The topics covered in AP Calculus are divided into two courses: AP Calculus AB and AP Calculus BC. Both courses are designed to cover a full-year college calculus curriculum and are intended for high school students.
AP Calculus AB:
Limits and Continuity
Differentiation: Definition and Basic Rules
Differentiation: Advanced Rules (Implicit Differentiation, Related Rates)
Applications of Derivatives (including Optimization and Related Rates)
Integrals: Definition and Basic Rules
Applications of Integrals (including Area Between Curves and Accumulation)
Fundamental Theorem of Calculus
Techniques of Antidifferentiation
Applications of Integration (including Motion Problems)
Differential Equations
Mathematical Modeling
Sequences and Series
AP Calculus BC:
AP Calculus BC includes all the topics covered in AP Calculus AB, plus the following additional topics:
Parametric Equations and Polar Coordinates
Vectors and Vector-Valued Functions
Infinite Sequences and Series (including Taylor and Maclaurin Series)
AP Calculus BC is generally considered more challenging and covers a broader range of topics compared to AP Calculus AB. Students who take AP Calculus BC and score well on the exam may receive credit for two semesters of college-level calculus.
It's important to note that the specific content and emphasis on certain topics may vary between different schools and teachers. Additionally, the curriculum may be updated, so it's advisable to consult the latest information from the College Board or the educational institution offering the course.