<p>Hey, </p>
<p>I was wondering if its possible to learn all the precalculus necessary for Calclulus AP by using a thin book called "Precalculus Mathematics in a Nutshell" by George F. Simmons in 20 days before school starts? </p>
<p>What do you think? Anyone familiar with this book?</p>
<p>I took a full textbook from 1994, and reviewed the parts it said to review to form the full-year curriculum. It took me about 4 weeks to do so.</p>
<p>I don't know about the book, but learning a whole year long class in 20 days would be very difficult!!! If your going to study anything at all, study trig!!!</p>
<p>probably not, I've been doing it for the summer (actually July+this month) and just about done, it's a different book though, so gl if you want to try that in 20 days</p>
<p>
[quote]
I don't know about the book, but learning a whole year long class in 20 days would be very difficult!!! If your going to study anything at all, study trig!!!
[/quote]
</p>
<p>It's not that hard at all. You just need to dedicate a good chunk of time to it, and make sure every minute of that time is spent progressing through the course. You have to be a pretty quick learner as well.</p>
<p>You shouldn't feel the need to rush through one math course just to get to the next one -- what really matters is how well you know a subject, not how fast you can go through it. Mathematics is not a race. Truly learning something requires repeated practice. Keep in mind that you will need those skills from Precalc when you get to higher math or physics courses, and if you gloss over them using a test prep book, you're only hurting yourself. You're going to be in competition with people who've actually had a full year of precalc, and learned it from a real textbook that didn't skip all the details. You don't want to have trouble with trig integrals because you've forgotten your half-angle formulas.</p>
<p>And you probably won't even get to retake Precalc in college -- this is your one and only chance to learn it, so learn it well! </p>
<p>I'm doing it right now. Except it's for a test-out. Yes, it's very possible; I covered our textbook in a month.</p>
<p>Easily possible, precal is no biggie...</p>
<p>Yeah, well the only reason I say 20 days is because school starts in september and I'd like to be able to request convincingly that I would like to get Calculus AP. Note, I would still have to take the Precalculus class for the credit, but I'll be able to take Calculus AP as well.</p>
<p>So the basic question is 1. whether I will be able to pass a precalculus class final with a B with this book in 20 days of learning and 2. whether I would be able to survive in calculus AP with this book I have.</p>
<p>I should also probably elabourate more on this book since some of you guys aren't too familiar with it. </p>
<p>The book is divided into three sections: Geometry, Algebra and Trigonometry. </p>
<p>The geometry section is about 30 pages, its full of all the hardcore basics and topics of geometry. I'm not too worried about this since I think I am pretty good with Geometry. It goes as far as describing some theorems I have never heard of: Ceva's Theorem and Brahmagupta's Formula. </p>
<p>The Algebra section goes through most topics I remember going through this past year in Algebra II in 55 pages. Here are the specific topic headings from the table of contents:</p>
<p>*) The real line
*) Integral and fractional exponents
*) Polynomials and factoring
*) Linear and quadratic equations
*) Inequalities and absolute value
*) The concept of a function
*) Lines, circles and parabolas
*) Logarithms
*) Polynomial division
*) Determinants and systems of linear equations
*) Arithmetic and geometric progressions
*) Permutations and combinations
*) The binomial theorem
*) Mathematical induction </p>
<p>Finally there is the Trigonometry section, now I am not familiar with trig and this is probably the part I have to study most closely. In the book its about 25 pages for this chapter. The topics it goes through is radian measures for angles, trigonometric functions, values of sin,cosine,tan for certain special angles, graphs of "", the major identities, inverse trig functions, law of cos and law of sines, and some complete proofs of identities. </p>
<p>"Unlike many textbooks dealing with precalculus mathematics, this volume contains none of the unnecessary "padding" in the form of irrelevant digressions or obscure formalities that tend to confusie even the brightest students."</p>
<p>Now I am wondering whether this content in the book will be able to prepare me for a precalculus final exam. When the author says "Precalculus Mathematics" does he mean the mathematics basics to learn precalculus, or the actual mathematics of precalculus that I can use to learn Calculus AP? </p>
<p>What do you guys think?</p>
<p>What they mean by the digressions are some topics like probability, permutations and combinations, and other statistics-related material foisted on precalculus learners, sometimes to fit curricula designed by the state and/or the SAT. What he has in there is all you need to know.</p>
<p>You'll also want to keep in mind that a lot of the "irrelevant digressions" are actually the funnest parts of the course. Math should be an experience, not just something to get over with. It's like traveling abroad and rushing through one attraction just to get to the next one. Math is a subject to be thoroughly savored and ruminated upon.</p>
<p>Not to mention -- if you don't learn stuff like vectors and probability now, when you are going to learn it? Higher courses may gloss over these topics, or teach them in a way that assumes prior knowledge -- you'll want to learn these topics while you're still ahead. Don't handicap yourself by foisting yourself upon a group of students with more mathematical experience. Remember, what matters in high school is what you get out of it, not how fast you go. My sister skipped straight from Algebra II to AP Calc, and her background's never been the same...</p>
<p>Enjoy your summer now. Take precalc during the school year. You'll learn it much better.</p>
<p>Ceva's Theorem? Wow - that's like AIME stuff right there! </p>
<p>Anyways, I never took Precalc. I was supposed to "test out" of it for AP Calc, like what you are doing right now. I didn't exactly request to test out of it, but my Alg 2 teacher thought I had the potential to go straight to Calc - so what I did was I borrowed a Precalc textbook and flipped through it over the summer (and this was the summer I went to Mathcamp LOL). I guess I did retain some Precalc stuff, but like fizix said above, math is an experience. I agree with rushing through history, rushing through social sciences...but not physical sciences/math. Especially math. Math is known as the "queen of science" and forms the basis of many science courses that you will encounter in the future, especially if you choose to major in science/engineering. A good foundation is crucial, and looking back to my freshman summer, I thought that I was way too ambitious, and too rash.</p>
<p>So back to my "anecdote," my Calc teacher never ended up giving me that Precalc test (I think he forgot) and I just went on straight into Calc. I did fine in the beginning, but there were points in Calc (esp during complex differentiation/integration) where my lack of trig formulas hindered me. Sure, I still picked it up in the end, but it did involve extra work in the middle of taking Calculus. That, and I know I could have done better in AMC/AIME if I actually took Precalc ;)</p>
<p>You could do fine in Calculus, but just know that without a solid foundation, one day it'll come back and haunt you. For me, since it's been so long ago, I've basically gleaned everything that I was supposed to learn through other various AP courses and activities, but I guess I wouldn't have had to do that if I started out with a solid foundation. That's all.</p>
<p>
[quote]
You don't want to have trouble with trig integrals because you've forgotten your half-angle formulas.
[/quote]
</p>
<p>Good point, what are those? =p</p>
<p>sin(A/2)=sqrt[(1-cosA)/2]
cos(A/2)=sqrt[(1+cosA)/2]</p>
<p>you can derive them though if you need them
:p</p>
<p>Well as long as I will be prepared enough to survive Calculus AP during the year, the "solid" foundations comments are a bit irrelevant if you are talking about college and beyond because I will still be required to take the pre-calculus course this year just to have the credit itself (the school board doesn't allow any complete skip-overs). Only now, with the "skipping" I will be able to take Calculus AP at the same time. </p>
<p>My concern is that I wouldn't be able to learn enough at all to pass that precalculus "test out", or if I will fail miserably through Calculus AP.</p>
<p>And to tell you the truth, I have little respect for school board curricula standards and timetables. Most of it is all arbitrary and a lot of stuffing just to fill 180 days in a school year. All of it is bureaucratic. Who says someone can't learn and enjoy precalculus, or any subject in half the time it is "taught" in public schooling? Anyways, I just personally wouldn't hold the public schooling as the ideal standard to how we should learn things. <rant over=""> :P</rant></p>
<p>Yeah, I hear the trig formulas - half-angle, double-angle, sum-to-product, product-to-sum, sum and difference, and power-reducing are pretty important. Also, try to do a little more with conic sections and try to begin differentiation and integration (just a little bit; a lot of AB is review).</p>
<p>Oh crud I forgot all my trig formulas. Time for multivariable calc in september.</p>
<p>so let me get something straight really quick... those topics I mentioned are pretty much what precalculus is about? So then, basically, precalculus is just another name for trigonometry? So if I just do the trigonometry section of the book really well, I am pretty much prepared no?</p>
<p>No, but trig is huge in Precalculus. Probably half of Precalc deals with trig identities and formulas. The other half's generally comprised of polynomials, series and sequences, probability, and random topics like polar coordinates, vectors, matrices...etc.</p>
<p>It depends how sharp you are. Feynman learned calculus in a weekend. Figure he was top of his HS class.</p>
<p>Precalc = Alg II + Some Trig + Other Crap</p>
<p>
[quote]
It depends how sharp you are. Feynman learned calculus in a weekend. Figure he was top of his HS class.
[/quote]
</p>
<p>Which goes to show you, as long as you know the idea behind everything and can apply them properly, math is a fairly straightforward subject that hardly requires an entire year to get through.</p>