AP Calculus AB – Syllabus (USA)
AP Calculus AB is a first-year college-level calculus course that focuses on limits,
derivatives, integrals, and the Fundamental Theorem of Calculus. The course emphasizes
conceptual understanding, problem-solving skills, and real-world applications.
Course Prerequisites
- Strong understanding of Algebra I and Algebra II
- Knowledge of functions and graphs
- Basic trigonometry
Unit 1: Limits and Continuity
- Introduction to limits
- Estimating limits graphically and numerically
- Limits using algebraic techniques
- One-sided limits and limits at infinity
- Continuity and discontinuity
- Intermediate Value Theorem
Unit 2: Differentiation – Definition and Basic Rules
- Definition of derivative
- Derivative as a rate of change
- Derivative from first principles
- Power rule
- Derivatives of polynomials and constants
Unit 3: Differentiation – Composite, Implicit, and Inverse Functions
- Product rule and quotient rule
- Chain rule
- Implicit differentiation
- Derivatives of inverse functions
- Derivatives of exponential and logarithmic functions
- Derivatives of trigonometric functions
Unit 4: Applications of Differentiation
- Motion: velocity and acceleration
- Related rates
- Linear approximation and differentials
- Mean Value Theorem
- Critical points and extrema
- Optimization problems
- Curve sketching
Unit 5: Integration and Accumulation of Change
- Antiderivatives
- Indefinite integrals
- Definite integrals
- Area under a curve
- Riemann sums
- Properties of integrals
Unit 6: Applications of Integration
- Fundamental Theorem of Calculus (Parts 1 and 2)
- Net change and accumulation functions
- Average value of a function
- Motion problems using integrals
- Area between curves
Unit 7: Techniques of Integration
- Substitution method (u-substitution)
- Integrating exponential and trigonometric functions
- Integration using algebraic manipulation
Graphical, Numerical, and Analytical Analysis
- Interpreting graphs of functions and derivatives
- Connecting graphical, numerical, and algebraic representations
- Use of technology for visualization and problem solving
Assessments
- Unit quizzes and chapter tests
- Cumulative practice tests
- Monthly grand assessments
- AP-style multiple-choice and free-response questions
Learning Outcomes
- Understand limits, derivatives, and integrals conceptually
- Apply calculus to real-world problems
- Analyze functions using multiple representations
- Prepare effectively for the AP Calculus AB exam