AP Calculus BC
AP Calculus BC covers topics such as limits and continuity, Infinite Series and Power Series
90%
of students score
4 and above
78%
students get a top score of
5 in
AP Calculus BC
80%
students showed exceptional
performance in their first semester of
AP Calculus BC
Course Concept
AP Calculus BC is an advanced placement course that covers topics in differential and integral calculus. It is designed for students who have a strong mathematical foundation and wish to pursue more rigorous coursework. The course delves deeper into calculus concepts than AP Calculus AB, covering additional topics such as advanced integration techniques, series and sequences, and parametric, polar, and vector functions. Students who successfully complete the AP Calculus BC exam may receive college credit or advanced placement in calculus courses at the university level. It is a challenging course that requires a solid understanding of pre-calculus and a strong work ethic to succeed. It is divided in:
- Understanding and Application of Calculus Concepts: Students will develop a deep understanding of calculus concepts, including limits, derivatives, integrals, and their applications in various contexts such as physics, engineering, and economics.
- Mastery of Differentiation and Integration Techniques: Students will learn and apply advanced techniques for differentiation, including implicit differentiation, logarithmic differentiation, and related rates. They will also study advanced integration techniques, such as integration by parts, partial fractions, and trigonometric substitutions.
- Analysis of Functions and Their Properties: Students will analyze the properties of functions, including continuity, differentiability, and behavior at critical points. They will explore the concepts of local and global extrema, concavity, inflection points, and asymptotes.
AP Calculus BC
Course Details:
- Dedicated Test Prep Manager to Oversee Your Program
- Physical & Digital Copies of the AP Guru Strategy Guides & Classroom Books
- Test Reports With Detailed Analytics
- Personalized Lesson Notes And Assignments
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+ GST
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$
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Course Concept
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COURSE SYLLABUS PDF- Concept of Instantaneous rate of change
- Understanding the Limit
- Proper Limits
- Finding Limits Analytically
- Limits of transcendental functions
- Limits and Continuity
- Infinite Limits and Limits at Infinity
- Intermediate Value Theorem
- Rate of change and tangent line
- Tangent line and the derivatives
- Understanding the Derivatives
- Differentiability and Continuity
- Basic Differentiation Rule
- The Product and Quotient Rule
- Velocity and Other Rate of Change
- The Chain Rule
- Differentiation from Tables and Symbolically
- Implicit Differentiation
- Inverse Functions
- Derivatives of Inverse Trigonometric Functions
- The Interpretation of the Derivative
- Straight Line Motion- Connecting Position Velocity and Acceleration
- Rate of change in other application
- Related rates
- Local Linearity
- L' Hospital's Rule
- Indeterminate Form
- Mean Value Theorem
- Extrema on an Interval
- First Derivative Test
- Curve Sketching
- Optimization
- Approximating Area with Riemann Sums
- Sigma Notation and Riemann Sums '
- Accumulation Functions
- Properties of Definite Integrals
- Antiderivatives and Indefinite Integrals
- Fundamental theorem of Calculus
- Integration by Substitution
- Integration of Transcendental Functions
- Introduction to Differential Equations
- Slope Fields
- Separation of variables
- Differential Equations Growth and decay
- Finding Average value of Integrals
- Another Look at Particle Motion
- Accumulation Functions In context
- Area Between Two curves
- Volumes By Cross Sections
- Volumes by Disc and Washer Methods
- Volume About a Line
- Parametric Equations and Calculus
- Parametric Equations and Arc Length
- Vector - Valued Functions
- Polar Coordinates
- Area and Arc Length of Polar Coordinates
- Series and Convergence
- Integral Test p -series
- Comparison of Series
- Alternating Series
- Ratio and Root Tests
- Taylor Polynomials
- Lagrange Error Bound
- Power Series and Intervals of Convergence
- Taylor and Maclaurin Series
- Representing Functions by Power Sales
- B1. Definitions
- B2. Theorems about Convergence or Divergence of Infinite Series
- B3. Test for Convergence of Infinite Series
- B4. Alternating Series and Absolute Convergence
- C1. Definitions : Convergence
- C2. Functions Defined by power Series
- C3. Finding a Power Series for a Functions : Taylor and Maclaurin Series
- C4. Approximating Functions with Taylor and Polynomials
- C5. Computations with Power Series
- C6. Computations with Power series
- C7. Power Series Over Complex Numbers
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- Specialist subject tutors who have graduated from top universities with a passion for teaching and a dedicated program manager to track your progress.
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- A teacher who is a 99th percentile scorer in the subject he or she teaches
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- Topic-wise worksheets and graded assessments (with marking schemes) to ensure mastery of each topic tested on the school exams.
- Doubt sessions after every couple of classes to review incorrect questions.
- Additional worksheets on topic areas of concern.
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Comprehensive Curriculum
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Maharnab
Physics, Math Tutor
Maharnab has pursued B.Tech in Electrical Engineering from IIT Roorkee and has over 5 years of teaching experience. He specializes in Maths and Physics for JEE, AP, IB, IGCSE, MYP, A-levels and SAT.
Bibhusit
Math and Physics Tutor
A postgraduate in Physics, Bibhusit has been a passionate researcher and educationist. He has been a part of various astrophysics research projects at ARIES, IISc and RRI. He is an accomplished teacher for students pursuing AP Physics, A Levels, IB, SAT, ACT, AP Calculus AB and BC. He also has 5+ years of online teaching experience.
Preeti
Chemistry Tutor
With 11 years of experience in teaching and e-learning, Preeti has immense experience in tutoring and grooming students from various international boards like IB, AP and IGCSE. She has acquired her M.Sc with B.Ed and works towards the overall development of students.
Eman
English Tutor
Eman has done her Bachelor's in English and Psychology. She is currently pursuing her MA in Music Education from Trinity Laban Conservatoire of Music and Dance, London, and has studied the learning patterns of students in depth and molded her teaching accordingly. She has 4 years of teaching experience, with students ranging from ages 6 to 50, and is brilliant in working with students with special needs.
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Complete Application
Step 1 of the APGuru process is the application phase. We'll ask for basic information such as your name, contact details, current educational level, and your specific goals or challenges. Once you've filled out the application, click the submit button. Your application will be promptly reviewed by our admissions team.
Take a Trial Class
Step 2 is the trial class, where applicants receive an invitation to experience our teaching methods and interact with instructors. During this session, students engage in discussions, ask questions, and evaluate whether APGuru aligns with their learning preferences and goals, helping them make an informed decision.
Join AP Guru
Step 3 of the APGuru process involves officially joining the program after a successful trial class. Students confirm their enrollment, select their desired course or program, and gain access to comprehensive study resources. They begin attending regular classes, receiving guidance from experienced instructors, and tracking their progress towards academic excellence.