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:

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Syllabus

Best-in-class content by leading faculty and industry leaders in the form of videos, cases and projects, assignments and live sessions

COURSE SYLLABUS PDF

Months

108

Assignments

Live Sessions

1. Limits and Continuity

Hours

Assignment

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

10. Infinite Sequences and Series

Hours

Assignment

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

2. Differentiation - Basic Derivative Rules

Hours

Assignment

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

3. Differentiation - Part 2 Composite Implicit and Inverse Functions

Hours

Assignment

The Chain Rule
Differentiation from Tables and Symbolically
Implicit Differentiation
Inverse Functions
Derivatives of Inverse Trigonometric Functions

4. Contextual Applications of Differentiations

Hours

Assignment

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

5. Analytic Applications of Differentiations

Hours

Assignment

Mean Value Theorem
Extrema on an Interval
First Derivative Test
Curve Sketching
Optimization

6. Integration - Accumulation of Change

Hours

Assignment

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

7. Differential Equations

Hours

Assignment

Introduction to Differential Equations
Slope Fields
Separation of variables
Differential Equations Growth and decay

8. Applications of Integration

Hours

Assignment

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

9. Parametric Equations, Polar Coordinates Vector Valued Functions

Hours

Assignment

Parametric Equations and Calculus
Parametric Equations and Arc Length
Vector - Valued Functions
Polar Coordinates
Area and Arc Length of Polar Coordinates

B. Infinite Series

Hours

Assignment

B1. Definitions
B2. Theorems about Convergence or Divergence of Infinite Series
B3. Test for Convergence of Infinite Series
B4. Alternating Series and Absolute Convergence

C. Power Series

Hours

Assignment

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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