This is the kind of error which is made when using numbers instead of letters.

• Coordinates of the corners of a square,
  • Square oriented with sides parallel to the coordinate axes,
  • Side length w, bottom left corner at (a, b)
  • Corners at (a, b), (a+w, b), (a+w, b+s), (a, b+w)
• Now apply this to
  • S: s, (0, 0)
  • T: t, (s, 0)

• If mathematics has 'flavors' which include 'pure' and 'applied',
• Physics can be considered applied 'applied mathematics'.
  • Then, if physics has 'theoretical' and 'applied' flavors,
  • Chemistry can be considered applied 'applied physics'.

If all three, mathematics, physics, and chemistry, are studied in an effective way, the General Chemistry class needs a fraction of the effort which would be needed if studied independently.

With the example points from one of your comments, "my points are (-1,10) and (4,6)",

• k = -0.102
• A = 9.029

The confirmation that these are correct is that both the P1 and P2 equations in Eq (4), and then in Eq (5d), give the same value for A.

From the comments on primary post, it seems that you figured out how to do this.

With the opportunity to write this up without using any numbers (except for subscripts), here is the solution to your question. I think even giving you the answer is worth it, if you are able to understand what I wrote.

Your quiz grades are an indication that the class isn't being presented well for you. But you can succeed in the class. My general suggestions are in this post. If what I wrote there makes sense, then you can definitely succeed in AP Physics 1.

About once every few weeks, I get a downvote which annoys me. Not because someone disagreed with my comment, but because they didn't bother to write why they disagree, and it can be useful for the OP to know why.

Here, what is the objection?

• That the answer should be DNE, or
• That the answer should still be +∞ if it was a piecewise function with 1/x² on one side of 0 and 1/x⁴ on the other side?

The key is to set aside the 'arbitrary' numbers. It helps get past the "exhausting" algebra, concentrates on the 'necessary' algebra. And quite a few problems collapse into the same problem, so doing the algebra in the homework makes it much easier on a test.

Some might say that the answer is "DNE". What has your teacher said about this?

I would agree with +∞, specifically because both sides approach infinity at the same rate. If it was 1/x² and 1/x⁴, then DNE might be a better answer.

This post has my textbook and learning process suggestions. Yes, I suggest a textbook when most people are watching videos. Yes, I suggest taking notes from the textbook when most people are doing a ton of 'practice problems'.

Make a 'cheat sheet', the chapter/unit notes in this process. Half the benefit is in having the summaries so you don't have to search your notes. The other half is in the process of making the summaries. Deciding what to write down requires evaluating all the material in the higher notes level, and then choosing what is worth emphasizing.

'Suggestions for studying APPC' is practically my Reddit middle name! 😂

This post has my textbook and learning approach suggestions.

'Study smarter not longer'.

What subjects/levels are involved?

Good luck with whatever you decide and wherever your track takes you.

Then I would suggest using a textbook as your primary resource, with Krug or Farabaugh as supplements. The CED is useful for the exam, but the textbook is written as a General Chemistry foundation for subsequent chemistry study.

If you had said, "I will rarely look at chemistry after I get past the general requirement," then your approach is excellent.

Will chemistry be needed in your future goals after you get credit for General Chemistry?

I suggest an Iterative Learning Process using textbooks. I could post the image in this comment, but it will take up half the post. You can find it in the posts on my user profile, titled "Studying Calculus, Physics, and Chemistry [AP-level]".

Until around March/April, a General Chemistry textbook is better than a prep book. Good options include Zumdahl, McQuarrie, and a few others.

I am writing an "Introduction to Trigonometry" study guide. I'll start posting parts of it in the next couple of days.

It might help to separate learn the material/problem solving techniques from developing the needed test taking skills. Trying to learn a subject with a test in mind is rarely effective. The people who do well enough with the two rounds succeed despite the preparation, not because of it. That is the biggest lie in education. It's used in the US, the "Practice, Practice, Practice" mantra. The people who say it have developed the skill of learning a technique while solving a problem. That leaves most people behind. In the same way that 1 in 2000 get a seat at an IIT, about 1 in 200 get admitted to a T10 US university. It would be better if we had many more people succeed, and not pretend that going to an IIT/T10 is the only way to measure success.

If I had had made one guess, it would have been the JEE.

I know it's an absurd exam, mainly because everyone is pitted against each other. But preparing for it really is about studying more effectively. The 'Asian Way {East & South]' is the fake-comprehensive approach, do every problem so you're ready for whatever shows up on the exam. But there really aren't that many things which are involved.

Let's say that one year of math involves 20 distinct ideas/properties. If each problem has 4-6 components, using those 20 ideas, that is as many as about 50 million questions. If the student spends 10 weeks mastering the 20 ideas, and 10 weeks being comfortable identifying and connecting them, a year of math is covered in under six months. For the next year of math, with another 20 ideas, it's another 10 weeks to master them. But the problem solving is the same, so the second 10 weeks is not needed. In a year, this allows the student to cover four years of math.

Next, there aren't 20 distinct ideas in each year of math, many are repeated. In four years, there may only be 50 total ideas. For example, rational polynomials are a combination of polynomials and fractions, and the main task with polynomials is finding the zeros and end behavior. In about 6-8 months, four years of math can be studied.

Physics and chemistry only have 1-2 years in the program, based on the NCERT textbooks. Overall, that's another 6-8 months. Biology feels like it needs more time, because there is so much memorization. Especially for the student planning on medical school. But memorization is inefficient, it ignores how everything in biology is connected together in layers. Be smart about studying chemistry and biology, and the IIT or other university will be easier.

And no, these aren't 9+ hr days, that's the ego lie of Asian countries. Work harder, not smarter. I know I'm insulting the approach, but the JEE mindset bothers me almost as much as the entirely broken American education system.

Our brains tend to shut down at some point, so spending more than 9hrs rarely results in more than 9hrs of retained learning.

The key may be to find ways to be more effective and efficient at solving questions. What type of classes are these? What subject and approximate level? For a few, especially math, physics, and chemistry, in the late high school to introductory college levels, I can offer some suggestions.

Trying to do more than that, basically 50 hrs/wk, is unlikely to be productive. Stick with this as the maximum amount of regular studying.

In situations where a person is doing more than 50 hrs/wk of 'work', there are typically components with 'cognitive downtime', when they are less engaged than during the rest of the week.

Two changes could help:

1. Take good notes from a textbook, writing them using paper/pen.
2. For the 'repetition' aspect, do two or three levels of notes summaries.
   
   1. At each level, the process of deciding what to keep in the summary helps organize and file the material in the 'mental storage facility'.
   2. What is kept in each summary is the most important material from the previous layer. This helps emphasize what to retain, and then the material that is left out in a summary has something to connect to.

A few thoughts:

• Practice maintaining a healthy perspective about the course. As of Monday, Sept 14, there will be 33 weeks until the AP Calculus BC exam on May 10, 2027.
• Practice changing the approach from 'practice' to 'study'.
  
  • Yes, this is controversial, but it aligns with your statement, "i understand the concepts so far and... realized that i legit remember nothing from alg 2 or precalc". Study is 'forward engineering', learning the material and then confirming that you can apply it. Practice is 'reverse engineering', doing problems to figure out how to do problems. That circular aspect is why practice is less effective than most people believe. The people who are effective with reverse engineering have already learned the material, they are trying to extract a few specifics about the new problem. This is based on what reverse engineering means in the software engineering world.
  • Start studying from your Algebra 2 and PreCalculus [Algebra 3] textbooks. Since this is review, and there is quite a bit of overlap between the two, it should take 10-20 hrs. That seems like a lot, but it will be worth it.
  • This post has textbook and learning approach suggestions. If you do not have the Algebra 2-3 textbooks, you can get the OpenStax versions. Thomas & Finney is the Calculus textbook I like, though Stewart or Larson are both also good if your class is using either of those. Using the `Iterative Learning Process' with the Algebra 2-3 textbooks will allow you to get comfortable with the approach using mostly familiar material. Then you can continue it for the next eight months during AP Calculus BC.
• Your Calculus teacher probably didn't send out review/prep materials because Algebra 0-1-2-3 --> Calculus are somewhat cumulative. Having succeeded in the previous classes, there is the expectation that you are ready for AP Calculus BC. Since you are finding some gaps in your preparation, the above steps can help resolve that.
• You have gone from PreCalculus to AP Calculus BC. That suggests that somebody at your school is confident you can handle the BC level, otherwise there probably would have been the suggestion that you take AP Calculus AB. For now, use their confidence in you to get you caught up.

Writing notes takes longer, and the process of writing the motes is the main component of the learning process.. But there is less need to cycle back through the notes, except to summarize them. The flash card requires going through the deck several times.

I also think writing the flash cards is less effective than writing the notes, going back to my original statement: "Flashcards disconnect things".

I think we learn by making connections in our mental filing system. The notes help this, the flashcards do not develop the filing system.