AP Calculus AB/BC Summer First Three Units Overview
SAT Score Range
•
10 sessions
•
BC
GL
EM
+12
This series was cancelled by the tutor on July 25, 2024. We're very sorry–you can explore more Calculus series here. All 1:1 and group chats related to this series are disabled 7 days after the last session.
About
Hello everyone!
In this series, we will go over the first three units plus one single topic from the fourth unit of the AP Calculus AB/BC curriculum:
Unit 1-Limits and Continuity
Unit 2-Differentiation: Definition and Basic Derivative Rules
Unit 3-Differentiation: Composite, Implicit, and Inverse Functions
The single topic in unit 4-Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms
Feel free to ask me to cover additional topics from other Units!
This series will start on July 2nd and it will last for about a month, with 3 classes per week and 90 minutes per class. The class dates are Tuesday, Thursday, and Saturday of each week. This series is meant to cover the content of the first three units of AP Calculus. We will go over important theorems, and formulas that it is covered in an AP Calculus class. We will also tackle AP styled questions so that you will be comfortable answering AP questions regarding these topics. This series is meant for people who just finished Algebra II or Pre-Calculus and plans to take AP Calculus AB/BC. That being said, after the completion of this series, you'll be fully prepared for your AP Calculus class next school year. Please look at the class dates for more description on the topics covered each day.
Additional notes: There will be a quick warm up question each lesson to refresh our mind about last lesson's topics. I will assign homework each lesson via google form but you DO NOT need to do it, it is on you if you feel like you want more practice. If you choose to do the homework, you will receive your grades back from google form. There will be a unit test for units 1 and 2 plus a final exam on ALL of the units. Once again, you do not need to do any test if you do not want to. The tests are there just for you to know your current understanding about the topics.
Have fun!
Tutored by
Hi, I’m Jiarui! 👋 I’m a senior from Upstate NY who’s really into math and science. I also love exploring new interests outside of school. You’ll usually find me playing tennis or soccer, spending time with friends, or experimenting in the kitchen as I learn how to cook. I enjoy tutoring and sharing what I’ve learned just as much as I enjoy picking up new things myself. Excited to be part of this community and connect with more people who love learning too! 🚀
Schedule
✋ ATTENDANCE POLICY
I am not really strict on attendances. I believe that if you really want to skip, there is nothing I can do to stop you from doing so. You are free to attend/skip whichever sessions you want. You will NOT be withdrawn from the series. That being said, I strongly advise you to attend all sessions since more class time will help you learn all the materials faster and digest it better. If you choose to skip a day's lesson, make sure that you check your messages as I will try to post each lesson's PDF and homework on there.
SESSION 1
2
Jul
SESSION 1
Office Hours
Office Hours
Tue 4:00 PM - 5:15 PM UTCJul 2, 4:00 PM - 5:15 PM UTC
I am going to introduce myself and go over our class expectations, class structures, the syllabus, and many more. This class will take about 30-45 minutes and I will stay for another 30 minutes just in case there are questions. Feel free to ask any questions about this series!
SESSION 2
4
Jul
SESSION 2
Limits and continuity
Limits and continuity
Thu 4:00 PM - 6:00 PM UTCJul 4, 4:00 PM - 6:00 PM UTC
We will start by introducing limits and how to evaluate limits based on graphs and tables.
Key question: What is limit in calculus?
Key topics:
1. Defining Limits and Using Limit Notation
2. Estimating Limit Values from Graphs
3. Estimating Limit Values from Tables
The last 30 minutes will be office hours, feel free to ask any questions!
SESSION 3
6
Jul
SESSION 3
Limits and continuity
Limits and continuity
Sat 4:00 PM - 6:00 PM UTCJul 6, 4:00 PM - 6:00 PM UTC
We will start with a warm up question and continue learning about limits!
Key topics:
1. Finding Limits of Piecewise Functions
2. Determining Limits Using Algebraic Manipulation
3. Exploring Types of Discontinuities
The last 30 minutes will be office hours, feel free to ask any questions about homework and other things!
SESSION 4
11
Jul
SESSION 4
Limits and continuity
Limits and continuity
Thu 4:00 PM - 6:00 PM UTCJul 11, 4:00 PM - 6:00 PM UTC
We will start with a warm up question and continue learning about limits!
Key topics:
1. Define Continuity at a Point
2. Confirming Continuity over an Interval
3. Removing Discontinuities
The last 30 minutes will be office hours, feel free to ask any questions about homework and other things!
SESSION 5
13
Jul
SESSION 5
Limits and continuity
Limits and continuity
Sat 4:00 PM - 5:00 PM UTCJul 13, 4:00 PM - 5:00 PM UTC
We will start with a warm up question and finish learning about limits!
This is the last topic of limits and this class will be shorter than usual as we are only covering one key topic.
Key topic:
1. Working with the Intermediate Value Theorem (IVT)
Reminder:
Unit test on limits and continuity next class.
You do not need to take the test if you do not want to. The test is just for reviewing purposes and a way for you to check your understandings.
The last 30 minutes will be office hours, feel free to ask any questions about homework and other things!
SESSION 6
16
Jul
SESSION 6
Limits and continuity
Limits and continuity
Tue 4:30 PM - 6:00 PM UTCJul 16, 4:30 PM - 6:00 PM UTC
NO warm up today!
Today is our test day: Unit 1-Limits and Continuity
20 MC questions in 60 minutes
After 60 minutes, I will stay for another 30 minutes. Feel free to ask any questions about homework, the test, and other things!
SESSION 7
18
Jul
SESSION 7
Differentiation: definition and basic derivative rules
Differentiation: definition and basic derivative rules
Thu 4:00 PM - 6:00 PM UTCJul 18, 4:00 PM - 6:00 PM UTC
We will start by introducing basic derivatives (differentiation).
Key questions: What is a derivative? What does it mean?
Key topics:
1. Defining the Derivative of a Function and Using Derivative Notation
2. Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
3. Applying the Power Rule
Important note: This is the easiest derivative rule and more difficult ones will be discussed next class. Please start memorizing the rules starting in today's class.
The last 30 minutes will be office hours, feel free to ask any questions!
SESSION 8
20
Jul
SESSION 8
Differentiation: definition and basic derivative rules
Differentiation: definition and basic derivative rules
Sat 4:00 PM - 6:00 PM UTCJul 20, 4:00 PM - 6:00 PM UTC
We will start with a warm up question and continue learning about basic derivatives!
Key topics:
1. Derivatives of Cos(x), Sin(x), e^(x), and ln(x)
2. The Product Rule
3. The Quotient Rule
Important note: As you can see, we are learning more derivative rules and they are getting harder! Please start memorizing the rules!
The last 30 minutes will be office hours, feel free to ask any questions about homework and other things!
SESSION 9
23
Jul
SESSION 9
Differentiation: definition and basic derivative rules
Differentiation: definition and basic derivative rules
Tue 4:00 PM - 6:00 PM UTCJul 23, 4:00 PM - 6:00 PM UTC
We will start with a warm up question and finish learning about basic derivatives!
This is the last topic of basic derivatives and this class will be shorter than usual as we are only covering two key topics.
Key topic:
1. Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
2. Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms(Unit 4 topic but it goes back to Unit 1: Limits)
Reminder:
Unit test on Differentiation: Definition and Basic Derivative Rules next class.
Please memorize ALL the derivative rules.
You do not need to take the test if you do not want to. The test is just for reviewing purposes and a way for you to check your understandings.
The last 30 minutes will be office hours, feel free to ask any questions about homework and other things!
SESSION 10
25
Jul
SESSION 10
Differentiation: definition and basic derivative rules
Differentiation: definition and basic derivative rules
Thu 4:00 PM - 6:00 PM UTCJul 25, 4:00 PM - 6:00 PM UTC
We will start with a warm up question and finish learning about basic derivatives!
This is the last topic of basic derivatives and this class will be shorter than usual as we are only covering two key topics.
Key topic:
1. Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
2. Review for Unit 2 test!
Reminder:
Unit test on Differentiation: Definition and Basic Derivative Rules next class.
Please memorize ALL the derivative rules.
You do not need to take the test if you do not want to. The test is just for reviewing purposes and a way for you to check your understandings.
The last 30 minutes will be office hours, feel free to ask any questions about homework and other things!