T.O.E Dream said:
I'm self-studying math, and after algebra 1 and geometry i moved onto pre-calculus. When I looked at the content between algebra 2 and pre-calculus they looked very similar and so i just began with pre-calc. But I'm afraid i made a mistake doing this although I'm having no problem with precalc so far. I want to finish pre calculus and trigonometry to begin calculus. Will me not learning algebra 2 affect my performance in calculus. Again, I'm self-studing at a very young age and I'm already ahead of my peers and I'm doing this for physics. Is this a good path to follow?
Thanks in Advance!
The answer to this is "yes" and "no;" my textbook may have been different from yours, so this may vary. Pre-calculus is like a review of algebra 2 with some new topics sprinkled in, but that's it--a
review. In other words, it can be very difficult to learn what you need to learn of Algebra 2/trig from Pre-calculus. You need to master Algebra 2 and trigonometry in order to do well in calculus. When I took pre-calculus, it just did not cover them in a proper depth (or maybe detail is the better word?) for that kind of mastery.
Pre-calculus books will assume that you already have taken algebra 2 and trigonometry, and they will "teach" it as such. Thus, the problems are usually harder than parallel problems from an algebra 2/trig book; it will not try to explain the concepts from them as much; and pre-calc may gloss over or entirely miss some intricate details that an algebra 2/trig book would have covered. So you don't really "need" to take Algebra 2/trig if your precalc books covers it all at the proper depth and detail, but the concepts that you learn from Algebra 2/trig must be completely mastered. Let me remind you that I'm speaking from my own experience, and yours may be different, but this is what my precalc book was like.
I didn't skip algebra 2/trig, and I didn't regret it.
If you're really desperate to get to calculus so quickly, so long as you can actually learn the concepts of algebra 2/trig and precalculus at the speed I'm about to mention, you can do what I did. I took algebra 2/trig at a normal rate in one year. Then the next year, I accelerated through Pre-calculus, finisihing it within 3 months. Then, I started calculus to be finished within that same school year. Note though that I could not
possibly have finished precalc so quickly if I hadn't had already mastered from the year before the enormous amount of algebra 2/trig review inside precalculus.
Also note, that if your GPA starts dropping or you feel yourself not picking up the concepts well enough, then stop and slow down. Calculus is vital for physics later on, and it is important that you learn it, and thus the prerequisite subjects, very well. There's no need to rush things, after all, if you are indeed very young.
But as the above poster says, it really depends on you. I'd add to that that it depends on how you learn, your text, your teacher (or tutor if you have one, in this case), your supplements (if any), and how quickly you learn.