AP Calculus AB / BC
Comprehensive Preparation Program
Course Overview
This course is designed to provide students with a strong conceptual and analytical foundation in calculus, preparing them thoroughly for the AP Calculus AB and AP Calculus BC examinations conducted by the College Board.
The program emphasizes deep conceptual understanding, rigorous problem-solving, and exam-oriented practice, enabling students to confidently handle both multiple-choice and free-response questions (FRQ) at the AP level. The course integrates theoretical explanations, graphical analysis, algebraic techniques, and real-world applications of calculus.
Course Structure:
AP Calculus AB Curriculum
1. Limits and Continuity
Understanding the concept of limits
Evaluating limits graphically, numerically, and analytically
Limit laws
One-sided limits
Infinite limits and limits at infinity
Continuity and types of discontinuities
Intermediate Value Theorem
2. Differentiation: Definition and Basic Rules
Definition of the derivative as a limit
Derivative as rate of change
Tangent line interpretation
Basic differentiation rules
Power rule
Product rule
Quotient rule
Chain rule
3. Derivatives of Transcendental Functions
Exponential functions
Logarithmic functions
Trigonometric functions
Inverse trigonometric functions
4. Applications of Derivatives
Increasing and decreasing functions
Local and absolute extrema
First derivative test
Second derivative test
Concavity and inflection points
Curve sketching
Optimization problems
Related rates
Linear approximation and differentials
5. Integration and Antiderivatives
Indefinite integrals
Basic integration rules
Integration of elementary functions
Initial value problems
6. Definite Integrals and the Fundamental
Theorem of Calculus
Riemann sums
Definite integrals
Properties of definite integrals
Fundamental Theorem of Calculus (Part 1 and 2)
7. Applications of Integration
Area between curves
Average value of a function
Accumulation functions
Motion along a line (position, velocity, acceleration)
AP Calculus BC Curriculum (Includes all AB topics + additional advanced topics)
1. Advanced Integration Techniques
Integration by parts
Integration using partial fractions
Improper integrals
2. Differential Equations
Slope fields
Solving separable differential equations
Exponential growth and decay models
Logistic models
3. Parametric, Polar, and Vector Functions
Parametric equations
Derivatives of parametric functions
Polar coordinates
Area in polar coordinates
Vector-valued functions
Motion in the plane
4. Infinite Sequences and Series
Sequences
Convergence and divergence
Geometric series
Power series
Taylor series
Maclaurin series
Radius and interval of convergence
Teaching Methodology
The course uses a concept-first approach combined with rigorous problem-solving:
Conceptual explanation of each topic
Visual understanding through graphs
Step-by-step analytical derivations
AP-style exam problem solving
Weekly problem sets
Timed mock tests
Free Response Question (FRQ) practice
Course Features
Complete coverage of AP Calculus AB / BC syllabus
Extensive AP-style problem solving
Exam strategies and time management training
Regular mock tests and performance analysis
Detailed solution discussions
Personalized feedback
Assessment and Practice
Students will regularly practice:
AP-style Multiple Choice Questions
Free Response Questions (FRQ)
Conceptual reasoning problems
Graphical interpretation questions
Application-based calculus problems
Ideal For
This course is recommended for students who:
Plan to take AP Calculus AB or BC
Want strong preparation for university-level mathematics
Are interested in STEM, engineering, economics, or data science
Outcome
By the end of the course, students will:
Develop a strong conceptual mastery of calculus
Solve complex problems with confidence
Be fully prepared for the AP Calculus AB / BC exam
Build a solid mathematical foundation for future STEM studies
