Unit 3 builds upon understanding from Unit 1 and Unit 2 of AP Calculus. The two main components of Calculus are differentiating and integrating. Of these two, differentiation is the focal point of the first few units in Calculus.  

This unit, in particular, emphasizes the analysis of functions, continued correct application and understanding of function notation, and the recognition of “inner” and “outer” functions within composites.  This unit makes up 9-13% of the Calculus AB exam and 4-7% of the Calculus BC exam.

This list will be a good place to start in terms of self assessing what you need to study or learn.  As you are looking through this list write down what topics on this list you don’t remember or still need to learn.  Go to the full study guide page then for this topic to get some more information!


Use when you are deriving a function that is a composition of functions:

Use when you have an equation that looks like this: 

*The first step would be to differentiate with respect to x* 

Use this formula to help find the derivative of the inverse function: 

Memorize these to help you solve problems quickly and efficiently! 

Selecting Procedures for Calculating Derivatives 

When you are selecting procedures for calculating derivatives decide if the function you are looking at is:

When you get into the next few units you will need to take the next derivate; especially when you get into describing functions and finding where it is increasing, decreasing, concave up and concave down.

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

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

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

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

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

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

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

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

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)

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)

Frequently Asked Questions

Check out these resources for the multiple choice section of the AP Calculus exam. With helpful videos reviewing multiple choice questions, and the best strategies that will help. Covering all sorts of problems and all the topics of AP Calculus, these resources will give you a better understanding of what to expect on the AP Calculus exam.

Multiple Choice Questions (MCQ)

Learn about the structure of the free response questions on the AP Calculus exam. With helpful resources, practice problems and reviews of previous FRQs you will feel comfortable with all of the different types of FRQs. And learn about strategies to ensure that you know how to approach each FRQ no matter what topic it covers. 

Free Response Questions (FRQ)

Exam Review 2020

Make sure to check out this question and answer section for AP Calculus! These resources will answer all the questions you have, and will help you prepare for your exam through trivia games and review sessions. 

Q & A sessions

Get a complete overview of the AP Calculus exam to help prepare for the test. Get a refresh on all the units with helpful guides, review sheets and videos, as well as helpful tips and tricks to prepare you for your exam. 

Big Reviews: Finals & Exam Prep

AP Cram Sessions 2021

Live Cram Sessions 2020

Connecting Multiple Representations of Limits

Examples

What will you learn? 🤔

Unit 1 Overview: Limits and Continuity

Limits

Introducing Calculus: Can Change Occur at An Instant?

Discontinuities

Jump Discontinuity ↔

Point Discontinuity 🕳

Essential Discontinuity ♾️

Removable Discontinuity 🚫

Exploring Types of Discontinuities

How to Determine Continuity at a Point

Defining Continuity at a Point

Confirming Continuity Over an Open Interval

Confirming Continuity Over a Closed Interval 

Confirming Continuity over an Interval

How to Remove Discontinuities

Removing Discontinuities

Connecting Infinite Limits and Vertical Asymptotes

Answers and Review for Multiple Choice Practice on Limits and Continuity

What can we help you do now?

Multiple Choice Practice for Limits and Continuity

Multiple Choice Questions

Working with the Intermediate Value Theorem (IVT Calc)

Defining Limits and Using Limit Notation

Estimating a Limit Value: Step by Step 

Estimating Limit Values from Graphs

Example Problem ❓

Estimating Limit Values from Tables

Example Problem: Using the Sum Rule to Determine a Limit ➕

Example Problem: Using the Constant Multiple Rule to Determine a Limit ➡

Example Problem: Using the Product Rule to Determine a Limit ✖️

Example Problem: Using the Exponent/Power Rule to Determine a Limit 💥

Determining Limits Using Algebraic Properties of Limits

Example Problem: Determining a Limit Using Factoring 

Example Problem: Determining a Limit Using Alternate Forms of Trigonometric Functions 

Determining Limits Using Algebraic Manipulation

Selecting Procedures for Determining Limits

The Squeeze Theorem 🥪

Determining Limits Using the Squeeze Theorem

What is a derivative? 

Computing Derivatives

An Introduction to Differentiation ⤴

Unit 2 Overview: Differentiation

What is a Derivative? 🤔

Defining Average and Instantaneous Rates of Change at a Point

Derivatives of Special Functions, Continued!💬

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

Multiple Choice Practice for Differentiation: Definition & Fundamental Properties

Answers and Review for Multiple Choice Practice on Differentiation: Definition & Fundamental Properties


What can we help you do now?

MC Answers and Review

Derivatives Defined

Defining the Derivative of a Function and Using Derivative Notation

Estimating Derivatives

Estimating Derivatives of a Function at a Point

Differentiability Rules 📌

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

The Power Rule ✊

Applying the Power Rule

Properties of Derivatives 🚩

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

Derivatives of Special Functions 💭

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

The Product Rule ✖️

The Product Rule

The Quotient Rule➗

The Quotient Rule

Exam Weighting ⚖

Developing Understanding 🧠

Main Topics and Sections: