AP Calculus AB/BC
It’s been said that change is the only true constant. Calculus helps make sense of change by grappling with questions that inspire thinkers from around the globe, across time, and in many disciplines. Can change occur in an instant? When is the next solar eclipse or the turning point for an economy? In AP Calculus AB, you’ll develop a deeper understanding of mathematical principles that can help you answer questions such as these. In AP Calculus BC, you’ll cover many of the mathematical principles in AP Calculus AB and build upon them. AP Calculus BC helps you prepare for further study in mathematics and other disciplines, such as engineering, computer science, or economics.
Course Content
BC
AB
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.
10%-12%
4%-7%
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.
10%-12%
4%-7%
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
You'll master using the chain rule, develop new differentiation techniques, and introduced to higher-order derivatives.
9%-13%
4%-7%
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 detemrine limits of certain indeterminate forms.
10%-15%
6%-9%
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.
15%-18%
8%-11%
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.
17%-20%
17%-20%
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.
6%-12%
6%-9%
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.
10%-15%
6%-9%
Course Content BC Only
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
You'll solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integrations. You'll also deepen your understanding of straight-line motion to solve problems involving curves.
11%-12%
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.
17%-18%
Tips
Clinton Truong
Score: 4
AB Subscore: 5
There are a few topics in the BC course that are guaranteed to appear on the exam including series, integration by parts, partial fraction decomposition, and Euler's method. Make sure to put the bulk of your studying into these topics as these are free points! Taylor and Maclaurin series were my main focus however I decided not to study much of the tests for convergences as they seemed too laborious to study if there were only a few questions on them.
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Know your basic derivatives and trig functions along with ln behaviors. These are free questions and you should be aiming to maximize the points you earn!
Grace Kang
Score: 4
AB Subscore: 4
AP Calc AB/BC can definitely get tricky, but it is very manageable. This may be one of the more basic tips, but doing lots of practice really is key. It is also very important to make sure that you are fully confident on the basics like taking derivatives and integrals. Also there is a lot of algebra involved so you also need to make sure that you have very solid algebra skills. Don’t just memorize formulas, but understand how they come about. If you are in BC and have already taken AB prior and are confident in your skills for AB, when studying for the AP exam, put most of your focus on series, sequences, polar, and parametric. Take a lot of full practice exams and be aware about time. It is a big help in learning how to manage your time and understanding which questions are easier compared to the more difficult ones to spend more time on.
Resources
Course Description
Know what is expected of you to know and what is the makeup of your exam. Each topic has its dedicated page.
Organic Chemistry Tutor
Quick and concise review videos for almost all topics.
Allen Tsao
Quick and concise review videos for almost all topics.
APSPU Google Drive
Personal resources we used whilst studying for the exam and course.
Fivable
Study guides for all units and topics.