#### Calculus

#### Calculus

### Calculus Series

## Road to a 5: AP CALCULUS AB AND BC WITH 5 SCORERS

9th session

This summer-long course will cover all 8 units of AP Calculus AB + the 2 additional units of AP Calculus BC BEFORE the school year begins. Essentially, Calculus BC includes all of AB + 2 additional units: Polars/Parametrics/Vectors and infinite sequences/series. Structure of the Series: 1. Office hours/Makeup session: - Will always be an hour before the official session - A space where you can ask questions on past assessments or problem sets - You can ask any AP Exam question in general - I will catch you up on anything that you have missed from a previous session 2. OFFICIAL SESSION: - lecture style w/notes - Problem Sets assigned PER "UNIT" - Official AP Exam Questions

Rodrigo N

## AP CALCULUS AB/BC REVIEW - MCQ + FRQ

2nd session

Review Core Concepts: Reinforce your understanding of key concepts in calculus, including limits, derivatives, integrals, and series. Practice Multiple Choice Questions (MCQs): Tackle a wide range of MCQs to test your knowledge and improve your problem-solving speed and accuracy. Work Through Free Response Questions (FRQs): Develop your ability to articulate solutions clearly and concisely through practice with past exam FRQs. Clarify Difficult Topics: Get personalized help on challenging areas to ensure you have a comprehensive understanding of the material. Exam Strategies: Learn effective strategies for tackling both the MCQ and FRQ sections

David S

## AP Calculus® Summer Bootcamp (2024-25)

9th session

In this series we will be going over the AP Calculus AB/BC curriculum in a lecture-style format with tons of practice along the way. This series is perfect for anyone taking AP Calculus in the upcoming school year as we’ll spend time on various concepts to not only get you ready for AP Calc, but to fully understand it for the AP national Exam. Note: All sessions have not been added, however there are only 4 more (reflected on syllabus). This series will end on August 22, 2024 -- Syllabus: [https://www.dropbox.com/scl/fi/pycxtn037zvay601f15zd/Syllabus-AP-Calc-Summer-2024-Bootcamp-3.pdf?rlkey=imq7wbft89tb08uc96wdb0x60&e=1&st=5bgmngz4&dl=0](https://www.dropbox.com/scl/fi/pycxtn037zvay601f15zd/Syllabus-AP-Calc-Summer-2024-Bootcamp-3.pdf?rlkey=imq7wbft89tb08uc96wdb0x60&e=1&st=5bgmngz4&dl=0) [](https://www.dropbox.com/scl/fi/pycxtn037zvay601f15zd/Syllabus-AP-Calc-Summer-2024-Bootcamp-3.pdf?rlkey=imq7wbft89tb08uc96wdb0x60&e=1&st=5bgmngz4&dl=0) Course structure: Instead of using existing lecture notes or following the order of the AP Calc curriculum, I have optimized the structure of our sessions so that we maximize the time learning important concepts and for understanding them. At the end, you will end up learning majority of the course. And by doing the practice problem sets (discussed later), you could master the entire curriculum. Lecture Notes: These will be posted in advance of about 2-3 sessions. You do not have to worry about printing them as they would be very minimal and I promote the idea of writing as I go so we all can stay at a good pace. Please write along as I do so that you can take the complete benefit of our sessions. Practice Problem Set and Homework: While each session will be done with the assumption that you haven't done the practice problems, they are still there for your benefit. However, in my many semesters of being in calculus classes, those who grind practice problems are the most successful. There is almost a direct correlation. Note about structure of sessions: Even though they are just 1hr 15min, I have left 45 minutes after our session for those who want to stay and ask me questions and/or go over additional practice. I will be available entirely from 3pm to 5pm. But for those who are feeling fine can leave freely! [](https://www.dropbox.com/scl/fi/pycxtn037zvay601f15zd/Syllabus-AP-Calc-Summer-2024-Bootcamp-3.pdf?rlkey=imq7wbft89tb08uc96wdb0x60&e=1&st=5bgmngz4&dl=0) Questions/Talk to me: I will dedicate my time to entirely ensuring that every student in my session is able to understand the concepts completely. I will always be available to ensure that you understand the concepts and practice problems. And if you have any other questions about high school, college admissions, etc, feel free to let me know!

Ammar R

## Get a 5! - AP Calculus BC/Calc II in a Month

10th session

I got a 5 on the AP Calculus BC exam, and you can too. Having previously taught Calculus 1 (the AB curriculum) and now seeing the staggering amount of demand for further maths, I've decided to host this intensive, yet comprehensive series on Calculus 2, including a FULL work-through of a real past exam. The first two sessions will serve as a review of differential calculus. Below are what we will cover: INTEGRATION AND APPLICATIONS (UNIT 1) 1. Introduction to accumulation of change 2. Left and right Riemann sums; over and under-approximation 3. Midpoint and trapezoidal sums 4. Definition of indefinite integral using as the limit of Riemann sums 5. The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals 6. Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation. 7. Integrating sums of functions, switching the bounds of integration, and with functions as bounds. 8. The reverse power rule, u-substitution, and integration by parts 9. Antiderivatives of all the previously mentioned functions 10. Improper integrals 11. Finding the average value of a function on an interval 12. Connecting position, velocity, and acceleration functions using integrals 13. Using accumulation functions and definite integrals in applied contexts 14. Finding the area between curves expressed as functions of x 15. Finding the area between curves expressed as functions of y 16. Finding the area between curves that intersect at more than two points 17. Volumes with cross sections: squares and rectangles 18. Volumes with cross sections: triangles and semicircles 19. Volume with disc method: revolving around x- or y-axis 20. Volume with disc method: revolving around other axes 21. Volume with washer method: revolving around x- or y-axis 22. Volume with washer method: revolving around other axes 23. The arc length of a smooth, planar curve and distance traveled 24. Calculator-active practice DIFFERENTIAL EQUATIONS (UNIT 2): 1. Modeling situations with differential equations 2. Verifying solutions for differential equations 3. Sketching slope fields 4. Reasoning using slope fields 5. Approximating solutions using Euler’s method 6. Finding general solutions using separation of variables 7. Finding particular solutions using initial conditions and separation of variables 8. Exponential models with differential equations 9. Logistic models with differential equations PARAMETRIC EQUATIONS AND VECTOR-VALUED FUNCTIONS (UNIT 3): 1. Defining and differentiating parametric equations 2. Second derivatives of parametric equations 3. Finding arc lengths of curves given by parametric equations 4. Defining and differentiating vector-valued functions 5. Solving motion problems using parametric and vector-valued functions 6. Defining polar coordinates and differentiating in polar form 7. Finding the area of a polar region or the area bounded by a single polar curve 8. Finding the area of the region bounded by two polar curves 9. Calculator-active practice INFINITE SERIES (UNIT 4): 1. Defining convergent and divergent infinite series 2. Working with geometric series 3. The nth-term test for divergence 4. Integral test for convergence 5. Harmonic series and p-series 6. Comparison tests for convergence 7. Alternating series test for convergence 8. Ratio test for convergence 9. Determining absolute or conditional convergence 10. Alternating series error bound 11. Finding Taylor polynomial approximations of functions 12. Lagrange error bound 13. Radius and interval of convergence of power series 14. Finding Taylor or Maclaurin series for a function 15. Representing functions as power series

Jose Roberto Cossich G

## Unit 2 AP Calc w/ guided notes

Starts

This unit will take a week to complete with one hour of instruction on Monday Wednesday Friday.

Arhan J

## AP Calculus AB/BC Curriculum

3rd session

Twice a week, we'll build on the Calculus curriculum, in order to get the perfect score! After getting a 5 on my test, I know exactly how to drill and learn the techniques necessary for good test taking. We'll crunch during the summer, and I'll highlight AB/BC topics as necessary. If you're taking AB next year, but want to get a head start, or if you're preparing for BC, this series is for you!

Anika M

## Learn Calculus the AP Way

Starts

Each session will bring you closer to understanding more about Calculus AB. We'll be learning Calculus the AP way by looking at past questions and areas students usually find difficult.

Tara O

## AP Calculus AB

4th session

Goes over everything needed for AP Calculus AB. Spans 14 sessions, and was initially taylored to one person but others can join as well.

William B

## AP Calculus AB/BC Overview + Practice Questions with 5 Scorer

15th session

This series is for prospective AP Calculus AB/BC students. We will be covering all units in AP Calculus BC (which includes all units of AP Calculus AB) and will solve questions from Barron's and Past Papers. All learners are expected to prepare a graphing calculator for every session.

Jeesung L

## AP Calculus BC

19th session

We will cover each unit for AP Calculus BC. We will also cover all AP Calculus AB material needed for the BC exam since AB is approximately 60%. We will also do official CollegeBoard MCQs and FRQs from the past 15 years. There will be notes provided but it is up to the learner's discretion to jot them down. Additionally, a graphing calculator is necessary to be able to do certain problems.

Johanna P

## Summer Calc!!

5th session

Each week we will dive into calculus to prepare you guys for school in the fall

Thrista V

## Get Ready For AP Calculus AB

3rd session

I will be covering Units 1-8 of the Collegeboard AP Calculus AB course. I will be following the Collegeboard curriculum. This course will require around 1-2 hours of work outside of our sessions because I am very briefly running through these topics (each unit has 5-14 topics) as a prep course for AP Calc AB. By the beginning of August, my goal is to cover all of Unit 1, so that you are all prepared for the upcoming school year. During our sessions, I encourage you to ask questions and try your best to participate and work through problems.

Deepthi S

## AP Calculus BC: Proofs and Applications

2nd session

From the abstract theory to effortless applications, this series will be an overview to everything a student will encounter in a Calculus BC class. Not only will students know the simple tricks to integrals and derivatives, the tutors will also explain the proofs and allow students to understand the WHY in the realm of Calculus. We will go over all the necessary topics in a typical calculus class - from simple derivatives all the way to Taylor Series and understanding advanced polar graphs. There will be multiple tutors hosting this series to ensure that all students understand the content thoroughly. All tutors are REQUIRED to have at least a 5 on the AP Calculus BC test, to best ensure the quality of the bootcamp. With the high quality of the bootcamp, students are required to attend every single session. If a student misses more than 2 sessions without prior notice, they will be booted for taking up a valuable spot of the series. To take the most out of the course, students should have a prerequisite of at least a precalculus or Algebra 2 class. Spots are LIMITED - only the first 15 people may sign up. First come, first serve.

Coly J

## Flipped Classroom - AP Calculus AB Summer Crash Course

4th session

This five-week series will function with a flipped classroom - meaning you'll learn topics in your own time, practicing and ask questions during the sessions. This series is designed to be very fast paced and learner-oriented, so expect to be active in sessions and dedicate some time to learning whenever it fits your own schedule! I will not be giving lectures. Communication through microphone is preferred, but I understand completely if you would rather use the chat. Sessions will be twice a week on Wednesdays and Sundays at 7:30 PM PT. The plan is to cover the AP Calculus AB curriculum by mid-August. If you plan on registering as a learner, please read the following: Outside sessions: - Watch videos and do Khan Academy practice problems - Write a problem and solution (this isn't nearly as hard as it sounds, don't fret!) During sessions: - We'll start off by checking in to see if there's any specific questions from learners - Learners will pick a topic from what we're covering that session and give a brief explanation, presenting their practice problem (other learners will try to solve it and give feedback on the problem) - We'll wrap everything up with some more practice problems! This can all sound very intimidating at first, but it'll get easier with practice! AP Calculus AB can be challenging, and I hope that this series helps serve to prepare for that challenge during the school year. Resources are currently TBD. Co-hosts welcome (please DM first)!

Margaret S

## Get Ready for AP Calculus AB with a 5-Scorer!

3rd session

Hello! Welcome to the AP Calculus AB Crash Course! In this series, we'll aim to get through the entire AP Calculus AB course. I'll also give you tips on how to prepare for the class & exam! Each session will have a unique focus that will be outlined in the individual descriptions. Generally, we'll do some notes followed with some fun, interactive practice! Also, please make sure you have a basic understanding of Algebra & Pre-Calculus. It's completely okay if you struggle with some Pre-Calculus topics, but a strong understanding of Algebra (especially solving equations) is really important. As we go on this learning journey together, I hope that you end up enjoying Calculus as much as I do! PS - I'll keep adding sessions as we go along! :)

Srishti W

## Ultimate AP Calculus AB/BC Summer Series

3rd session

Each week, we will go over one unit in the entire AP Calculus AB/BC course. Every session will also include a bunch of previous free-response questions and multiple-choice questions relevant to the topic.

Francis Anthony G

## Crash Course Calculus - Limits, Derivatives, Integration, and More!

6th session

We'll go through the basics of calculus and cover some important concepts. This would be a great introduction for anybody looking to take calculus in the next year and a great review for people who have taken it and are looking to review. This curriculum is definitely not set in stone, I am extremely flexible and would love to teach what you guys would like to learn in calculus!

Bill C

## Rigorous Calculus Course

2nd session

In this series we will cover the proofs behind well known theorems in Calculus. Learners will learn the techniques and strategies involved in proving and deriving mathematical theorems, as well as achieve a deeper understanding of each theorem they prove. Learners will engage by answering questions and doing exercises that will guide them to understand the proofs.

Thomas S

## AP Calculus AB/BC Unit 1-5 Overview

Starts

Goal: Headstart during the summer For: Anyone who are taking AP Calculus AB/BC next year and want to headstart before the school Date: this series will start on July 22nd and will last for 4 weeks(2 classes per week). Class Time: 90 min per class (last 30min is office hour for homework) In this series, we will go over the first 5 units of the AP Calculus AB/BC curriculum. 1. Unit 1: Limits and Continuity(2 days) 2. Unit 2: Differentiation: Definition and Basic Derivative Rules(2 days) 3. Unit 3: Differentiation: Composite, Implicit, and Inverse Functions(1 day) 4. Unit 4: Contextual Applications of Differentiation(1 day) 5. Unit 5: Analytical Applications of Differentiation(2 days) Class Overview: 1. 3-5 Warm-up questions 2. Lecture with slideshow (will provide pdf notes if you need) 3. Homework after each class 4. Makeup session will be announced in each class 5. AP questions will be assigned in google form (not required)

Hyunji K

## AP Calculus BC August Bootcamp

Starts

Content: This series will be covering AP Calc BC at a fast pace. We will cover all the content and do a final practice session while doing practice problems along the way. Expectations: Learners are required to actively engage and enjoy Calculus as well as ask plenty of questions. We may also have games and fun activities for review at the beginning of each class. Prerequisites: Learners must have completed Precalculus through self-study or as a course and be ready to learn a lot of topics in a short amount of time. Homework policy: Homework will contain the topic's practice so please make the time to finish the homework and the assessments. Materials needed: * Paper and pencil/pen to take notes * Calculator (optional for this Bootcamp but required for the AP exam) - we may cover some aspects of the calculator. I hope to see you there!

Rajalakshmi S

## AP Calculus Exam Prep

Starts

We'll go over two AP Calculus practice exams, as well as the FRQ sections from 2024, 2023, and 2022.

William B