AP Calculus AB – Part 1: Limits, Continuity & Foundations of Differentiation
📚 Course Overview
Part 1 establishes the critical foundation for all calculus concepts through Gyan Academy's enterprise-grade Learning Management System. This comprehensive module masterfully covers Limits, Continuity, and the Definition of the Derivative—the essential building blocks for success in Parts 2 & 3 and ultimately achieving a score of 5 on the AP Calculus AB exam.
Our concept-driven curriculum, aligned with the College Board's AP framework, emphasizes deep understanding over rote memorization. Through our intelligent LMS platform, you'll experience personalized learning paths, real-time progress tracking, interactive assessments, and 24/7 access to expert faculty support—just like students at leading universities worldwide.
Concept Mastery
Deep understanding of limits, continuity, and derivative fundamentals
Problem-Solving
Analytical reasoning skills for complex calculus applications
LMS Analytics
Track your progress with real-time performance dashboards
Exam Readiness
Strategic preparation for AP Calculus AB MCQs and FRQs
✨ Learning Outcomes
Master graphical, numerical, and algebraic methods for evaluating limits, including one-sided limits and limits at infinity
Apply the three-part definition of continuity and use the Intermediate Value Theorem to solve complex problems
Fluently apply Power, Product, Quotient, and Chain rules to polynomial, rational, and composite functions
Differentiate all six trigonometric functions and their compositions with confidence
Solve problems involving implicitly defined functions and related rates scenarios
Develop MCQ speed and FRQ communication skills aligned with College Board rubrics
🚀 Gyan Academy LMS Features
Experience enterprise-level learning technology with these powerful features:
📊 Progress Dashboard
Track lesson completion, quiz scores, and overall course progress in real-time with visual analytics
🎮 Interactive Quizzes
6 module quizzes with instant feedback, detailed explanations, and performance analytics
📱 Multi-Device Access
Learn anywhere, anytime on desktop, tablet, or mobile—sync across all devices automatically
💬 24/7 Doubt Support
Priority messaging to expert faculty with guaranteed 24-hour response time
📝 Smart Notes
Downloadable PDFs, formula sheets, and derivative rule flowcharts for offline study
🏅 Certificates
Earn trackable completion certificates to showcase on college applications
📅 Course Curriculum
Module 1: Limits & Continuity (Lectures 1-8)
Introduction to limits, limit notation, estimating limits from graphs and tables, limit properties, algebraic manipulation, one-sided limits, continuity at a point, Intermediate Value Theorem
Module 2: Definition of Derivative (Lectures 9-14)
Derivative as limit of difference quotient, derivative notation, tangent lines and rates of change, differentiability vs continuity, power rule introduction
Module 3: Basic Derivative Rules (Lectures 15-21)
Power rule mastery, sum and difference rules, constant multiple rule, derivatives of polynomials, derivatives of rational functions using quotient rule
Module 4: Product & Chain Rules (Lectures 22-26)
Product rule for derivatives, chain rule for composite functions, combining product and chain rules, derivatives of exponential functions
Module 5: Trigonometric & Implicit (Lectures 27-30)
Derivatives of sin x, cos x, tan x, cot x, sec x, csc x, implicit differentiation techniques, related rates introduction
🎁 What's Included in Your LMS Access
- 🎥 30 HD Video Lectures (50 Minutes Each) with professional on-screen annotations, dynamic graphing demonstrations, and step-by-step problem solving
- 📄 Comprehensive Lecture Notes PDF including limit evaluation flowcharts, continuity checklists, derivative rule summaries, and formula reference sheets
- ✏️ Practice Problem Bank (100+ problems with detailed step-by-step solutions organized by difficulty level—Basic, Intermediate, Advanced, AP Exam)
- 📊 Module Quizzes (6 quizzes with instant LMS feedback, performance analytics, and personalized recommendations for improvement)
- 📝 Mini Mock Exam (15 MCQs + 2 FRQs with College Board rubric-based scoring and detailed answer explanations)
- 🧮 Formula Sheet & Derivative Rules Flowchart for quick reference during practice and exam preparation
- 💬 Priority Doubt Support via LMS messaging system with guaranteed response within 24 hours from expert faculty
- 🏆 Certificate of Completion (trackable and verifiable for college applications and portfolios)
- 🎁 BONUS: AP Calculus AB Calculator Guide (TI-84 Plus CE and TI-Nspire CX scripts for limit and derivative calculations)
- 🔄 Lifetime Access to course updates and new content additions within the LMS platform
🎓 Who Should Enroll?
- High school students preparing for AP Calculus AB exam (Grade 11-12)
- Students who have completed Precalculus or equivalent mathematics course
- Learners seeking deep conceptual understanding over memorization
- Self-motivated students who value flexible, self-paced learning
- Students aiming for college credit and advanced placement
- Anyone wanting to build strong calculus foundations for STEM careers
Join thousands of successful students on Gyan Academy's enterprise-grade learning platform