Struggling with Pre-Calc After Acing Calc I?

[haxtor21]

Hello PF.

I have a certain issue that I am thinking about currently. Here is the situation:
I am a high school senior and I took Pre calculus in high school, and had a very bad grade. On top of that my teacher was very lacking too (in terms of explaining the material). I dual enrolled at a community college, took the palcement test, got placed in Calc I, and here I am about to finish my semester with an A in calculus.

1) My problem is that i don't have a grasp on using (remembering) identities (double angle, etc.), i forgot about parabolas, hyperbolas, and I also forgot how to do matrix problems. My calc proff. also mentioned various other theories that i would have learned if i took College Algebra & Trig at my community college. I feel like i don't know my pre-calc stuff as well as I would like to. I was planning to tutor math up to calculus after this semester and now feel intimidated. What do you recommend?

2) I am finding myself spending major time on reading and re-reading the theory of my calculus sections. I am finding myself in a constant dilemma that i don't have a full grasp/intuition/insight of some theories of calculus. I sometimes feel like a robot doing my problems. Just sometimes. Is there any sort of novel-like material that explains the fundamental theories behind areas of math such as arithmetic, geometry, algebra, calculus ?. I have this gut feeling that my math background is not complete, that i want to know and understand where these theories came from and by what means they were formulated. I also read about the various math theorists but this is too impractical and scattered.

Help would be greatly appreciated.

PS: I am planning to major in EECS.

 

[khemist]

Sounds like you just need to get a pre calc book and reread.

To be honest, I was in a similar boat as you. However, whenever those identities came up, or something from pre calc was needed, I simply looked it up or asked my teacher, who was usually willing to point me in the right direction. As you progress in calculus, the identities will be used more and more, and the simple act of repetition will most likely help you learn/ memorize the correct tools.

for example, in calc 2, there are many, many table integrals that COULD be memorized, but again, the simple act of seeing those problems over and over was enough for me to remember it, rather than sitting down and attempting to use flash cards to memorize certain integrals that are difficult to solve.

I hope this helps! You could try going to your college library and check out books on those subjects you mentioned, for they will most likely have proofs and theorems that might help you.

 

[General_Sax]

"I was planning to tutor math up to calculus after this semester and now feel intimidated. What do you recommend?"

You're planning to tutor yourself to the calculus level, and you got an A in calculus? If you're going to self-study, then I think you should try to learn new material.

BTW, I think almost every student has trouble remembering Trig. identities/formuals for hyperbola/etc.

 

[_DJ_british_?]

Fact is, your teacher really don't believe you will remember all these formulas. They want you to know about them enought so that when you'll encounter a problem using them, you'll remember that you have seen them before and know where to find them (book, internet and such). Most of the time, students think in a "rot memorising" kind of way...it's good for exam, but on the long run, you only have to know that what you've learned exist and you can find it somewhere. About tutoring, you want to tutor up to high school kids about subjects you forgot? Either you forget about it or you study seriously your basics. I've tutored kids and a good grasp of calculus (or any higner mathermatics, for that matter) doesn't help. You have to know what algebra, geometry, linear algebra and set theory is about. The hardest questions I came across to answer came from people I tutored (not just kids). So you REALLY have to know what you're teaching, otherwise they'll find someone else (and there's a plenty)! But I don't want discourage you because tutoring is a very awesome and rewarding thing...I just don't think you're ready yet!

 

[khemist]

I would agree that tutoring is useful, but how about using your classmates and teachers, and you don't have to pay a cent! Try to form study groups, use your teacher's office hours. If you put in the required amount of time in any class, a tutor will be wasted money.

I have used a tutor before, and don't get me wrong, it did help me, but I have found out that using classmates is EXTREMELY helpful in understanding material, as is using your teacher (go figure!).

 

[haxtor21]

I think I didn't come across the way I wanted to.

I am planning to be a tutor myself starting next semester. I was planning to take it easy and only tutor stuff UP TO Calculus (except Stats), even though i could tutor Calculus.

I think i might borrow a precalc book and just review everything.

EDIT: Tutoring will take place at my community college.

 

[Acut]

About item 2:
Feeling like a robot is normal in the beginning!
I only truly understood calculus after I saw its applications. Then, everything became sort of obvious.