We get a lot of questions about the difference between Algebra II with Trig and Precalculus.
Much of this comes from the publishers themselves. Here is my view…
1. Algebra II with Trig and Precalc are usually the same things – very little difference. To see this you could buy the Alg II with Trig book and the Precalc book by the same author/publisher and put side by side. Almost identical. Why do this? Marketing. If a school requests precalc, you want to have something to offer. If Alg II with trig, same thing. Do not miss a sale because of a cover. While you might find some texts that differ, I would not get caught in the mud worrying about it. See below for ACT/SAT.
2. If one takes Algebra II only, then you need some trig. Could do a one semester in trig using our book, websites, or something like a Trig for Dummies book. As long as you get the basics of trig formulas, simplification of trig identities, the law of sines and cosines, and some practical uses, you are good. For those who have had some algebra II, we direct to the quizzes for our text. found here http://www.mhhe.com/math/precalc/barnettcat7/ and have them work quizzes from chapter 1-5. If they can do this with 80% or better, they have the Alg II portion and can now move to trig. If they can do well on chapter 6-8, they have trig. (Again – about 80%)
3. ACT and SAT are key. I am not saying teach to the test – but yes, teach to the test. These exams are written so student MUST understand the material to do well – at least in the math part. This is all you need for college and for $ for college (if anyone cares;) The big problem in college calculus is a lack of understanding of basic algebra. Students often can do the work if they see examples of like problems, but given something new, they do not know the concepts enough to make it work. So, they flunk out of college calculus.
4. Cookbook math – related to ACT/SAT we often tell people math is like cooking. I can cook a decent meal with a cookbook if I follow instructions. Hardly makes me a chef since I do not understand how ingredients go together. A true cook could be let loose with ingredients and make-up a meal. They understand how things work. Math is like this. Too often we teach cookbook math, meaning the student can only solve a problem if formulated in the steps they have seen before. But, if thrown a real-world problem, they are lost. I realize this is not so much about Alg II etc – but this is a HUGE issue we see in science and engineering. We have a huge demand for people to do this kind of work, but most cannot hack it because they are cookbook math people.
More details in The Math Problem.