AP Calculus BC is roughly equivalent to both first and second
semester college calculus courses and extends the content
learned in AB to different types of equations and introduces the
topic of sequences and series. The AP course covers topics in
differential and integral calculus, including concepts and skills of
limits, derivatives, definite integrals, the Fundamental Theorem
of Calculus, and series. The course teaches students to approach
calculus concepts and problems when they are represented
graphically, numerically, analytically, and verbally, and to make
connections amongst these representations.
Students learn how to use technology to help solve problems,
experiment, interpret results, and support conclusions.
Students who are enrolled in AP Calculus BC are expected to:
- Work with functions represented in multiple ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations.
- Understand the meaning of the derivative in terms of a rate of change and local linear approximation and use derivatives to solve problems.
- Understand the meaning of the definite integral as a limit of Riemann sums and as the net accumulation of change and use integrals to solve problems.
- Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
- Communicate mathematics and explain solutions to problems verbally and in writing.
- Model a written description of a physical situation with a function, a differential equation, or an integral.
- Use technology to solve problems, experiment, interpret results, and support conclusions.
- Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
- Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.
I. Functions, Graphs, and Limits
- Analysis of Graphs
- Limits of Functions (including one-sided limits)
- Asymptotic and Unbounded Behavior
- Continuity as a Property of Functions
- Parametric, Polar, and Vector Functions
- Concept of the Derivative
- Derivative at a Point
- Derivative as a Function
- Second Derivatives
- Applications and Computation of Derivatives
- Interpretations and Properties of Definite Integrals
- Applications of Integrals
- Fundamental Theorem of Calculus
- Techniques and Applications of Antidifferentiation
- Numerical Approximations to Definite Integrals
IV. Polynomial Approximations and Series
- Concept of Series
- Series of constants
- Taylor Series
The textbook below is required to purchase for Semester B (Jan–May):
Cracking the AP Calculus BC Exam,
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