AP Calculus BC Tutor

How MEB can help you with AP Calculus BC?

If you require private online AB Calculus BC tutoring, you can get excellent help from My Engineering Buddy. We offer online tutoring sessions for many subjects, including AP courses, for wallet-friendly fees. You can get more details by clicking here and book sessions by contacting the student helpline on WhatsApp. It is a great place to learn exam-worthy tips, tricks, and problem-solving lessons. You can get help preparing review notes, cheat sheets, and exam formula sheets for AP Calculus BC and many other subjects.

About AP Calculus BC

The College Board AP Calculus BC is equivalent to a first-semester calculus college course and the subsequent single-variable calculus course. Its syllabus consists of differentiation, integration, vector, polar, and parametric functions, and series. Students generally sign-up for AP Calculus BC once they have completed precalculus.

In the AP Calculus BC course, the students learn to use mathematical rules and procedures to determine values and expressions. It prepares them to communicate better and present solutions and results using correct mathematical language, notation, and conventions, vital in higher education, research, and professional careers.

AP Calculus BC prerequisites

The student shall complete algebra, trigonometry, geometry, analytic geometry, and elementary as prerequisite subjects for AB Calculus BC. The course requires prior knowledge of compositions, combinations, and inverses for algebraic transformations and general functions. The students should know the properties of rational, exponential, linear, trigonometric, inverse trigonometric, logarithmic, piecewise-defined, and polynomial functions. They should have the skills to solve equations and plot graphs for these functions.

AP Calculus BC Exam

The AP Calculus BC Exam tests how well a student understands the calculus concepts covered in the AP Calculus BC units. It also checks the ability to determine the proper processes and formulas appropriate for solving problems and communicating the solutions with the correct notations. The exam has multiple-choice and free-response questions. Students can use a graphing calculator is for some parts of the exam.

Remember that a student may not take AP Calculus AB and Calculus BC exams in the same year.

Is AP Calculus BC hard?

More than 80% of AP Calculus BC students scored 3 or more, and about 45% got a perfect 5, according to collegevine.com. It has a lengthy syllabus requiring students to focus and persist through the course units. For a good chance of success in the AP Calculus BC exam, students shall solve a lot of practice questions and gain speed and accuracy. You can use the Albert.io AP Calculus BC score calculator to know your grade.

What is the difference between AP Calculus AB and AP Calculus BC?

The main difference between the two programs, AP Calculus AB and BC, is not the difficulty level but the pace of the courses. That’s because the first seven units are standard for both the AP Calculus programs. AP Calculus BC has three extra units covered in the same duration. AP Calculus AB covers a one-semester college calculus course material in one year. In contrast, AP Calculus BC has two semesters worth of calculus syllabus packed in the same timeframe.

It is not mandatory to complete AP Calculus AB before signing up for AB Calculus BC. The two courses have no dependency on each other, and students can enroll in either of the courses based on their requirements.

Would you get a formula sheet for AP Calculus BC?

Students don’t get an AP Calculus BC formula sheet during the exam. It is a concept-based course where the students apply their calculus knowledge. They shall learn valuable tricks and problem-solving techniques while preparing for the exam. A student can bring up to two approved calculators to the exam.

Is AP Calculus BC worth taking?

It is prudent to take AP Calculus BC to get college credit while studying in high school. Universities consider it a good indicator of an applicant’s interest in the subject and view it favorably for admissions. The student is also more confident with the application process and, later on, during the college stint. Successful AP Calculus BC students can save on the tuition fees for the college subject as they have already cleared the AP exam.

AP Calculus BC topics

Here is the list outlining the AP Calculus BC units.

Part 1: Limits and Continuity (4 – 7% of the total score)

Solve problems that involve limits change. Learn about the basic concepts of functions.

Topics:

• Measuring instantaneous change using limits
• Definition of limits and learning their properties in different applications
• Understanding asymptotes
• Studying a function’s continuity at a given point or over a domain
• Finding limits at infinity
• Reasoning with the squeeze theorem and the intermediate value theorem

Part 2: Differentiation and its fundamental properties (4 – 7% of the total score)

Study how to use limits for definition and determination of derivatives

Topics:

• Function derivatives definition
• Calculating derivatives for elementary functions
• Learn how differentiability relates to continuity
• Use differentiation rules

Part 3: Differentiation of inverse, implicit, and composite functions (4 – 7% of the total score)

Study derivatives of higher orders. Learn the chain rule and advanced differentiation techniques.

Topics:

• Solving higher-order derivatives of functions
• Implicit differentiation
• Differentiate composite functions with the chain rule
• Inverse function differentiation

Part 4: Applying differentiation in various contexts (6 – 9% of the total score)

Learn to define and solve real-world problems that involve instantaneous rates of change by applying derivatives. Use mathematical reasoning to derive the limits of some indeterminate forms.

Topics:

• Extracting relevant mathematical information of real-world problems involving rates of change from verbal descriptions
• Solve motion equations with differentiation
• Extending knowledge of motion problems to other rates of change situations
• L’Hospital’s rule
• Local linearity and approximation

Part 5: Analysis using differentiation (8 – 11% of the total score)

Practice solving optimization problems using calculus. Learn the relationship between graphs of a function and its derivatives.

Topics:

• Function properties and derivatives of functions
• Mean Value and Extreme Value Theorems
• Candidates test
• First and second derivative tests
• Implicit relations’ behavior
• Solve optimization problems
• Drawing graphs of functions and derivatives

Part 6: Accumulation of change and integration (17 – 20% of the total score)

Use limits to define definite integrals. Learn how the fundamental theorem connects differentiation and integration. Use various integration techniques to solve problems and study the application of properties of integrals.

Topics:

• Use Riemann Sums for approximating integrals
• Indefinite integrals
• Use definite integrals to determine accumulated change over an interval
• The Fundamental Theorem of Calculus
• Antiderivatives
• Integration techniques
• Definite integrals and accumulation functions
• Properties of integrals

Part 7: Differential equations (6 – 9% of the total score)

Learn about exponential growth and decay. Methods to solve differential equations.

Topics:

• General and particular solutions separable differential equations
• Interpret verbal descriptions of change to derive separable differential equations
• Derive and apply exponential growth and decay model
• Sketch curves using families of solution

Part 8: Applications of integration (6 – 9% of the total score)

Study net change over time. Learn how to determine areas and volumes with functions.

Topics:

• Modeling particle motion
• Use definite integrals to determine the average value of functions
• Learn to solve accumulation problems
• Area between curves
• Deriving volume using cross-sections, disc method, and the washer method

Part 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (11 – 12% of the total score)

Learn to solve vector-valued functions, parametrically defined functions, and polar curves applying differentiation and integration. Solve curve problems with knowledge of straight-line motion.

Topics:

• Find parametric function derivatives and vector-valued functions
• Calculate the position of a particle’s planar movement
• Use definite integrals to calculate the accumulation of change in length over an interval
• Calculate velocity, speed, and acceleration particles in curvilinear motion
• Determine the polar curves’ region area
• Derivatives of polar coordinates’ functions

Part 10: Infinite Sequences and Series (17 – 18% of the total score)

Learn about infinite series’ convergent and divergent behaviors. Practice how to use infinite series to represent familiar functions. Determine the maximum error possible associated with some approximations that involve series.

Topics:

• Understanding convergence of infinite series with limits
• Tests for convergence and divergence
• Calculating the interval and radius of series convergence
• Types of series: Harmonic, geometric, and p-series
• Approximation of sums of convergent infinite series and error boundaries related to it
• Using Maclaurin series or Taylor series to represent a function for an appropriate interval

The AP Calculus BC College Board official web page has up-to-date information about everything related to the course and the exam.

Resources to help in preparation for the AP Calculus BC exam

We have compiled a list of great resources and textbooks for students preparing for the AP Calculus BC exam.

You can get past AP Calculus BC free-response exam questions for practice from the College Board AP Calculus BC questions webpage.

Khan Academy: Students can prepare for the AP Calculus BC exam with the Khan Academy AP Calculus BC resources. You will find online lessons, quizzes, videos, and practice questions on the AP Calculus BC curriculum webpage. Khan Academy is an official College Board test prep partner for AP courses.

The Albert.io AP Calculus page is another excellent place for AP Calculus BC free-response and multiple-choice questions that you can use to practice for the exam.

AP Calculus BC textbooks

• Calculus for AP – 1st edition – A Complete Course by James Stewart, Stephen Kokoska. Publisher – Cengage Learning
• Calculus – Early Transcendentals Single Variable by Howard Anton, Irl C Bivens, Stephen Davis. Publisher – Wiley
• Calculus – Graphical, Numerical, Algebraic – AP Edition by Ross L. Finney, Franklin D Demana, Bert K. Waits, Daniel Kennedy. Publisher – Prentice Hall
• Calculus AP Edition by William Briggs, Lyle Cochran, Bernard Gillett. Publisher – Pearson
• Calculus – Single and Multivariable AP Edition by Deborah Hughes-Hallett, Andrew M. Gleason, William G McCallum. Publisher – Wiley
• Calculus – AP Edition by Ron Larson, Bruce H Edwards. Publisher – Cengage Learning
• Calculus for AP by Ron Larson, Paul Battaglia. Publisher – Cengage Learning
• Rogawski s Calculus for AP – Early Transcendentals Second Edition by Jon Rogawski, Ray Cannon. Publisher – W. H. Freeman