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Overview of AP Calculus AB
AP Calculus AB is a college-level course offered by the College Board to high school students who are interested in studying biology at an advanced level. It was opted by 135,458 students in 2023 as it is one of the preferred AP courses. The subject was given a difficulty rating of 5.5 out of 10 by class alumnae on a reddit survey. AP Calculus AB is known for its challenging curriculum and rigorous exams.The course covers a broad range of topics in calculus, including derivatives, integrals, and the fundamental theorem of calculus.
Course content
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.
- 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
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.
- The chain rule for differentiating composite functions
- Implicit differentiation
- Differentiation of general and particular inverse functions
- Determining higher-order derivatives of functions
Unit 4: Contextual Applications of Differentiation
You’ll apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.
- Identifying relevant mathematical information in verbal representations of real-world 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
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.
- 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
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.
- Using definite integrals to determine accumulated change over an interval
- Approximating integrals using Riemann Sums
- Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
- Antiderivatives and indefinite integrals
- Properties of integrals and integration techniques
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.
- Interpreting verbal descriptions of change as separable differential equations
- Sketching slope fields and families of solution curves
- Solving separable differential equations to find general and particular solutions
- Deriving and applying a model for exponential growth and decay
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 areas of regions or volumes of solids defined using functions.
- Determining the average value of a function using definite integrals
- Modeling particle motion
- Solving accumulation problems
- Finding the area between curves
- Determining volume with cross-sections, the disc method, and the washer method
Exam Date
AP Calculus AB Exam
Will be conducted on
Mon, May 13, 2024 | 12 PM Local
AP Calculus AB Exam Guide
AP Calculus AB is known for its challenging curriculum and rigorous exams. In the AP Calculus AB exam guide, we provide you with the exam structure, topics, study resources, and student performance over the past 10 years of AP Calculus AB exams to put together the comprehensive AP Calculus exam guide.
Explore more in AP Calculus AB
AP Calculus AB Course Resources
AP Calculus AB Course
The College Board website offers a variety of extra resources to help AP Calculus AB students succeed on the exam. These resources include the AP Calculus Course at a Glance, the AP Calculus Course and Exam Description, the AP Calculus Scoring Guidelines, and more. To help students prepare for the AP Calculus AB exam, we have provided a list of extra resources below.
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AP Calculus AB and BC Course and Exam Description
This is the core document for this course. Unit guides clearly lay out the course content and skills and recommend sequencing and pacing for them throughout the year. The CED was updated in the summer of 2020 to include scoring guidelines for the example questions.
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