# Thread: What to expect from pre-calc?

1. ## What to expect from pre-calc?

So next year (my last year!) I'm doing a pre-calculus course, sort of. It's not strictly pre-calculus, but it's the closest our school system has to offer AFAIK.

Anyway, since I know the majority of you have been through high-school and stuff already, I was wondering what exactly to expect from this. From what I gather from my teachers, it's basically the hardest math course I can do in our school. But I haven't exactly been told anything specific about the course, other than that I can't use a calculator (I think). Although I'm pretty sure you can't use a calculator for calculus anyway, but what about the other stuff in the course?

Course Description:
Mathematics 3207 is considered to be part of the Advanced Math program. It is the last course in a series of four which make up the senior high advanced stream. We recommend that students have either Math 2205 or Math 3205 completed before taking this course. Topics include Sequences and Series, Functions with an emphasis on Graphing and an Introduction to Calculus, Trigonometry, Complex Numbers, and essential Algebra necessary for success in post-secondary Mathematics. Students should have access to a graphing calculator.

2. Functions with an emphasis on Graphing
After awhile these get annoying. Basically, studying functions and the the shapes that their graphs result in.

f(x) = x <------------ line

Circles, curves of such, etc. etc.. I imagine you already know this kind of stuff.

Introduction to Calculus,
Introduction to the real stuff....

Trigonometry
Cos, sin, tan.... If you've programmed with them, and understand it, that'll help. Combine it into formulas and such. I can never remember these well.

Complex Numbers
i is a number such that i^2 = -1.

It's technically impossible, but somehow works. Enjoy it.

essential Algebra necessary for success in post-secondary Mathematics.
Probably linear equations and how to solve systems of them. If you haven't covered Gauss-Jordan stuff, yet, this'll be it.

Or a C compiler and a strange and bizarre love of ASCII art.

It's not so much any of those concepts giving you trouble as much as putting them all together. I'm relatively lazy with math, and can't be bothered to do much of it, and I don't usually remember everything. Heck, if I ever need to write down math-related notes, I usually write down pseudocode-programming-style notations. For example, instead of a traditional "not equals" sign, I literally write !=.

I probably got a bunch of mistakes in this post anyway that real math folks will correct!

But overall, if you're good at it, then this should be fun. As with programming, just remember to always do the homework assignments.

BTW, I was under the impression you were already in college/university. Guess I need to check profiles more often.

3. Sounds like the equivalent to an English AS level maths. If you can understand trigonometry, which you have probably done already, then basic calculus should be nothing to worry about. Just a couple of simple rules to differentiate or integrate plus some other stuff.

For algebra you can expect to do linear equations, simultaneous linear equations, quadratics, and perhaps polynomials. They should let you use a calculator for most things, but I wouldnt bother with a graphics calculator, they are a rip off, and theres plenty of progs that do that stuff for you. Or even better code your own

I was studying this sort of stuff last year as an external student. It was fun to start off with, but when I got a list of all the things I needed to learn it started to dawn on me that it was just a matter of memorizing procedures, which kinda killed the fun. So anyway, I went off to code a slew of unfinished games instead, and now I wish I stayed and did the maths. Its good stuff to know. Good luck with it

4. That sucks if you can't use a calculator on the tests, but it makes sense I guess. I know my TI-89 helped way too much in calculus (now that I think about it, it gave me an unfair advantage, but oh well).

I'd still highly recommend the TI-89. If nothing else, you can use it to check answers when you're doing homework, since it can do symbolic operations like solving equations and differentiating/integrating. You might also need to have another scientific (non-graphing) calculator if they allow that on tests.

Just don't let the calculator be a crutch! For the last two calculus courses I took, we weren't allowed to use any calculator on the tests, and I completely screwed up my derivatives on the final (which was the easiest part of the exam)

5. Calculus is the study of certain kinds of operations on FUNCTIONS. Unlike the math you've already learned, the basic objects of calculus are not numbers, but FUNCTIONS. So to understand calculus, you need to understand functions, and this is the purpose of pre-calc.

A calculator isn't going to help you much. You are learning concepts, not performing tedious calculations on paper that would be better done by a computer. You'll probably be learning about functions, series (both convergent and divergent, and why it matters), infinitesimals, and complex numbers (as the course description says). These are things you have to comprehend in your mind. The calculator is no use there.

And don't let anybody scare you or tell you "calculus is hard." The fact is, calculus is easier than many other branches of "advanced" mathematics. It's a fact that if you are repeatedly told that you're not going to "get" something, you ARE going to have trouble with it, no matter how smart you are. Just go into this telling yourself "this stuff is easier than long division" and don't let anybody tell you otherwise. It's just MORE stuff, not HARDER stuff.

6. Of all the things you are taught in that class, the most likely to be neglected is graphing. The ability to visualize functions in your mind will put you way ahead of others in future mathematics classes you take. (Also, the development of the ability will make your brain smarter. At math, anyway.) So make sure you become a ninja at that.

7. Originally Posted by JaWiB
I'd still highly recommend the TI-89. If nothing else, you can use it to check answers when you're doing homework, since it can do symbolic operations like solving equations and differentiating/integrating. You might also need to have another scientific (non-graphing) calculator if they allow that on tests.
This person hasn't used an HP graphing calculator (probably :-) ). Get an HP-50 and put it in RPN mode. It is a true hacker's calculator. Unless you've already got a graphing calculator...

Edit: inserted 'probably'

8. Here's what I gather from it :

Sequences and Series
Sequences we've pretty much been doing since we're kids. It's a straighforward concept, and since this is intro, it's likely you won't learn any of the hardcore stuff involving sequences (aka limits, inf, sups and such), but rather the definition of what a sequence is as well as maybe some of the more famous sequences like the Fibonacci sequence.

Functions with an emphasis on Graphing and an Introduction to Calculus
Pretty much what MacGyver said, although "Introduction to calculus" can mean a lot of things, so it's hard to say what that specifically means.

Trigonometry
cos, sin, tan, cosin, cotan, cosec. All pretty straightforward stuff, and if you've been on this board long enough (which I believe you have), you've probably seen them somewhere before. You probably won't learn much more. This should be the easiest part of the course (except maybe the trig proofs)

Complex Numbers
Complex numbers are just a superset of the real numbers (aka the real numbers + some more numbers), and were essentially created in order to maintain the fundamental Theorem of algebra. They're interesting little buggers, but they can be tricky at first if you haven't learned anything about vectors before. But they're as "real" as the numbers -2 and 1/4.

essential Algebra necessary for success in post-secondary Mathematics
This doesn't mean very much, and more likely hints to the fact that you'll have to use algebra in the other subjects. If anything, it could be a slight intro to vectors.

Hope that's of help.

9. Don't expect anything. Well, I guess you could expect to take the SAT Subject Test Math IIC soon. If you want. It has some good credit in the whole college application process you might soon be undertaking.

10. Originally Posted by JaWiB
That sucks if you can't use a calculator on the tests, but it makes sense I guess. I know my TI-89 helped way too much in calculus (now that I think about it, it gave me an unfair advantage, but oh well).
...
Just don't let the calculator be a crutch! For the last two calculus courses I took, we weren't allowed to use any calculator on the tests, and I completely screwed up my derivatives on the final (which was the easiest part of the exam)
I always found calculators were of no use in calculus. Since it often involves manipulation of unknown values, often markers will mark 100% for the solution and 0% for the answer. I had a TI-8-something (the graphing one) and found it no use in any of my calculus or algebra courses. I'm thinking you're better off without a calculator at all for this course.

And what brewbuck said is absolutely right. I've taken 3 engineering calculus courses and although they were rigorous, if you kept your head in the game, you could always logically work a problem out. Now I'm taking a probability and stats course (which, for lack of a better term, I like to call "memorization math") and I am getting absolutely reamed just because of all the differring cases (i.e. fifity different formulas for fifty different situations). Now I'm starting to wish I was back in calc, where you could take just one or two formulae and re-arrange them to solve anything you want.

11. To expand on Happy's answers:

Originally Posted by Happy_Reaper
Sequences we've pretty much been doing since we're kids. It's a straighforward concept, and since this is intro, it's likely you won't learn any of the hardcore stuff involving sequences (aka limits, inf, sups and such), but rather the definition of what a sequence is as well as maybe some of the more famous sequences like the Fibonacci sequence.
My pre-calc class had sequences and we were expected to find limits, but not inf and sup and lim sup (tasty!). So yours might. They will probably cover geometric series and finding their sum via the formula.

cos, sin, tan, cosin, cotan, cosec. All pretty straightforward stuff, and if you've been on this board long enough (which I believe you have), you've probably seen them somewhere before. You probably won't learn much more. This should be the easiest part of the course (except maybe the trig proofs)
You might see new ways of look at these, too (rather than just geometrically), particularly as periodic functions, and also, how they are related to points on the unit circle. You'll have to be able to recognize crap like what's their period. Under graphing you might be expected to graph these, and also functions of the form f(x) = sin(ax+b). This could lead to polar coordinates and polar representations of complex numbers. And you'll probably learn the joys of trig identities
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12. This is almost equivalent to my pure math 30 course during my high school years. Don't really have to worry about it, just do all of the practice problems and you are gonna have a high mark. Even though it said to be pre-calculus, most of the time these things are not gonna be show up again until calculus 2. This course is not gonna be hard if you consider yourself not bad at math already, it is just a preparation for you to go into the math courses in post secondary. This is a course that you need to pay attention in, as its probably harder than your grade 10 and grade 11 math.

The three that is probably the most important are:

Trig- you are using it alot when you are in math courses during your post secondary

Graphs - a very important part of calculus, know it well before going to university, my friends had a hard time in catching up (especially if you are in Electrical, Computer or Software engineering) during Signals and Transform. It is also very significant in vector calculus.

Series- my friend, haunted me for a long time in Vector Calculus and Differential Calculus so its a good start if you know this well too.

As i said, just do some practice problems and you are gonna be fine

13. I hate Maths.In this semestar I have to learn Integrals(double,triplle)

14. Originally Posted by crvenkapa
I hate Maths.In this semestar I have to learn Integrals(double,triplle)
They're kind of one of the two most fundamental pieces of calculus, so they're pretty necessary.

15. Originally Posted by Happy_Reaper
cos, sin, tan, cosin, cotan, cosec. All pretty straightforward stuff, and if you've been on this board long enough (which I believe you have), you've probably seen them somewhere before. You probably won't learn much more. This should be the easiest part of the course (except maybe the trig proofs)
cos, sin and tan are pretty simple. But sec, cosec and cotan I've had a bit of trouble with. And especially when dealing with radians and exact values and stuff. Stuff like tan(2pi/6)/sec(pi/3)cos(4pi/5). I can get it into degrees of sin and cos just fine, but simplifiying radicals kills me.

Originally Posted by JaWiB
Just don't let the calculator be a crutch!
Too late . Seriously, I can barely do anything in my head anymore. I remember in the lower grades, like 4-6 or something, they made us do "mental math". But after that, I just started using the calculator for absolutely everything. Which means my calculatorless university entrance exam should be interesting. Interesting in the worst possible way.

Originally Posted by Rashakil Fol
Unless you've already got a graphing calculator...
We were required to get one in Grade 9. I have a TI-83 Plus.

Oddly enough, I haven't tried coding any of this stuff. Probably because when I get home from school, I don't feel like writing my day in C++ .

As far as I can tell, from all your descriptions, the only thing I haven't seen before is complex numbers. I think nearly everything else we've touched on already this year. I think we might have supposed to have done limits, but I'm not sure (I saw it on last years final exam I think). I know there was a section dropped from the year because we ran out of time. Statistics was the unit I believe.