2023年AP微积分BC考试大纲 AP Calculus BC发表时间：20220822 23:56 Course Content Unit 1: Limits and Continuity Unit 2: Differentiation: Definition and Fundamental Properties Unit 3: Differentiation: Composite, Implicit, and Inverse Functions Unit 4: Contextual Applications of Differentiation Unit 5: Analytical Applications of Differentiation Unit 6: Integration and Accumulation of Change Unit 7: Differential Equations Unit 8: Applications of Integration Unit 9: Parametric Equations, Polar Coordinates, and VectorValued Functions Unit 10: Infinite Sequences and Series AP Calculus BC Exam Date Mon, May 9, 2022, 8 AM Local Unit 1: Limits and Continuity You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions. Topics may include: How limits help us to handle change at an instant Definition and properties of limits in various representations Definitions of continuity of a function at a point and over a domain Asymptotes and limits at infinity Reasoning using the Squeeze theorem and the Intermediate Value Theorem On The Exam 4%–7% of exam score Unit 2: Differentiation: Definition and Fundamental Properties You’ll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills. Topics may include: Defining the derivative of a function at a point and as a function Connecting differentiability and continuity Determining derivatives for elementary functions Applying differentiation rules On The Exam 4%–7% of exam score Unit 3: Differentiation: Composite, Implicit, and Inverse Functions You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higherorder derivatives. Topics may include: The chain rule for differentiating composite functions Implicit differentiation Differentiation of general and particular inverse functions Determining higherorder derivatives of functions On The Exam 4%–7% of exam score Unit 4: Contextual Applications of Differentiation You’ll apply derivatives to set up and solve realworld problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms. Topics may include: Identifying relevant mathematical information in verbal representations of realworld problems involving rates of change Applying understandings of differentiation to problems involving motion Generalizing understandings of motion problems to other situations involving rates of change Solving related rates problems Local linearity and approximation L’Hospital’s rule On The Exam 6%–9% of exam score Unit 5: Analytical Applications of Differentiation After exploring relationships among the graphs of a function and its derivatives, you'll learn to apply calculus to solve optimization problems. Topics may include: Mean Value Theorem and Extreme Value Theorem Derivatives and properties of functions How to use the first derivative test, second derivative test, and candidates test Sketching graphs of functions and their derivatives How to solve optimization problems Behaviors of Implicit relations On The Exam 8%–11% of exam score Unit 6: Integration and Accumulation of Change You’ll learn to apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. You’ll apply properties of integrals and practice useful integration techniques. Topics may include: Using definite integrals to determine accumulated change over an interval Approximating integrals with Riemann Sums Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals Antiderivatives and indefinite integrals Properties of integrals and integration techniques, extended Determining improper integrals on The Exam 17%–20% of exam score Unit 7: Differential Equations You’ll learn how to solve certain differential equations and apply that knowledge to deepen your understanding of exponential growth and decay and logistic models. Topics may include: Interpreting verbal descriptions of change as separable differential equations Sketching slope fields and families of solution curves Using Euler’s method to approximate values on a particular solution curve Solving separable differential equations to find general and particular solutions Deriving and applying exponential and logistic models On The Exam 6%–9% of exam score Unit 8: Applications of Integration You’ll make mathematical connections that will allow you to solve a wide range of problems involving net change over an interval of time and to find lengths of curves, areas of regions, or volumes of solids defined using functions. Topics may include: Determining the average value of a function using definite integrals Modeling particle motion Solving accumulation problems Finding the area between curves Determining volume with crosssections, the disc method, and the washer method Determining the length of a planar curve using a definite integral on The Exam 6%–9% of exam score Unit 9: Parametric Equations, Polar Coordinates, and VectorValued Functions You’ll solve parametrically defined functions, vectorvalued functions, and polar curves using applied knowledge of differentiation and integration. You’ll also deepen your understanding of straightline motion to solve problems involving curves. Topics may include: Finding derivatives of parametric functions and vectorvalued functions Calculating the accumulation of change in length over an interval using a definite integral Determining the position of a particle moving in a plane Calculating velocity, speed, and acceleration of a particle moving along a curve Finding derivatives of functions written in polar coordinates Finding the area of regions bounded by polar curves On The Exam 11%–12% of exam score Unit 10: Infinite Sequences and Series You’ll explore convergence and divergence behaviors of infinite series and learn how to represent familiar functions as infinite series. You’ll also learn how to determine the largest possible error associated with certain approximations involving series. Topics may include: Applying limits to understand convergence of infinite series Types of series: Geometric, harmonic, and pseries A test for divergence and several tests for convergence Approximating sums of convergent infinite series and associated error bounds Determining the radius and interval of convergence for a series Representing a function as a Taylor series or a Maclaurin series on an appropriate interval On The Exam 17%–18% of exam score 微信扫码咨询 来电垂询：13269125778（微信同号） 携手大洋彼岸，与您一起抵达成功的彼岸
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