Online AP Calculus-BC Preparation and training

Topics may include:
‍1. How limits help us to handle change at an instant
2. Definition and properties of limits in various representations
3. Definitions of continuity of a function at a point and over a domain
4. Asymptotes and limits at infinity
5. Reasoning using the Squeeze theorem and the Intermediate Value Theorem
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Topics may include:
‍1. Defining the derivative of a function at a point and as a function
2. Connecting differentiability and continuity
3. Determining derivatives for elementary functions
4. Applying differentiation rules

Topics may include:
1. The chain rule for differentiating composite functions
2. Implicit differentiation
3. Differentiation of general and particular inverse functions
4. Determining higher-order derivatives of functions

Topics may include:
1. Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change
2. Applying understandings of differentiation to problems involving motion
3. Generalizing understandings of motion problems to other situations involving rates of change
4. Solving related rates problems
5. Local linearity and approximation
6. L’Hospital’s rule

Topics may include:
1. Mean Value Theorem and Extreme Value Theorem
2. Derivatives and properties of functions
3. How to use the first derivative test, second derivative test, and candidates test
4. Sketching graphs of functions and their derivatives
5. How to solve optimization problems
6. Behaviors of Implicit relations

Topics may include:
1. Using definite integrals to determine accumulated change over an interval
2. Approximating integrals using Riemann Sums
3. Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
4. Antiderivatives and indefinite integrals
5. Properties of integrals and integration techniques

Topics may include:
1. Interpreting verbal descriptions of change as separable differential equations
2. Sketching slope fields and families of solution curves
3. Solving separable differential equations to find general and particular solutions
4. Deriving and applying a model for exponential growth and decay

Topics may include:
1. Determining the average value of a function using definite integrals
2. Modeling particle motion
3. Solving accumulation problems
4. Finding the area between curves
5. Determining volume with cross-sections, the disc method, and the washer method

Topics may include:
1. Finding derivatives of parametric functions and vector-valued functions
2. Calculating the accumulation of change in length over an interval using a definite integral
3. Determining the position of a particle moving in a plane
4. Calculating velocity, speed, and acceleration of a particle moving along a curve
5. Finding derivatives of functions written in polar coordinates
6. Finding the area of regions bounded by polar curves

Topics may include:
1. Applying limits to understand the convergence of infinite series
2. Types of series: Geometric, harmonic, and p-seriesA test for divergence and several tests for convergence
3. Approximating sums of convergent infinite series and associated error bounds
4. Determining the radius and interval of convergence for a series
5. Representing a function as a Taylor series or a Maclaurin series on an appropriate interval