BL
AR
Ammar R
Series Details
About
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
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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 could 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!
Syllabus: There will be one available in the future! Ill send out an update once it its!
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!
✋ ATTENDANCE POLICY
Please try your ultimate best to attend every session, and let me know if you would have to miss a session so that we can work out how to cover the content for what you would've missed.
Dates
July 8 - August 19
Learners
12 / 30
Total Sessions
25
About the Tutor
BL
AR
Hi, I'm Ammar, an undergraduate student at Emory University who's passionate about math and science while still giving love to computer science/programming. I am planning on majoring in Chem and Physics. Please feel free to reach out to me with any questions, I am always available for advice or what not.
View Ammar R's Profile
Upcoming Sessions
25
8
Jul
AC
Session 1
AP Calculus
In this session, we will review some pre-calculus concepts (e.g. rational functions) and give a brief introduction to what is to come in calculus! I hope this session will give you the feel of how chill and productive we can be for the upcoming weeks together!
9
Jul
AC
Session 2
AP Calculus
In this session, we will continue working with the idea of limits and continuity, specifically: finding limits from graphs, what are one-sided limits, representing horizontal and vertical asymptotes as limits, and exploring discontinuities.
10
Jul
AC
Session 3
AP Calculus
In this session, we will continue working with limits but introduce how we can use algebraic manipulation to determine limits (e.g. direct substitution, factors/cancel). We will also talk about in some cases where limits cannot exist. This will be a practice heavy session, so everything we've learned so far would be given light.
11
Jul
AC
Session 4
AP Calculus
We will start today's session with a Q&A of the practice questions/homework questions. Then begin talking about how we can confirm continuity over integrals, continue practicing our skills of limits. Towards the end introduce the Intermediate Value Theorem (IVT). I know there are alot of concepts coming your way, so keep up with the practice and I'm sure you would get them!
15
Jul
AC
Session 5
AP Calculus
We'll start the session by putting everything together and seeing how it connects. If you are confused on what is going on, it should start coming together. If time permits, we will go over some practice MCQ.
16
Jul
AC
Session 6
AP Calculus
This session will be very heavy on the concepts of derivatives. I will begin very conceptual (such as what is an instanteous rate of change), then move onto finding rate of change (average and/or instatenous) from graphs. After we feel like we have the hang of it, I’ll slowly bring in the calculus. Then, knowing limits, lets use the definitions of a derivative to compute them for a given function. Finally I’ll show the tricks we will begin using to save us ourselves time.
17
Jul
AC
Session 7
AP Calculus
Continuing from the end of the previous lecture, how can we use techniques to help us solve derivatives, and can our TI84 do it? We’ll discuss the power rule, product rule, quotient rule. Briefly touch on chain rule as well. I understand you might be completely lost after this session, but don’t give up! Try following my steps through the practice problems and you will get it!
18
Jul
AC
Session 8
AP Calculus
We have learned so much over the past 2 sessions, lets just practice this whole session and I will show you tips and tricks that you can also use to help you find derivatives. This will take alot of practice, but I am more than confident that you can do it!
22
Jul
AC
Session 9
AP Calculus
New week, new concept. Let’s begin identifying the following on a graph: minimums, maximums, absolute minimums, absolute maximums, intervals of increase/decrease, etc. Then we’ll end the session with using our derivation techniques to find out those properties on a graph.
23
Jul
AC
Session 10
AP Calculus
This session will begin with the idea of a second derivative and what it means graphically. And then lets apply this to the idea of concavity. Afterwards, we will continue practicing what we’ve learned this week while applying last week’s material.
24
Jul
AC
Session 11
AP Calculus
Let’s do another concept, physics. In this session, we will apply the concepts of derivatives to straight-line motion through position, velocity, and acceleration. Since this is just an application of what we know, we will continue the session with doing additional practice problems of what we’ve done since last week.
25
Jul
AC
Session 12
AP Calculus
In this session, lets end the week with doing implicit differentiation and related rates. Additionally work on some word problems applying related rates and straight-line motion. If time permits, I’ll get you started on an FRQ which you’ll submit before the next session.
29
Jul
AC
Session 13
AP Calculus
We’re almost done with derivation for now, so let’s start connecting a function, it’s first derivative, and its second derivative. This will go back to understanding whether a particle is speeding up or down. And looking at the behavior of implicit relations.
30
Jul
AC
Session 14
AP Calculus
This session we’ll look at linear approximations of functions and use L’Hopital’s rule for determining limits of indeterminate forms.
31
Jul
AC
Session 15
AP Calculus
We’ll move away from differentiation and begin to understand the concept of integration and the accumulation of change. In this session, we’ll learn to approximate areas under curves using Riemann sums, look at the summation notation and what the notation for a definite integral looks like.
1
Aug
AC
Session 16
AP Calculus
I know we’ve going fast already with all these concepts, but let’s keep it up and stay strong! In this session, we’ll look at the Fundamental Theorem of Calculus and interpret the behavior of accumulation functions that involve area. And end off by seeing some techniques of how we can take antiderivatives.
5
Aug
AC
Session 17
AP Calculus
Let’s begin the session by reviewing what we know about defininate integrals, and introduce indefinate integrals. Understand why we have a +C in our answer. And we’ll continue to practice taking antiderivatives while seeing how our Riemann sums approximations compare.
6
Aug
AC
Session 18
AP Calculus
In this session, we’ll learn to integrate with substitutions (u-sub) and briefly introduce the idea of integrating functions using long division and completing the square. I will leave off this bit for the practice problem set as it’s algebra heavy and not a calculus concept per-se.
7
Aug
AC
Session 19
AP Calculus
From today there will be a structure change. The 45 minutes would be dedicated to our normal AB lesson, then the remaining time would be BC concepts. AB students can stay on and continue to practice and can ask questions once the BC lesson is over (approx 40 min as well).
Today’s session would be to use integrals to find the average value of a function on an interval. And go back to 1D motion and apply integrals.
Then for BC students, we’ll learn the technique of integrating by parts, and prove it using the product rule.
8
Aug
AC
Session 20
AP Calculus
In today’s session, we’ll find area between curves with respect to x. Then for BC, we’ll continue integrating by parts and introduce the algebra behind partial fractions. The idea of evaluating improper integrals will be left for practice problems.
12
Aug
AC
Session 21
AP Calculus
Continuing from last session, we’ll find area between curves with respect to y. Then for BC students, we’ll introduce the idea of a convergent and divergent infinate series and what is a sequence. AB session should be way shorter today with a long BC focus.
13
Aug
AC
Session 22
AP Calculus
Today’s session we’ll begin with the idea of a differential equation and mainly focus on verifying solutions for differential equations. Then for the BC portion, we’ll begin to understand our FIRST test, the nth-term test for divergence. Also, slightly introduce what are harmonic and p-series.
14
Aug
AC
Session 23
AP Calculus
We’ll continue with differential equations today and guide ourselves into sketching slope fields briefly and start practicing on the idea of seperation of variables. Then for BC students, we’ll understand Euler’s method. I would recommend AB students to also understand Euler’s method as its very nice and won’t distrupt from what you already understand.
15
Aug
AC
Session 24
AP Calculus
Let’s continue practicing with differential equations and just introduce solutions using initial conditions while also seperating variables. Then for BC students, we’ll look at parametric equations and their derivatives.
19
Aug
AC
Session 25
AP Calculus
In this session, we’ll look at exponential models with differential equations and continue practicing with some MCQ. Then for BC students, we’ll look at arc lengths of curves, integrating vector-valued functions and solving 1D motion problems using parametric/vector-valued functions.