Offering TUTORING for various APs and competitive math, contact ritvikrustagi7@gmail.com if interested
There are two sections on the AP Calculus BC Exam. Section 1 is the multiple choice section while section 2 is the free response section. Each section also has 2 parts to them. One involves a calculator while the other doesn't.
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Section 1: Multiple Choice Question
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Part A: 30 MCQ in 60 minutes (Calculator not allowed)
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Part B: 15 MCQ in 45 minutes (Calculator allowed)
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Section 2: Free Response Section
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Part A: 2 FRQ in 30 minutes (Calculator allowed)
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Part B: 4 FRQ in 60 minutes (Calculator not allowed)
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People tend to like the free response section more due to partial credit. On a multiple choice question, if you get it wrong there's no chance of receiving partial points unlike the free response section. Many people believe that extra preparation is required for the multiple choice section. However, if you are fluent with all the topics and know how to apply them, then the multiple choice questions are simply very short free response questions with answer choice.
Some resources can help you prepare faster than others since they come straight to the point are designed to maximize your chance of getting a 5 on the AP exam. The book on the right was made by Ritvik Rustagi, founder of TMAS Academy.
It contains over 250 pages and hundreds of problems to help you prepare for the AP exam. All problems also have detailed solutions, and are organized by the unit.
The videos on the TMAS Academy youtube channel can be helpful to review. They are short and come straight to the point to make preparing for these exams easier.
Guide to Preparing for the AP Exam
AP Calculus BC is a very long 10 unit course. There are two types of people that take the course, and the methods used to study should be different for each group. One group consists of students taking the course in school while the other includes students that self study the course. There's also a group of students that have done AP Calculus AB before taking this course. They will find BC to be significantly easier than others since majority of the topics on AP Calculus BC are repeated from AP Calculus AB.
For students taking this course in a proper classroom setting, make sure to listen to the teacher and follow along the course as your teacher covers the material. Taking this course in a classroom setting already puts you above students that are self studying. Some popular books used in a classroom setting include the following books below.
For students self-studying, choose a textbook from the slideshow above. It's different from the review textbooks in terms of gaining depth for the content. Some students are able to prepare for the exam solely through the review textbooks, but others need to use in-depth textbooks to gain a rich understanding of the topic. After you have chosen a book, make sure to pace yourself so you can finish the course on time. Try to allocate time properly for each of the 10 units so you have enough time to not only learn the theory but practice. At the end of the day, successful mathletes spend between 5 to 10% of their time learning the theory, and the rest practicing.
Course Overview
Unit # | Topics | Weightage on Exam |
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Sequences | ||
and Series | ||
Unit 10: Infinite | ||
Sequences | ||
and Series | ||
Unit 10: Infinite | ||
Sequences | ||
and Series | ||
Unit 10: Infinite | ||
and Series | ||
Sequences | ||
Unit 10: Infinite | ||
Unit 10: Infinite | ||
Sequences | ||
and Series | ||
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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
Vector-Valued
Functions | ||
Unit 10: Infinite
Sequences
and Series |
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 Vector-Valued Functions
Unit 10: Infinite Sequences and Series
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What is a limit?
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Approximating limits with tables, graphs, or functions
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Does a limit exist at a point?
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Properties of Limits
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Squeeze Theorem
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Types of Discontinuity
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Limits at Infinity
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Intermediate Value Theorem
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Average rate of change
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Instantaneous rate of change
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What is a derivative?
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Limit definition of a derivative
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Continuity and differentiability relationship
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Power Rule
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Derivative rules: addition and subtraction
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More derivative rules
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Derivative of Trigonometric Functions
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Product and Quotient Rule
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Chain Rule
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Implicit differentiation
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Differentiating inverse functions
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Differentiating inverse trigonometric functions
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Differentiating higher order derivatives
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Interpreting derivatives
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Relating calculus to motion
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Related rates
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Approximating a value for a function using local linearity
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L’Hopital’s Rule
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Mean Value Theorem
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Intermediate Value Theorem
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Extreme Value Theorem
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Critical points
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Relative extrema
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Determining if a function is increasing/decreasing
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The First Derivative Test
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Candidates Test
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Determining concavity
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The Second Derivative Test
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Optimization
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Behaviors of implicit relations
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Riemann Sums
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Definite Integral
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Fundamental Theorem of Calculus
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Accumulation functions
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Properties of definite integrals
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Antiderivatives
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Indefinite Integral
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U-Substitution
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Integration with long division
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Integration with completing the square
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Integration by parts
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Integration with partial fractions
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Improper Integrals
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Slope fields
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Draw solution curve on a slope field
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Euler's Method
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Solving differential equations (general and particular solutions)
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Separation of variables
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Modeling growth patterns
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exponential growth/decay
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Logistics Models
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Average value of a function
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Interpreting definite integrals
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Area between curves
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Volume of solid with known cross section: squares, rectangles, triangles, semi-circles
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Volume of solids of revolutions
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disks and washers
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Length of curve for an interval
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Differentiating parametric functions
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Integrating parametric functions
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Distance and Displacement formulas for parametric functions
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Vector-valued functions: differentiating and integrating
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Differentiating polar curves
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Finding the area between polar curves
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Infinite series
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Divergent vs convergent series
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Geometric series
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nth term test for divergence
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Integral test
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p-series and harmonic series
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Direct comparison test
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Limit comparison test
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Alternating series test
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Ratio test
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Determining absolute or conditional convergence
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Alternating series error bound
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Taylor and Maclaurin polynomials
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Lagrange error bound
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Radius and interval of convergence of power series using ratio test
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Writing functions as power series
4-7% Exam Weightage
You are very unlikely to see a problem from this unit on the free response section. However, expect around 5 multiple choice questions on this topic. They will be relatively straight forward compared to other questions. You will need to be fluent with continuity and evaluating limits by considering factors such as discontinuity.
4-7% Exam Weightage
Despite the low weightage of this unit, it's fundamentals that must be known to differentiate for harder problems from other units. There won't be many problems that solely use topics from this unit on the free response question. However, there will always be some parts of a free response question that involve topics from this unit.
4-7% Exam Weightage
Expect to see topics from this unit on some parts of free response questions. There is always one application of the chain rule on the free response section, and some regarding that topic on the multiple choice section. The rest of the topics are likely to appear on the multiple choice section.
Pay close attention to the chain rule and differentiating inverse trigonometric functions. That doesn't mean you should neglect the other topics since they will also appear on the exam.
6-9% Exam Weightage
Pay close attention to related rates. The word problems regarding related rates cause many people to mess up on the exam. Resources for related rates can be found in the TMAS Academy AP Calculus BC book.
There will almost always be one multiple choice question and one part from a free response question that uses L'Hopital's Rule. In addition to that, it's common to see a problem that involves a factor like motion and causes you to differentiate and interpret in the context of the problem.
8-11% Exam Weightage
Don't be surprised if you have to deal with a problem from this unit on the free response section. There will always be at least one part of at least one free response question that will involve topics from this unit. Popular topics are finding the relative extrema using the first and second derivative tests. Sometimes the mean value theorem and intermediate value theorem can show up on the free response section (not that common).
On the multiple choice section, expect to see 1-2 problems regarding the mean and intermediate value theorem. There will always be at least one question that involves critical points and finding relative extrema.
You will definitely encounter multiple problems that will ask you to find absolute extrema on both the multiple choice and free response sections.
17-20% Exam Weightage
This topic has a very high yield on both the free response and multiple choice sections. You will very likely see an entire free response question that incorporates topics from this unit. There were will also be many multiple choice questions from this section. Make sure to check out the TMAS Academy AP Calculus BC book as it contains tons of problems for every unit including this one.
6-9% Exam Weightage
Most people tend to like this unit in comparison to others as there are less topics. There's a high chance of receiving an entire free response question that involves differential equations. Most of the times, the parts will consist of sketching a slope field and using separation of variables to solve the differential equation.
Expect to see 4-5 questions on the multiple choice section that involve this unit.
6-9% Exam Weightage
This unit is on the harder site when it comes to visualization. There's a good chance of seeing a free response question for this unit. There will be at least 4 multiple choice questions on top of that for this unit.
Make sure to watch the AP Calculus AB/BC Unit 8 Rapid Review video to see visualizations for these solids of revolutions and solids with known cross sections. It will help you a lot on the AP exam.
11-12% Exam Weightage
You will guaranteed see a free response question from this unit on the AP exam. It will either be a parametric, vector-valued, or polar related problem. Remember all your formulas regarding how to differentiate/integrate all the certain types of functions,
On the multiple choice section, expect to see around 5 questions from this unit, and they will most likely appear on the calculator part of the multiple choice section.
17-18% Exam Weightage
You will guaranteed see a free response question from this unit on the AP exam. It will often ask you to write the Taylor polynomial and use a few of the convergence tests.
This topic also has a high yield on the multiple choice section. Expect to see at least 7 MCQ that consist of topics from this unit.