> Given the list I posted as a start (which I repeat below > along with a few topics I omitted)... > > Polynomial Arithmetic > Factoring and Simplification > Simultaneous Equations > Graphing > Probability > Conic Sections > Binomial Expansion > Logs and Exponents > Absolute Value and Radicals > Complex Numbers > Series > Composite Functions > Combinatorics > > What would you limit this list to? This is almost identical > to the Dolciani S&M book minus the trig.
Perhaps the schools in my area were slow, as I don't believe any of them got much past about halfway through the Dolciani Algebra 2 book -- no trig., no logarithms, no conic sections, no probability, no combinatorics, and no binomial expansions at the Pascal's triangle level or above. And this was with perhaps at most 25% of the student body taking Algebra 2 at some point in high school. All the other topics from among those you listed, and some more such as mathematical induction and an introduction to calculus, were covered in the 4th year math course (variously called, depending on the school, "precalculus" or "mathematical analysis").
But that was then and there. For now, I would drop conic sections, maybe just touch on logarithms (focus mostly on solving equations such as 2^(x+3) = 5 and some very basic rewriting of expressions involving logarithms, and leave for precalculus things like logarithm graphs and the base change formula), perhaps do binomial expansions by relating it to combinatorics (e.g. when expanding (x + y)^8, the number of x^3*y^5 terms will be the number of times 3 x's and 5 y's appear when you list all 8-term ordered sequences ######## in which each # is an x or a y), perhaps restrict radical equations to those that can be solved by squaring both sides at most once, skip composite functions (I've always felt that precalculus is where you make the transition from numbers and operations on numbers to functions and operations on functions), and only deal with complex numbers to the extent of adding, subtracting, multiplying, dividing, and graphing them and using them in solving quadratic equations.
I think including some material on sequences and series is fine, although in my opinion many books are way overly formula oriented when dealing with arithmetic and geometric sequences and series. For example, instead of using a formula to determine how many terms are in the arithmetic sequence 16, 23, 30, ..., 681, notice that subtracting 16 from each of the terms doesn't change how many terms there are, which gives 0, 7, 14, ..., 665. Now notice that dividing each term by 7 doesn't change how many terms there are, which gives 0, 1, 2, ..., 95. Finally, notice that adding 1 to each term doesn't change how many terms there are, which gives 1, 2, 3, ..., 96. At this point it's obvious there are 96 terms, since if you start counting them, the count of the term is equal to the term. (Yes, this is like your "street fighting math" method you posted at .)
You can also incorporate some elementary algebra in obtaining various sequences and series results, as illustrated in the handout "seq-and-series.pdf" that I posted at .