AP Calculus BC: Course Overview

Updated on: 27th August, 2024

Welcome, Math Enthusiasts, to an in-depth exploration of AP Calculus BC! Building upon the foundation laid by AP Calculus AB, Calculus BC delves deeper into advanced calculus concepts. Get ready for an enriching journey into sequences, series, parametric, polar, and vector functions, as well as advanced integration techniques, differential equations, infinite series, and advanced topics. The AP Calculus BC Exam is scheduled for 12th May 2025.

AP Calculus BC in Brief

In this blog, we aim to be the go-to guide for students, providing a comprehensive overview of the entire AP Calculus BC syllabus in a concise and engaging manner.

Importance of AP Calculus BC

Advanced Calculus Concepts: Calculus BC explores advanced topics beyond the scope of Calculus AB, offering a more in-depth understanding of mathematical analysis.
Higher-Level Problem-Solving Skills: The course hones critical thinking and problem-solving skills to tackle complex mathematical challenges.
College Credits Opportunity: Success in the AP exam may earn college credits, providing an advantageous start in higher education.
Versatility in Mathematical Fields: Calculus BC opens doors to various mathematical disciplines, including pure mathematics, applied mathematics, physics, and engineering.

AP Calculus BC Exam Syllabus

Unit Name	Topics Covered	Weightage in Exam
Unit 1: Limits and Continuity	Introducing Calculus: Can Change Occur at an Instant? Defining Limits and Using Limit Notation Estimating Limit Values from Graphs Estimating Limit Values from Tables Determining Limits Using Algebraic Properties of Limits Determining Limits Using Algebraic Manipulation Selecting Procedures for Determining Limits Determining Limits Using the Squeeze Theorem Connecting Multiple Representations of Limits Exploring Types of Discontinuities Defining Continuity at a Point Confirming Continuity over an Interval Removing Discontinuities Connecting Infinite Limits and Vertical Asymptotes Connecting Limits at Infinity and Horizontal Asymptotes Working with the Intermediate Value Theorem (IVT)	4%–7%
Unit 2: Differentiation: Definition and Fundamental Properties	Defining Average and Instantaneous Rates of Change at a Point Defining the Derivative of a Function and Using Derivative Notation Estimating Derivatives of a Function at a Point Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist Applying the Power Rule Derivative Rules: Constant, Sum, Difference, and Constant Multiple Derivatives of cos x, sin x, ex LIM , and ln x The Product Rule The Quotient Rule Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions	4%–7%
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions	The Chain Rule Implicit Differentiation Differentiating Inverse Functions Differentiating Inverse Trigonometric Functions Selecting Procedures for Calculating Derivatives Calculating HigherOrder Derivatives	4%–7%
Unit 4: Contextual Applications of Differentiation	Interpreting the Meaning of the Derivative in Context Straight-Line Motion: Connecting Position, Velocity, and Acceleration Rates of Change in Applied Contexts Other Than Motion Introduction to Related Rates Solving Related Rates Problems Approximating Values of a Function Using Local Linearity and Linearization Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms	6%–9%
Unit 5: Analytical Applications of Differentiation	Using the Mean Value Theorem Extreme Value Theorem, Global Versus Local Extrema, and Critical Points Determining Intervals on Which a Function Is Increasing or Decreasing Using the First Derivative Test to Determine Relative (Local) Extrema Using the Candidates Test to Determine Absolute (Global) Extrema Determining Concavity of Functions over Their Domains Using the Second Derivative Test to Determine Extrema Sketching Graphs of Functions and Their Derivatives Connecting a Function, Its First Derivative, and Its Second Derivative Introduction to Optimization Problems Solving Optimization Problems Exploring Behaviors of Implicit Relations	8%–11%
Unit 6: Integration and Accumulation of Change	Exploring Accumulations of Change Approximating Areas with Riemann Sums Riemann Sums, Summation Notation, and Definite Integral Notation The Fundamental Theorem of Calculus and Accumulation Functions Interpreting the Behavior of Accumulation Functions Involving Area Applying Properties of Definite Integrals The Fundamental Theorem of Calculus and Definite Integrals Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation Integrating Using Substitution Integrating Functions Using Long Division and Completing the Square Integrating Using Integration by Parts Using Linear Partial Fractions Evaluating Improper Integrals Selecting Techniques for Antidifferentiation	17%–20%
Unit 7: Differential Equations	Modeling Situations with Differential Equations Verifying Solutions for Differential Equations Sketching Slope Fields Reasoning Using Slope Fields Approximating Solutions Using Euler’s Method Finding General Solutions Using Separation of Variables Finding Particular Solutions Using Initial Conditions and Separation of Variables Exponential Models with Differential Equations Logistic Models with Differential Equations	6%–9%
Unit 8: Applications of Integration	Finding the Average Value of a Function on an Interval Connecting Position, Velocity, and Acceleration of Functions Using Integrals Using Accumulation Functions and Definite Integrals in Applied Contexts Finding the Area Between Curves Expressed as Functions of x Finding the Area Between Curves Expressed as Functions of y Finding the Area Between Curves That Intersect at More Than Two Points Volumes with Cross Sections: Squares and Rectangles Volumes with Cross Sections: Triangles and Semicircles Volume with Disc Method: Revolving Around the x- or y-Axis Volume with Disc Method: Revolving Around Other Axes Volume with Washer Method: Revolving Around the x- or y-Axis Volume with Washer Method: Revolving Around Other Axes The Arc Length of a Smooth, Planar Curve and Distance Traveled	6%–9%
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions	Defining and Differentiating Parametric Equations Second Derivatives of Parametric Equations Finding Arc Lengths of Curves Given by Parametric Equations Defining and Differentiating VectorValued Functions Integrating Vector1 Valued Functions Solving Motion Problems Using Parametric and Vector-Valued Functions Defining Polar Coordinates and Differentiating in Polar Form Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve Finding the Area of the Region Bounded by Two Polar Curves	11%–12%
Unit 10: Infinite Sequences and Series	Defining Convergent and Divergent Infinite Series Working with Geometric Series The nth Term Test for Divergence Integral Test for Convergence Harmonic Series and p-Series Comparison Tests for Convergence Alternating Series Test for Convergence Ratio Test for Convergence Determining Absolute or Conditional Convergence Alternating Series Error Bound Finding Taylor Polynomial Approximations of Functions Lagrange Error Bound Radius and Interval of Convergence of Power Series Finding Taylor or Maclaurin Series for a Function Representing Functions as Power Series	17%–18%

AP Calculus BC Exam Structure

Section I: Multiple-Choice Questions (MCQs)

Number of Questions: 45 questions
Part A: 30 questions (calculator not permitted)
Part B: 15 questions (graphing calculator required)
Duration: 1 hour 45 minutes
Weighting: 50% of Exam Score
Question Types: Algebraic, exponential, logarithmic, trigonometric, and general types of functions. Questions include analytical, graphical, tabular, and verbal types of representations.

Section II: Free-Response Questions (FRQs)

Number of Questions: 6 questions
Part A: 2 questions (graphing calculator required)
Part B: 4 questions (calculator not permitted)
Duration: 1 hour 30 minutes
Weighting: 50% of Exam Score
Question Types: Various types of functions and function representations with a mix of procedural and conceptual tasks. At least two questions incorporate a real-world context or scenario.

Top 10 Majors backed up by AP Calculus BC

1. Pure Mathematics: AP Calculus BC provides a strong foundation for students pursuing majors in pure mathematics, including abstract and theoretical mathematics.
2. Applied Mathematics: The advanced calculus concepts covered in AP Calculus BC are directly applicable in various fields of applied mathematics, including mathematical modeling and analysis.
3. Physics: Calculus BC extends the calculus knowledge required for physics majors, covering advanced topics essential for understanding complex physical phenomena.
4. Engineering: The broader range of calculus concepts in AP Calculus BC aligns with the mathematical needs of various engineering disciplines, including aerospace, electrical, and mechanical engineering.
5. Computer Science: The analytical and problem-solving skills developed in Calculus BC are valuable for computer science majors, especially those involved in algorithm design and optimization.
6. Economics: Advanced calculus techniques find applications in economic modeling, making it beneficial for students pursuing majors in economics.
7. Actuarial Science: Calculus BC provides a deeper understanding of mathematical concepts essential for actuarial science, particularly in risk modeling and analysis.
8. Statistics: The analytical skills developed in AP Calculus BC contribute to success in statistics majors, especially in advanced statistical modeling.
9. Mathematical Biology: The study of sequences, series, and differential equations in Calculus BC is relevant to students interested in mathematical biology, where modeling biological systems requires advanced mathematical tools.
10. Applied Physics: Calculus BC is beneficial for students interested in applied physics, where advanced mathematical techniques are essential for understanding complex physical systems.

TutelaPrep’s College Navigator allows students to search for colleges based on their preferred country and course. Not only that, it also provides valuable insights into each college’s specific admission requirements for those exams. Through College Navigator, you can even connect with alumni at your chosen colleges to get a firsthand feel for campus life and academics.

We hope this article helped you with the subject knowledge. Reach out to us by filling out our assistance form if you need any help with the preparations.

Previous Post Next Post