 is the next test that we will learn and it is related to improper integrals from Unit 6! 

We only will use the test part of the theorem but not the comparison part.


Use the integral test to determine whether the following series converges or diverges.

Integral Test for Convergence

Administration 1

Administration 2

Administration 3

AP Calculus AB/BC Exam Prep | Reviews +  Free Practice | Fiveable

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

1.0 Unit 1 Overview

AP Calc Unit 1 Trivia

1.6 Determining Limits Using Algebraic Manipulation

1.10 Exploring Types of Discontinuities

1.0 What is a Limit?

1.1 Introducing Calculus: Can Change Occur at An Instant?

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: Differentiation: Definition & Fundamental Properties

2.0 Unit 2 Overview

AP Calc Unit 2 Trivia

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

2.0 Unit 2 Overview: Differentiation

2.8 The Product Rule

2.9 The Quotient Rule

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: Differentiation: Composite, Implicit & Inverse Functions

AP Calculus AB/BC Unit 3 Trivia

Interpreting Derivatives through Tables and in context

Helping Students Master Taking Derivatives Part II (for Teachers) 

3.4 Differentiating Inverse Trigonometric Functions

3.2 Implicit Differentiation

The Chain Rule

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 the Differentiation

AP Calculus Unit 4 Trivia

4.5 Solving Related Rates Problems

L'Hospital's rule

4.6 Approximating Values of a Function Using Local Linearity and Linearization

4.3 Rates of Change in Applied Contexts other than Motion

4.4 Intro to Related Rates

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

AP Calc Unit 5 Trivia

Optimization Problems

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

5.11 Solving Optimization Problems

5.10 Introduction to Optimization Problems

Concavity

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 and Accumulation of Change

6.1 Unit 6: Integration and Accumulation of Change

6.0 Unit 6 Overview

AP Calc Unit 6 Trivia

6.0 U-Substitution

Presentation Slides, FTC and Integral Defined Functions

6.12 Using Linear Partial Fractions

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

AP Calculus Unit 7 Trivia 

7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables

7.2 Verifying Solutions for Differential Equations

7.6 Finding General Solutions Using Separation of Variables

7.4 Reasoning Using Slope Fields

7.3 Sketching Slope Fields

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

8.10 Volume with Disc Method: Revolving Around Other Axes

Position, Velocity & Acceleration

8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

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

8.7 Volumes with Cross Sections: Squares and Rectangles

8.4 Finding the Area Between Curves Expressed as Functions of x

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)

AP Calculus Unit 9 Trivia 

9.4 Defining and Differentiating Vector-Valued Functions

9.1 Defining and Differentiating Parametric Equations

Polar Coordinates and Calculus (for BC teachers)

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

9.7 Defining Polar Coordinates and Differentiating in Polar Form

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 and Series (BC Only)

AP Calc Unit 10 Trivia

10.5 Harmonic Series and p-Series

10.3 The nth Term Test for Divergence

10.6 Comparison Tests for Convergence

10.7 Alternating Series Test for Convergence

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)

AP Calculus AB/BC Multiple Choice Help (MCQ)

Calculus Multiple Choice Questions

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)

2018 Free Response Questions

Review: Table/Data Questions

2018 FRQ Review

Presentation Slides, 2016 FRQ

2019 FRQ Review

Presentation Slides, Justifying and Explaining your answers

Blogs

Perfect Memes for AP Calculus AB/BC

How to Get a 5 in AP Calculus AB/BC

Is AP Calculus AB/BC Hard? Is AP Calculus AB/BC Worth Taking?

Calculator Functions That'll Save Your Life

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

AP Calculus Game of 5s - Units 6-10

AP Calculus Game of 5s - Units 1-5

Q and A

Calculus Slides, Q and A

Q&A Student Study Session

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

Download AP Calculus Cheat Sheet PDF Cram Chart

2021 AP Calculus AB Exam Guide

2021 AP Calculus BC Exam Guide

Fall Semester Review (2019)

AP Cram Sessions 2021

🌶️ AP Calculus BC Finale Watch Party Admin 3

🌶️ AP Calculus AB Finale Watch Party Admin 3

🌶️ AP Calculus AB + BC Finale Watch Party Admin 2

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

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

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

Live Cram Sessions 2020

Slides from the Presentation

Slides from Stream

Your guide to the 2021 AP Calculus AB exam

Format of the 2021 AP AP Calculus AB exam

When is the 2021 AP Calculus AB exam and how do I take it?

How should I prepare for the exam?

Pre-work: set up your study environment

AP Calculus AB 2021 Study Plan

👑 UNIT 1: Limits and Continuity

🤓 UNIT 2: Differentiation: Definition and Basic Derivative Rules


🤙🏽 UNIT 3: Differentiation: Composite, Implicit & Inverse Functions


👀 UNIT 4: Contextual Applications of Differentiation


✨ UNIT 5: Analytical Applications of Differentiation


🔥 UNIT 6: Integration and Accumulation of Change


💎 UNIT 7: Differential Equations


🐶 UNIT 8: Applications of Integration

Your guide to the 2021 AP Calculus BC exam

Format of the 2021 AP Calculus BC exam 

When is the 2021 AP Calculus BC exam and how do I take it?

AP Calculus BC 2021 Study Plan


🤓 UNIT 2: Differentiation: Definition and Basic Derivative Rules

👀 UNIT 4: Contextual Applications of Differentiation


🦖 UNIT 9: Parametric Equations, Polar Coordinates & Vector-Valued Functions


♾ UNIT 10: Infinite Sequences and Series

Overview

📖 Content

✋ Justification

💯 Scoring

Earning Points

♾️ Derivatives

♾️ Integrals

♾️ New Representation

♾️ Appropriate Units

Part A - Calculator Section

📖 Worked Example

📊 Past Trends

📱 A Note on Calculators

Part B - Non-Calculator Section

FAQs About FRQs

Calculus Free Response Questions

Table of Contents 📊

🧠 Exam Format and Logistical Details

❓ Types of Problems 

⭕️ How to Approach MC Questions 

Multiple Choice Help (MCQ)

Overview ♾️

Format 📄

Tips and Tricks ✏️

Where to Practice 📍

Closing Thoughts 💭

Exam Weighting ⚖

Developing Understanding 🧠

Mathematical Practices ➗

Main Ideas for this Unit 💬

Unit 10 Overview: Infinite Series and Sequences

What is a Sequence?

The Limit of A Sequence

Some Notation and Terminology on Sequences

What is a Series?

Convergence and Divergence of Series

Problems

Defining Convergent and Divergent Infinite Series

How do we find the error bound?

Alternating Series Error Bound

What are Taylor Series, and how do you find them?

Finding Taylor Polynomial Approximations of Functions

What is the Lagrange Error Bound and how do we find it?

Lagrange Error Bound

Radius and Interval of Convergence of Power Series

Some Important Maclaurin Series to Remember

Finding Taylor or Maclaurin Series for a Function

What is a power series?

How can we manipulate Power Series?


Conclusion and What’s Next?

Representing Functions as Power Series

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SAT Crams

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ACT Crams

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College Guide

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College Server

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Bookmarks

10.4 Integral Test for Convergence

AP Calculus AB/BC ♾️

What is the Integral Test?

Problems

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