AP Calculus AB/BC

"The limit does not exist." In unit 1 of AP Calc AB/BC, we cover everything you need to know about limits and continuity: limit notation, estimating and calculating limits, L'Hopital's Rule, squeeze theorem, theories of continuity, infinite limits, limits at infinity, and the intermediate value theorem. 

Unit 1 – Limits & Continuity

1.12 Confirming Continuity over an Interval

1.5 Determining Limits Using Algebraic Properties of Limits

1.13 Removing Discontinuities

1.11 Defining Continuity at a Point

1.2 Defining Limits and Using Limit Notation

1.4 Estimating Limit Values from Tables

1.15 Connecting Limits at Infinity and Horizontal Asymptotes

1.14 Connecting Infinite Limits and Vertical Asymptotes

Unit 1 Overview: Limits and Continuity

1.16 Working with the Intermediate Value Theorem (IVT Calc)

1.7 Selecting Procedures for Determining Limits

1.3 Estimating Limit Values from Graphs

1.1 Introducing Calculus: Can Change Occur at An Instant?

1.6 Determining Limits Using Algebraic Manipulation

1.8 Determining Limits Using the Squeeze Theorem

1.10 Exploring Types of Discontinuities

1.9 Connecting Multiple Representations of Limits

In unit 2 of AP Calc AB/BC, we introduce the derivative—definitions of the derivative, derivative rules (power rule, quotient rule, product rule, and trig rules), and differentiability of a function. With these resources, you will become a master of differentiation!

Unit 2 – Fundamentals of Differentiation

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

2.1 Defining Average and Instantaneous Rates of Change at a Point

2.3 Estimating Derivatives of a Function at a Point

2.5 Applying the Power Rule

2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

2.7 Derivatives of cos x, sinx, e^x, and ln x

2.2 Defining the Derivative of a Function and Using Derivative Notation

2.8 The Product Rule

2.9 The Quotient Rule

2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Unit 2 Overview: Differentiation

In unit 3 of AP Calc AB/BC, we dive deeper into derviatives! We will cover the derivatives of composite, implicit, and inverse functions, including inverse trigonometric functions. We'll delve into higher order derivatives, chain rule, and how to select a procedure to calculate derivatives. 

Unit 3 – Composite, Implicit, & Inverse Functions

3.1 The Chain Rule

3.5 Selecting Procedures for Calculating Derivatives

3.6 Calculating Higher-Order Derivatives

3.2 Implicit Differentiation

3.4 Differentiating Inverse Trigonometric Functions

3.3 Differentiating Inverse Functions

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

In unit 4 of AP Calc AB/BC, we'll cover derivatives as they relate to position/velocity/acceleration, rates of change, and related rates. You'll learn the contextual meaning of derivatives, approximating values using linearization, and finding limits with L'Hopital's Rule. You'll understand the real-life applications of differentiation!

Unit 4 – Contextual Applications of Differentiation

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

4.7 Using L'Hopitals Rule for Determining Limits in Indeterminate Forms

4.1 Interpreting the Meaning of the Derivative in Context

Unit 4 Overview: Contextual Applications of Differentiation

4.4 Intro to Related Rates

4.3 Rates of Change in Applied Contexts other than Motion

4.6 Approximating Values of a Function Using Local Linearity and Linearization

4.5 Solving Related Rates Problems

In unit 5 of AP Calc AB/BC, we talk about mean value theorem, Rolle's theorem, extreme value theorem, global & local extrema, functions increasing & decreasing, first derivative test, concavity, second derivative test, and optimization problems. You'll be ready to analyze all types of graphs using the fundamentals of differentiation!

Unit 5 – Analytical Applications of Differentiation

Unit 5 Overview: Analytical Applications of Differentiation

5.1 Using the Mean Value Theorem

5.4 Using the First Derivative Test to Determine Relative (Local) Extrema

5.6 Determining Concavity

5.3 Determining Intervals on Which a Function is Increasing or Decreasing

5.7 Using the Second Derivative Test to Determine Extrema

5.10 Introduction to Optimization Problems

5.11 Solving Optimization Problems

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

5.8 Sketching Graphs of Functions and Their Derivatives

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

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

5.12 Exploring Behaviors of Implicit Relations

In unit 6 of AP Calc AB/BC, we wil cover accumulation change with definite integrals, Riemann sums, the Fundamental Theorem of Calculus, u-substitution, antiderivatives, indefinite integrals, and properties of integrals, integration by parts, and partial fraction decomposition. You'll understand the fundamentals of integration and its applications!

Unit 6 – Integration & Accumulation of Change

Unit 6 Overview: Integration and Accumulation of Change

6.1 Integration and Accumulation of Change

6.11 Integrating Using Integration by Parts

6.12 Integrating Using Linear Partial Fractions

6.13 Evaluating Improper Integrals

6.14 Selecting Techniques for Antidifferentiation (AB)

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

In unit 7 of AP Calc AB/BC, we delve into differential equations, slope fields, Euler's method, finding particular solutions using initial conditions & separation of variables, and logistic models for exponential growth and decay. With these resources, you'll develop a deeper understanding of differential equations as mathematical models.

Unit 7 – Differential Equations

7.9 Logistic Models with Differential Equations

7.5 Approximating Solutions Using Euler’s Method

7.3 Sketching Slope Fields

7.4 Reasoning Using Slope Fields

7.6 Finding General Solutions Using Separation of Variables

7.2 Verifying Solutions for Differential Equations

7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables

Unit 7 Overview: Differential Equations

7.1 Modeling Situations with Differential Equations

7.8 Exponential Models with Differential Equations

In unit 8 of AP Calc, we dive into integration as it relates to the average value of a function, net changes, particle motion (position/velocity/acceleration), areas between curves, and volumes (with cross sections, disc method, & washer method). You'll develop a solid understanding of integration and its applications in real life!

Unit 8 – Applications of Integration

Unit 8 Overview: Applications of Integration

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

8.1 Finding the Average Value of a Function on an Interval

8.12 Volume with Washer Method: Revolving Around Other Axes

8.8 Volumes with Cross Sections: Triangles and Semicircles

8.5 Finding the Area Between Curves Expressed as Functions of y

8.6 Finding the Area Between Curves That Intersect at More Than Two Points

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

8.4 Finding the Area Between Curves Expressed as Functions of x

8.7 Volumes with Cross Sections: Squares and Rectangles

8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals

8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

8.10 Volume with Disc Method: Revolving Around Other Axes

8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled

In unit 9 of AP Calc BC, we review parametric equations, arc lengths, polar coordinates, vector-valued functions, and areas under polar curves. With these resources, you'll ace the AP Calc BC exam!

Unit 9 – Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)

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

9.2 Second Derivatives of Parametric Equations

Unit 9 Overview: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions

9.5 Integrating Vector-Valued Functions

9.3 Finding Arc Lengths of Curves Given by Parametric Equations

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

9.1 Defining and Differentiating Parametric Equations

9.4 Defining and Differentiating Vector-Valued Functions

Let's learn about series in unit 10 of AP Calc BC. We cover infinite sequences and series, including all the divergence and convergence tests: nth term test, integral test, comparison tests, alternating series tests, and Taylor polynomials. 

Unit 10 – Infinite Sequences & Series (BC Only)

10.10 Alternating Series Error Bound

Unit 10 Overview: Infinite Series and Sequences

10.13 Radius and Interval of Convergence of Power Series

10.15 Representing Functions as Power Series

10.4 Integral Test for Convergence

10.11 Finding Taylor Polynomial Approximations of Functions

10.9 Determining Absolute or Conditional Convergence

10.8 Ratio Test for Convergence

10.7 Alternating Series Test for Convergence

10.2 Working with Geometric Series

10.12 Lagrange Error Bound

10.14 Finding Taylor or Maclaurin Series for a Function

10.6 Comparison Tests for Convergence

10.3 The nth Term Test for Divergence

10.5 Harmonic Series and p-Series

10.1 Defining Convergent and Divergent Infinite Series

Frequently Asked Questions

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Unit 1 Review - Limits & Continuity

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Unit 2 Review - Differentiation: Definition & Fundamental Properties

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AP Cram Sessions 2021

🌶️ AP Calc Cram Review: Unit 6 BC Concepts (Integration by parts, Using Linear Partial Fractions, and  Improper Integrals)

AP Calc BC Cram Unit 6: BC Concepts (Integration by parts, Using Linear Partial Fractions, and Improper Integrals)

🌶️ AP Calc Cram Review: Unit 6: Integration and Accumulation of Change

AP Calc AB Cram Unit 6: Integration and Accumulation of Change

🌶️ AP Calc Cram Review: Unit 8: Applications of Integration

AP Calc AB Cram Unit 8: Applications of Integration

🌶️ AP Calc Cram Review: Unit 2: Differentiation: Definition and Fundamental Properties

AP Calc AB Cram Unit 2: Differentiation: Definition and Fundamental Properties

🌶️ AP Calculus AB + BC Finale Watch Party Admin 2

AP Calc AB Finale Slides

🌶️ AP Calc Cram Review: Unit 10: Infinite Sequence and Series Part 2

🌶️ AP Calc Cram Review Free Response Practice

AP Calc AB Cram Free Response Practice

🌶️ AP Calc Cram Review: Unit 10: Infinite Sequence and Series Part 1

AP Calc BC Finale Slides

🌶️ AP Calc Cram Review: Unit 7 and 8 BC Concepts (Euler's Method, Logistics Models, and Arc Length)

AP Calc BC Cram Unit 7 and 8 BC Concepts (Euler's Method, Logistics Models, and Arc Length)

🌶️ AP Calc Cram Review: Unit 9: Parametric Equations, Polar Coordinates

AP Calc BC Cram Unit 9: Parametric Equations, Polar Coordinates

🌶️ AP Calc Cram Review: Unit 7: Differential Equations

🌶️ AP Calc Cram Review: Free Response Practice

🌶️ AP Calc Cram Review: Unit 1: Limits and Continuity

🌶️ AP Calc Cram Review: Unit 4: Contextual Applications of Differentiation

AP Calc AB Cram Unit 4: Contextual Applications of Differentiation

🌶️ AP Calc Cram Review Free Response Tips and Tricks

AP Calc BC Cram Free Response Tips and Tricks

🌶️ AP Calc Cram Review: Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

🌶️ AP Calc AB Finale May 3, 2021

AP Calc AB Finale 

AP Calc AB Cram Unit 7: Differential Equations

🌶️ AP Calculus AB Finale Watch Party Admin 3

🌶️ AP Calc Cram Review: Unit 5: Analytical Applications of Differentiation

AP Calc AB Cram Unit 5: Analytical Applications of Differentiation

AP Calc BC Cram Unit 10: Infinite Sequence and Series Part 2

🌶️ AP Calc BC Finale May 3, 2021

AP Calc BC Finale 

🌶️ AP Calculus BC Finale Watch Party Admin 3

AP Calc AB Cram Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

AP Calc AB Cram Unit 1: Limits and Continuity

AP Calc BC Cram Unit 10: Infinite Sequence and Series Part 1

Live Cram Sessions 2020

Tabular Calculus FRQs 

AP Calculus AB/BC Practice Questions (MCQ): 🤙🏽 Unit 3 – Composite, Implicit, & Inverse Functions: 3.3 Differentiating Inverse Functions

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