systems of inequalities

6. Polynomials and Polynomial Functions

• Operations: addition, subtraction, multiplication
• Special products (difference of squares, perfect squares/cubes)
• Factoring techniques (GCF, trinomials, grouping)
• Solving polynomial equations

7. Rational Expressions and Functions

• Simplifying and factoring rational expressions
• Multiplying, dividing, adding, and subtracting rational expressions
• Solving rational equations
• Application problems and modeling

8. Radicals and Rational Exponents

• Simplifying square roots and higher-order radicals
• Performing operations with radicals
• Understanding and applying rational exponents
• Solving radical equations

9. Quadratic Equations and Functions

• Solving quadratics: factoring, completing the square, quadratic formula
• Graphing: vertex and standard forms
• Discriminant and root types
• Real-world applications (projectile motion, area problems)

10. Exponential and Logarithmic Functions

• Exponential growth and decay models
• Laws of exponents
• Introduction to logarithms and their properties
• Solving exponential/logarithmic equations
• Applications in science and finance

11. Conic Sections (Optional Bonus Unit)

• Identifying and graphing: circles, ellipses, hyperbolas, and parabolas
• Recognizing standard forms and relationships

12. Sequences, Series, and Binomial Theorem (Optional Bonus)

• Arithmetic & geometric sequences
• Using sigma notation
• Binomial expansion using Pascal’s Triangle