Content for Algebra I/II and Precalculus and Trig.?

I'm wondering if someone who is experienced can list all the content that a person should have mastered in the subjects of Algebra I/II and Precalculus and Trig.

I completed College Algebra at community college just this past year and I'm going to be taking Precalc./Trig this upcoming year. I just want to make sure that I have everything down that I need to know. Our instructor, despite being nice and helpful, didn't cover everything in our book and I'm not even sure exactly whether there are official topics designated for each area. For example, we didn't do logarithms in my College Algebra class, but my friend's class had them.

I'm just wondering if there is a standard set of topics that go with each class that students should know whether or not the book or instructor actually covers them. Thanks everyone.

symbolipoint
Homework Helper
Gold Member
Precalculus is a heavy combination of College Algebra and Trigonometry. If you did not cover all essential parts (whatever those are) in your College Algebra course, then you should see again what you still need to cover in your PreCalculus course. Trigonometry should also be available as a separate course and more complete than as done in your PreCalculus course.

I recommend checking any common College Algebra textbook to know what the contents should be for College Algebra; and also check a good Trigonometry book to know what is or should be the contents of a Trigonometry course. I ALSO RECOMMEND reviewing what you missed on logarithms and log and exp functions on your own before enrolling in your PreCalculus course.

Some of the absolutely necessary contents of College Algebra are these:
Linear and quadratic relationships, inequalities, absolute value; as an intense review of intermediate algebra;
Polynomial Functions and their graphs;
Rational Functions and their graphs;
Conic Sections, ..
Inverses of Functions;
Exponential and Logarithmic Functions;
Functions for the Domain of Whole Numbers (sequences and series);
Applications for several of the above listed topics.
Limits of Functions (which is why College Algebra is included in Pre-Calculus);
Other assorted topics sometimes including binomial theorem, linear algebra/linear systems

462chevelle
Gold Member
Trig necessities are

Right angle relationships
Unit circle
graphs of trig functions
identities.. lots and lots of identities.
sum and difference
pythagorean
half angle
double angle
reciprocal
Solving trig equations
Obliques (law of sines and cosines)
Vectors
Polar coordinates and complex numbers. Demoivres method.

verty
Homework Helper
@OP:
I think you'll get the most relevant advice if you list the topics in your textbook so we can say which are more important and which are less so or which can be left for later.

The Art of Problem Solving precalculus book table of contents tells you what a good class would cover.

@OP:
I think you'll get the most relevant advice if you list the topics in your textbook so we can say which are more important and which are less so or which can be left for later.

Hi, verty

I'll have to come back to this thread a bit later (busy weekend!), but for now I can give you all my College Algebra book name and ISBN:

Intermediate Algebra (by Charles McKeague)
ISBN-13: 978-0495384977

I haven't picked up my Precalculus and Trig. book yet, but it's definitely listed in the school bookstore. I'll have to try to look through it when I get the chance.

I'll be back soon guys. Thanks so much again! Also, feel free to give recommendations for readings and books in these topics. If they're cheap enough or are just like the best of the best, then I may be willing to buy one this summer. :thumbs:

symbolipoint
Homework Helper
Gold Member
Hi, verty

I'll have to come back to this thread a bit later (busy weekend!), but for now I can give you all my College Algebra book name and ISBN:

Intermediate Algebra (by Charles McKeague)
ISBN-13: 978-0495384977

I haven't picked up my Precalculus and Trig. book yet, but it's definitely listed in the school bookstore. I'll have to try to look through it when I get the chance.

I'll be back soon guys. Thanks so much again! Also, feel free to give recommendations for readings and books in these topics. If they're cheap enough or are just like the best of the best, then I may be willing to buy one this summer. :thumbs:

College Algebra is much more advanced than Intermediate Algebra. Intermediate Algebra is a subset of the contents of College Algebra. You have three months now before the autumn semester begins. You should get any good College Algebra or Precalculus book NOW and study the course on your own, before the next semester begins, to prepare yourself for your autumn term in Precalculus.

verty
Homework Helper
Hi, verty

I'll have to come back to this thread a bit later (busy weekend!), but for now I can give you all my College Algebra book name and ISBN:

Intermediate Algebra (by Charles McKeague)
ISBN-13: 978-0495384977

I haven't picked up my Precalculus and Trig. book yet, but it's definitely listed in the school bookstore. I'll have to try to look through it when I get the chance.

I'll be back soon guys. Thanks so much again! Also, feel free to give recommendations for readings and books in these topics. If they're cheap enough or are just like the best of the best, then I may be willing to buy one this summer. :thumbs:

Ok, this book seems to use matrices from early on which I find a little strange. Matrices in a book where completing the square is found in chapter 8? Cramer's rule in an appendix?

From what I can see, it looks to be set at a good level for intermediate algebra although some topics are advanced. So you'd want to learn everything from chapters 1-11 but with a few exceptions. Matrices you should probably just skip altogether; the different quotient is not going to mean much until you learn about limits; and quadratic inequalities are a little complicated, I would place them last in order of topics to learn from this book. I suppose you'll have learn most of what is left already in class, so perhaps just learn the few remaining topics? The rest you can learn when you get there, I think.

My precalculus course did not even offer conic sections. So conic sections is not something I would worry about. Even in Calculus 2 we completely skipped Hyperbolic functions

Rocket50
Gold Member
It really depends on the course level. However, as stated above, try the AoPS book contents or Sullivan's book.

The art of problem solving is not a book I would recommend. I bought that textbook before, and needless to say the explanations were terrible. Sometimes I felt like the instructions for certain problems were too vague, and the end goal was not clear. Then there were certain chapters on topics that most of my TAs never even heard about. For someone who is just starting to study precalculus/alegbra/trig, the AOPS books are not for you. Just find a regular text somewhere, and start from chapter 1.

Rocket50
Gold Member
The art of problem solving is not a book I would recommend. I bought that textbook before, and needless to say the explanations were terrible. Sometimes I felt like the instructions for certain problems were too vague, and the end goal was not clear. Then there were certain chapters on topics that most of my TAs never even heard about. For someone who is just starting to study precalculus/alegbra/trig, the AOPS books are not for you. Just find a regular text somewhere, and start from chapter 1.

In this case, it is only to check out a list of topics.

The explanations are actually quite good, as they show why it works.

As for covering extra topics, they do it because those topics are covered on major math contests.

In this case, it is only to check out a list of topics.

The explanations are actually quite good, as they show why it works.

As for covering extra topics, they do it because those topics are covered on major math contests.

I did not find their explanations that good, but as I have stated earlier these text are for people who are preparing for mathematical competitions, meaning people who already have a solid foundation in mathematics, not someone just trying to self-learn with almost zero foundation. It is like telling a person with no knowledge of analysis that they take spivak for their first calculus course.

Rocket50
Gold Member
I did not find their explanations that good, but as I have stated earlier these text are for people who are preparing for mathematical competitions, meaning people who already have a solid foundation in mathematics, not someone just trying to self-learn with almost zero foundation. It is like telling a person with no knowledge of analysis that they take spivak for their first calculus course.

Uh... Quite a people take Spivak as their first calculus course. But yes, I agree that these books cater mainly towards people training for mathematical competitions. However, I had little interest in those contests and still managed to use the books (much more fruitfully than the regular school textbooks).

Uh... Quite a people take Spivak as their first calculus course. But yes, I agree that these books cater mainly towards people training for mathematical competitions. However, I had little interest in those contests and still managed to use the books (much more fruitfully than the regular school textbooks).
I tend be skeptical of people when they state such things about taking spivak as their first calculus course. Most of the time, they had some AP-BC calculus that allowed them to take such a course. Very few will actually understand what to do in spivak's book without some sort of training in proofs and analysis. I do not debate that there are some incredibly gifted people out there, but most of time when someone mentions spivak, they are just parroting what someone else told them.

symbolipoint
Homework Helper
Gold Member
My precalculus course did not even offer conic sections. So conic sections is not something I would worry about. Even in Calculus 2 we completely skipped Hyperbolic functions
Conic Sections needs to be included in both Intermediate Algebra and in College Algebra.

Conic Sections needs to be included in both Intermediate Algebra and in College Algebra.
I do not think that they do, or my precalculus class would have covered them. Also my college algebra classes we did not even include them. If you are making a statement, then I don't see the harm in including them.

symbolipoint
Homework Helper
Gold Member
I do not think that they do, or my precalculus class would have covered them. Also my college algebra classes we did not even include them. If you are making a statement, then I don't see the harm in including them.
One must study conic sections as a part of staying aligned with the study of the natural or physical sciences, engineering, or as for a major field in mathematics.

462chevelle
Gold Member
we studied conic sections in college algebra. we didnt cover matrices though. the last thing we covered was log and exponential functions

One must study conic sections as a part of staying aligned with the study of the natural or physical sciences, engineering, or as for a major field in mathematics.
I do not deny that understanding conic sections is important, but including them in a college algebra course or not including them does not make or break a person. The college algebra at my school did not include them, nor did my calculus course. I think in Calc III we might go over them. My point is that the conic sections are not a necessity to learn at college algebra level, but if one where to learn them it does not hurt them.

462chevelle
Gold Member
In Calc 1 we have had problems with conics, and it helps to know what kind of function you're dealing with whenever you know the equations. We also used the equation of a circle to describe the unit circle in trig.

In Calc 1 we have had problems with conics, and it helps to know what kind of function you're dealing with whenever you know the equations. We also used the equation of a circle to describe the unit circle in trig.
It depends on what the school's curriculum is. My school does not teach it, but I have not suffered because I do not know it. The main point is that knowing it, is fine. If you're not required to learn it, then there is not harm done.