AP Calculus AB, BC

File:Gottfried Wilhelm von Leibniz.jpgWhy should I learn Calculus?

If you have finished trigonometry/precalculus successfully, you have the knowledge required to understand calculus.  Calculus is the language with which this universe operates.  And calculus is the language with which scientific concepts are described.  To be a part of the intellectual circle, to converse with your internship mentor in a meaningful way, you must speak their language.

Once you know calculus, the number of science research topics you can handle at least triples in general, and those new ones are the higher level (=likely to win) ones.

At a practical level, scoring a 5 (=highest) on AP Calculus BC is an indisputable way of stating that you know all of Algebra 1 & 2, Geometry, Trigonometry, and Precalculus.  Not to mention calculus.  No matter which school you go to, it is likely that you will be placed in the math course of your choice after you present them with your AP test grade of 5.

It also makes you stand apart from the herd.  Here is a good explanation on the reality you are facing: A Perspective on Math Education for Top Students

I am busy now.  Why should I learn Calculus now?

You need to learn calculus when you are ready and when you have a chance because you will have to take it anyway sometime before you graduate from high school if you are aiming for top colleges or a career in science.  The shocking truth is that you are not so busy now.  This will become clear to you only when you look back a year or two later.  If you don’t have time to study calculus now, you will have less time later when you will find yourself having to take calculus on top of many other AP courses later.  When you realize this for yourself, it will be too late.  You will just have to muddle through enjoying less, learning less, and possibly getting a lower grade.  By having studied calculus, and also having done the AP test, you will not only enjoy the benefits of the knowledge in your science research topic selection and internship opportunities, but also have time to study deeper and enjoy more other subjects in your un-stressful schedule.

How is this course taught?

This course is taught as a live class via the Internet.  Using WebEx software and webcams, you will see and talk to the teacher and your classmates as if everyone is in the same room.  This means you can take this course from anywhere in the world with the Internet access.

All classes are recorded and provided to students for download/replay.  By downloading them, you can keep and review the lectures indefinitely.

We also offer pre-recorded lectures we call e-Learning.  These are lectures are short (under 5 minutes) and to the point without any distractions.  These lectures also use animations and simulations extensively to make understanding intuitive and instinctive.  A large part of teaching will be done by this e-Learning and students are expected to study them before joining the class.

Students learn calculus everyday school day in school.  How can you cover everything by teaching once a week?

There is no way we can cover everything by learning 90 minutes a week.  Although we will set up “office hours” in which you can ask questions, most of the learning will actually happen during 1. e-Learning lecture study and 2. your self study with the textbook.  In other words, you will do the most studying on your own.  That’s the right way and the only way for you to learn well.  If you study only during our class time, you will not do well on the AP test.

Will there be homework?

Most definitely.  Some will be online homework that is automatically graded, others will be graded manually.

How many hours per week do I need to spend to study for this course?

We expect students to spend from 3 to 5 hours a week on their own to study.  This does not include class time or office hours.

Why are there two different AP Calculus tests?

That’s how College Board made it.  Calculus AB test covers A and B while Calculus BC test covers A, B and C.  As you can see below, C is the smallest part of three.  It takes about half as long to learn C compared to B.  It is wise to study a little more to cover up to C, then take the higher AP Calculus BC.

Will I be able to get a 5 (perfect score) in AP Calculus BC if I take this course?

Yes, if you do all the assignments honestly.

What are the requirements for this course?

  1. You must have a headset communicate with the teacher.
  2. You must have a tablet to write during the class
  3. You must have a webcam (any of these models will work) to show your attitude to the teacher and classmates.
  4. Must have obtained 90% or higher on Trigonometry at Sabio Academy or Equivalent
  5. For those who didn’t take Trigonometry at Sabio Academy must take CM 100 before starting this course
  6. Must have the latest version of Mathematica (Purchase Mathematica) installed on the computer used for attending class.

Who is teaching this course?

The instructor is James Choi.

Do I need to buy a textbook?

Yes. This is the official textbook that everyone must have.

In addition, we recommend the following books below.  We use three low priced books to encourage students to own a handy calculus library as explained this column: Have a Personal Textbook Library On The Cheap

The materials taught in AP Calculus didn’t change much for the last 50 years.  Thus using a book published 30 years ago won’t make any difference.  It is always to better have multiple reference books because invariably you will find some book easier to understand than others depending the chapter.

Do I need a calculator?

Yes.  AP Calculus test requires you to use a calculator for 50% of the test.  You will need to have a TI Nspire CAS calculator from the start to become completely familiar with it.  We are using Mathematica to understand the concepts (that’s why we don’t need color calculator), but we cannot take Mathematica to the test.  Thus we will also learn how to do the same in a much less powerful way using Nspire.  If you must, you can also buy a colored version TI Nspire CX CAS which costs about twice.

Do I need to use Mathematica for this class?

Yes.  Mathematica is an integral part of this class.  You are already expected to know how to Plot, Manipulate, Graphics already.  We will teach you how to do calculus on Mathematica in this class.

Why do you use Mathematica in this course.  No one else is using it to teach Calculus?

Of all types of mathematics, calculus is the most visual subject of them all.  In fact, those who are good at calculus are those who are good at visualizing.  Once visualized, most students can understand calculus intuitively and instinctively without having learn all these theorems and proofs.

However, until now, everyone has been forced to learn it analytically, that is, by using equations and symbols.  Those, only those who born with visualization skills found it easy while the rest of us remembered it as a nightmare.  If we could learn the same concept with shapes and movements, then the whole calculus and multivariable calculus will become trivially simple.  Mathematica is the tool that makes visualization possible.

When does the course start?

Contact the Sabio office.

How much is the tuition?

3 Payments of $899 each = $2697  (early registration discount)
3 payments of $990 each = $2970  (if paid on time)

How do I enroll in this course?

  1. (Only if this is your first Sabio course) Fill out this form and pay $50 registration fee to create your ID/password in our database.
  2. Make sure you checked all the requirements above, then make an appropriate payment below by clicking the session of your choice.
  3. If paid before TBD (early registration) $899  Afterwards $990
    • Enroll in TBD session
    • We may open another session.  Please let us know your time preference.
    • Installment 2 if paid before TBD $899 Afterwards $990
    • Installment 3 if paid before TBD $899 Afterwards $990

Syllabus (follows Calculus: Early Transcendentals 6e James Stewart)

Calculus A
13 Sessions of 90 minutes each

  1. Limits and Derivatives
  2. Differential Rules
  3. Application of Differentiation

Calculus B
15 Sessions of 90 minutes each

  1. Integrals
  2. Applications of Integrals
  3. Techniques of Integration
  4. Further Applications of Integration
  5. Differential Equation

Calculus C
8 Sessions of 90 minutes each

  1. Parametric Equations and Polar Coordinates
  2. Infinite Sequence and Series

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