• Course Overview:

AP Calculus AB and BC are college-level courses that provide students with a strong foundation in differential and integral calculus. These courses are designed for students pursuing careers in science, technology, engineering, mathematics, and health professions. Students develop a deep understanding of limits, derivatives, integrals, and their applications using graphical, numerical, analytical, and verbal representations. This course follows the official College Board AP Calculus framework and culminates in the AP Exam in May.

🟦 Unit 1: Limits and Continuity

        1.1 Can Change Occur at an Instant?

        1.2 Defining Limits and Using Limit Notation

        1.3 Estimating Limit Values from Graphs

        1.4 Estimating Limit Values from Tables

        1.5 Determining Limits Using Algebraic Properties

        1.6 Determining Limits Using Algebraic Manipulation

        1.7 Selecting Procedures for Determining Limits

        1.8 Determining Limits Using the Squeeze Theorem

        1.9 Connecting Multiple Representations of Limits

        1.10 Exploring Types of Discontinuities

        1.11 Defining Continuity at a Point

        1.12 Confirming Continuity Over an Interval

        1.13 Removing Discontinuities

        1.14 Infinite Limits and Vertical Asymptotes

        1.15 Limits at Infinity and Horizontal Asymptotes

        1.16 Intermediate Value Theorem (IVT)

🟦 Unit 2: Differentiation: Definition and Fundamental Properties

        2.1 Defining Average and Instantaneous Rate of Change at a Point

        2.2 Defining the Derivative of a Function and Using Derivative Notation

        2.3 Estimating Derivatives of a Function at a Point

        2.4 Connecting Differentiability and Continuity

        2.5 Applying the Power Rule

        2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple

        2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)

        2.8 The Product Rule

        2.9 The Quotient Rule

        2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x) 

🟦 Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

        3.1 The Chain Rule

        3.2 Implicit Differentiation

        3.3 Differentiating Inverse Functions

        3.4 Differentiating Inverse Trigonometric Functions

        3.5 Selecting Procedures for Calculating Derivatives

        3.6 Calculating Higher-Order Derivatives

🟦 Unit 4: Contextual Applications of Differentiation

        4.1 Interpreting the Meaning of the Derivative in Context

        4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

        4.3 Rates of Change in Applied Contexts Other Than Motion

        4.4 Introduction to Related Rates

        4.5 Solving Related Rates Problems

        4.6 Approximating Values of a Function Using Local Linearity and Linearization

        4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms

🟦 Unit 5: Analytical Applications of Differentiation

        5.1 Using the Mean Value Theorem

        5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

        5.3 Determining Intervals on Which a Function is Increasing or Decreasing

        5.4 Using the First Derivative Test to Determine Relative Local Extrema

        5.5 Using the Candidates Test to Determine Absolute (Global) Extrema

        5.6 Determining Concavity of Functions over Their Domains

         5.7 Using the Second Derivative Test to Determine Extrema

        5.8 Sketching Graphs of Functions and Their Derivatives

        5.9 Connecting a Function, Its First Derivative, and Its Second Derivative

        5.10 Introduction to Optimization Problems

        5.11 Solving Optimization Problems

        5.12 Exploring Behaviors of Implicit Relations

🟦 Unit 6: Integration and Accumulation of Change

        6.1 Exploring Accumulation of Change 

        6.2 Approximating Areas with Riemann Sums

        6.3 Riemann Sums, Summation Notation, and Definite Integral Notation

        6.4 The Fundamental Theorem of Calculus and Accumulation Functions

        6.5 Interpreting the Behavior of Accumulation Functions Involving Area

        6.6 Applying Properties of Definite Integrals

        6.7 The Fundamental Theorem of Calculus and Definite Integrals

        6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

        6.9 Integrating Using Substitution

        6.10 Integrating Functions Using Long Division and Completing the Square

        6.11 Integrating Using Integration by Parts (BC topic only)

        6.12 Integrating Using Linear Partial Fractions (BC topic only)

        6.13  Evaluating Improper Integrals (BC topic only)

        6.14 Selecting Techniques for Antidifferentiation        

🟦 Unit 7: Differential Equations

        7.1 Modeling Situations with Differential Equations

        7.2 Verifying Solutions for Differential Equations

        7.3 Sketching Slope Fields

        7.4 Reasoning Using Slope Fields

        7.5 Euler's Method (BC topic only)

        7.6 General Solutions Using Separation of Variables

        7.7 Particular Solutions using Initial Conditions and Separation of Variables

        7.8 Exponential Models with Differential Equations

        7.9 Logistic Models with Differential Equations (BC topic only)        

🟦 Unit 8: Applications of Integration

        8.1 Average Value of a Function on an Interval

        8.2 Position, Velocity, and Acceleration Using Integrals

        8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

        8.4 Area Between Curves (with respect to x)

        8.5 Area Between Curves (with respect to y)

        8.6 Area Between Curves - More than Two Intersections

        8.7 Cross Sections: Squares and Rectangles

        8.8 Cross Sections: Triangles and Semicircles

        8.9 Disc Method: Revolving Around the x- or y- Axis

        8.10 Disc Method: Revolving Around Other Axes

        8.11 Washer Method: Revolving Around the x- or y-Axis

        8.12 Washer Method: Revolving Around Other Axes

        8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC topic only)        

🟦 Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions  (BC topic only)

        9.1 Defining and Differentiating Parametric Equations

        9.2 Second Derivatives of Parametric Equations

        9.3 Arc Lengths of Curves (Parametric Equations)

        9.4 Defining and Differentiating Vector-Valued Functions

        9.5 Integrating Vector-Valued Functions

        9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions            

        9.7 Defining Polar Coordinates and Differentiating in Polar Form

        9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

        9.9 Finding the Area of the Region Bounded by Two Polar Curves        

🟦 Unit 10: Infinite Sequences and Series (BC topic only)

        10.1 Defining Convergent and Divergent Infinite Series

        10.2 Working with Geometric Series

        10.3 The nth Term Test for Divergence

        10.4 Integral Test for Convergence

        10.5 Harmonic Series and p-Series

        10.6 Comparison Tests for Convergence

        10.7 Alternating Series Test for Convergence

        10.8 Ratio Test for Convergence

​        10.9 Determining Absolute or Conditional Convergence

        10.10 Alternating Series Error Bound

        10.11 Finding Taylor Polynomial Approximations of Functions

        10.12 Lagrange Error Bound

        10.13 Radius and Interval of Convergence of Power Series

        10.14 Finding Taylor Maclaurin Series for a Function

        10.15 Representing Functions as a Power Series

Dear DeBakey Parents,

AP Calculus is an advanced math course that plays a crucial role in your child’s future success in high school and beyond. While it can be challenging at times, your support at home makes a big difference!

Here are a few simple ways you can help your child succeed in AP Calculus:

✅ Review their notes daily

✅ Complete all assignments with care and effort

✅ Come to class prepared and ready to learn

✅ Encourage a Positive Attitude: Let your child know it’s okay to struggle—and that learning from mistakes is part of the process. A growth mindset leads to stronger problem-solving skills.

✅ Create a Consistent Study Routine: Set aside a regular time and quiet space for homework and review. Even 15–20 minutes a day can reinforce learning and reduce stress.

✅ Ask Questions and Stay Involved: You don’t have to be a math expert! Ask your child to explain what they learned in class—it helps them process concepts and builds confidence.

✅ Use the Resources Available: Encourage your child to use the tutorial sessions, online videos, and teacher office hours when they need help. We’re here to support them every step of the way.

With consistent study habits and strong home support, students are more likely to stay confident, engaged, and on track for success. Thank you for being an essential part of their learning journey!