Precalculus Complete Bootcamp: Your Path to Calculus Success

Comprehensive, step-by-step lessons for mastering functions, trigonometry, and more for calculus readiness.

What you'll learn
Understand and Analyze Functions – Evaluate, graph, and manipulate linear, quadratic, polynomial, rational, exponential, and trigonometric functions.
Master Function Transformations and Inverses – Apply shifts, reflections, stretches, and compressions, and learn how to find and verify inverse functions.
Work with Complex Numbers – Perform operations with complex numbers, graph them on the complex plane, and solve equations with imaginary components.
Solve Quadratic and Polynomial Equations – Factor, use the quadratic formula, complete the square, and apply the Rational Root Theorem to solve equations.
Graph and Analyze Rational and Exponential Functions – Identify asymptotes, intercepts, and transformations while solving exponential growth and decay problems.
Develop a Strong Foundation in Logarithms – Convert between logarithmic and exponential forms, apply logarithm properties, and solve logarithmic equations.
Master Trigonometry – Learn trigonometric identities, graph trigonometric functions, solve equations, and apply trigonometry to real-world problems.
Understand and Solve Systems of Equations – Use algebraic methods, graphing, and matrices to solve systems of linear and nonlinear equations.
Work with Vectors and Their Applications – Learn vector addition, scalar multiplication, dot and cross products, and applications in geometry and physics.
Perform Matrix Operations and Applications – Master matrix addition, multiplication, inverses, determinants, and solve systems using Cramer’s Rule.
Explore Conic Sections – Analyze circles, ellipses, hyperbolas, and parabolas by understanding their equations and graphical representations.
Understand Sequences and Series – Work with arithmetic and geometric sequences, summations, and the Fibonacci sequence, with real-world applications.
Tackle Probability, Combinations, and Permutations – Learn counting principles, probability rules, and combinatorial techniques for real-world applications.

Requirements
Pen, Paper, and a Positive Attitude – Taking notes and practicing problems regularly will help reinforce learning and improve retention.
Curiosity and Willingness to Learn – No advanced math background is needed, just a desire to improve problem-solving skills and build a strong foundation for calculus.
A Scientific or Graphing Calculator (Optional) – While not required, a calculator can be helpful for solving problems involving exponents, logarithms, and trigonometry.

Description
Are you aiming to strengthen your mathematics foundation, prepare for advanced courses, or simply master the essential concepts of Precalculus in a clear and structured way? This Precalculus course has been meticulously designed to guide you through every major topic that forms the core of higher-level mathematics. Whether you’re a high school student gearing up for college-level math or an adult learner refreshing your skills, our step-by-step video lessons, interactive examples, and practical exercises will empower you to approach complex problems with confidence.Why Enroll in This Course?Comprehensive CoverageFrom Functions (Chapter 1) to more advanced topics like Vectors (Chapter 8), Matrices (Chapter 10), and Conic Sections (Chapter 11), this course leaves no stone unturned. You’ll gain a solid grounding in fundamental concepts such as polynomials, quadratic equations, rational functions, and trigonometry, right through to specialized areas like parametric equations, sequences and series, and basic statistics.Clear, Step-by-Step InstructionEach lesson is purposefully sequenced to build upon previously learned material, ensuring a gradual and logical progression. Complex ideas—such as factoring polynomials, solving exponential and logarithmic equations, or applying transformations to graphs—are broken down into digestible steps, supported by intuitive explanations and guided practice.Real-World ApplicationsMathematics is more than theoretical exercises. Our lessons highlight how Precalculus concepts apply to engineering, physics, finance, biology, and beyond. Through word problems and practical examples, you’ll see exactly how these techniques translate to the world around you.Interactive Learning ExperienceEngage with quizzes, practice sets, and detailed walkthroughs. Topics like systems of nonlinear equations, probability, and matrices come to life with examples that push you to think critically and reinforce your learning at every step.Flexible, On-Demand FormatYour learning journey is entirely self-paced. Access lessons anytime, anywhere, and revisit challenging topics as often as you need. Coupled with lifetime course access, you’ll never feel pressured to learn at someone else’s pace.What You Will Learn:Chapter 1: FunctionsIdentify, evaluate, and manipulate a wide variety of functions. Learn the intricacies of domain, range, piecewise definitions, inverses, and function transformations—all core skills for higher-level mathematics.Chapter 2: Complex NumbersTransform your understanding of the real number system by exploring the imaginary unit i, complex plane graphing, absolute values, and operations with complex numbers—paving the way to solve more advanced equations.Chapter 3: Quadratic FunctionsMaster techniques for solving and graphing quadratics, from factoring and completing the square to applying the quadratic formula. Explore vertex form transformations, parabola properties, and real-world applications involving maxima and minima.Chapter 4: Polynomial FunctionsDelve deeper into polynomial behaviors, from basic classification to advanced factoring, the Remainder and Factor Theorems, and graphing high-degree functions. Perfect your ability to find real and complex roots using synthetic division and the Rational Zero Theorem.Chapter 5: Rational FunctionsLearn to identify asymptotes, intercepts, and discontinuities. Gain confidence in graphing complex rational functions and solving rational inequalities often encountered in calculus and beyond.Chapter 6: LogarithmsDemystify logarithms and exponentials with properties, conversions, and real-life applications. From compound interest to population growth, you’ll be ready to tackle a range of practical exponential/logarithmic problems.Chapter 7: TrigonometryGain a foundational understanding (or refresh your skills) in trigonometric ratios, identities, graphing, and applications—vital for careers in engineering, physics, and other STEM fields.Chapter 8: VectorsExplore vector operations, projections, and geometrical interpretations (dot and cross products, angles between vectors), essential tools for physics, computer graphics, and 3D modeling.Chapter 9: Systems of EquationsGo from linear to nonlinear systems, discovering solutions graphically, algebraically, and via matrix methods. Develop problem-solving versatility for real-life, multi-variable challenges.Chapter 10: MatricesStreamline solving complex systems through matrix operations, determinants, and inverses. You’ll learn Gaussian elimination, Gauss-Jordan elimination, and Cramer’s Rule.Chapter 11: Conic SectionsUnderstand the geometry and equations of circles, ellipses, parabolas, and hyperbolas—key shapes in physics, astronomy, and architecture.Chapter 12: Sequences and SeriesFrom arithmetic to geometric progressions and beyond, learn how sequences underpin calculations in finance, computer science, and statistical modeling.Chapter 13: Other TopicsDiscover the power of factorials, permutations, combinations, the Binomial Theorem, basic probability, and an introduction to statistics—rounding out a complete Precalculus toolkit.Who Should Take This Course?High school students preparing for AP Calculus or university-level mathCollege students seeking a thorough review of PrecalculusAdult learners refreshing their math skills for professional or personal developmentSTEM enthusiasts eager to solidify a robust math foundationEmbark on this Precalculus journey and gain the knowledge, confidence, and problem-solving strategies you need to excel in advanced mathematics and beyond. Enroll now and start building your future success!

Who this course is for
High School Students Preparing for Calculus – Ideal for students who want a solid Precalculus foundation before advancing to Calculus.
College Students Needing a Math Refresher – Great for those in college-level math or science courses requiring strong Precalculus skills.
STEM Students and Professionals – Beneficial for engineering, physics, computer science, and finance students who rely on mathematical reasoning.
Test Prep Students – Perfect for those preparing for standardized tests like the SAT, ACT, GRE, or other math-based entrance exams.
Self-Learners and Enthusiasts – Designed for anyone who enjoys learning math, wants to strengthen problem-solving skills, or needs a structured review.
Adults Returning to Math After a Break – Ideal for learners who want to refresh their math skills for career advancement, personal development, or further studies.