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AP Calculus covers core math concepts critical to success in advanced studies. Here are the key topics you'll encounter:
Limits and Continuity: Understand limits and continuity and learn methods for assessing limits analytically, graphically, and numerically.
Derivatives: Master the differentiation rules and apply them to solve problems involving rate of change, motion, and optimization, as well as to analyze and graph functions.
Integrals: Learn definite and indefinite integrals, practice various integration methods, and use integrals to find areas under curves and volumes of solids.
Fundamental Theorem of Calculus: Connect differentiation and integration using the Fundamental Theorem to evaluate definite integrals and understand accumulation functions.
Application of Integrals: Solve problems involving area, volume, and other physics applications and understand the mean value of a function.
Differential Equations: Solve basic differential equations and apply them to model real-world phenomena, including understanding slanted fields.
Sequences and Series (AP Calculus BC): Analyze the properties and convergence of sequences and series and explore methods for determining convergence.
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Achieving a high AP Calculus exam score requires strong math skills and effective test-taking strategies. Here are some strategies to help you perform your best on the exam:
Time Management: Allocate your time wisely between multiple-choice and free-response sections. Don't spend too much time on one question; if you get stuck, move on and return to it later if time permits.
Read the Questions Carefully: Take the time to read each question carefully before attempting to solve it. Incorrect interpretation of a question may result in errors and loss of points.
Show all Your Work: In the free answer section, clearly show your work's stages. Partial credit is often awarded for correct methods, even if the final answer is incorrect. Make sure your reasoning is easy to follow.
Use the Calculator Wisely: Be familiar with the graphing calculator functions permitted during the exam. Use it to check your work, solve complex equations, and check your results, but don't rely on it exclusively.
Double-check your Answers: Review your answers for errors or incomplete answers if time permits. Double-check your calculations to make sure you answer all parts of each question.
Covers differential and integral calculus.
Topics include limits, derivatives, definite and indefinite integrals, and the Fundamental Theorem of Calculus.
Generally considered equivalent to a first-semester college calculus course.
Consists of two main sections: multiple-choice and free-response.
Passing the AP Calculus AB exam can earn you college credit for one semester of calculus at many universities.
Suitable for students who want a solid introduction to calculus without the additional complexity of BC topics.
Includes all AP Calculus AB topics.
Covers more advanced topics such as parametric, polar, and vector functions, as well as more complex integration techniques.
Equates to both the first and second semesters of college calculus.
Similar structure to the AP Calculus AB exam with multiple-choice and free-response sections. But it includes additional questions on the topics covered.
Contains a subsection within the free-response section specifically for BC-exclusive topics.
Passing the AP Calculus BC exam typically earns you credit for first- and second-semester college calculus courses.
Best for students who have a strong mathematical background and are prepared for a fast-paced, rigorous course.
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