```Date: Oct 3, 2012 12:29 PM
Author: Dave L. Renfro
Subject: Re: An Algebra 2 Test

Robert Hansen wrote:http://mathforum.org/kb/message.jspa?messageID=7899711> 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'tbelieve any of them got much past about halfway throughthe Dolciani Algebra 2 book -- no trig., no logarithms,no conic sections, no probability, no combinatorics, andno binomial expansions at the Pascal's triangle level orabove. And this was with perhaps at most 25% of the studentbody taking Algebra 2 at some point in high school. All theother topics from among those you listed, and some more suchas mathematical induction and an introduction to calculus,were covered in the 4th year math course (variously called,depending on the school, "precalculus" or "mathematicalanalysis").But that was then and there. For now, I would drop conicsections, maybe just touch on logarithms (focus mostly onsolving equations such as 2^(x+3) = 5 and some very basicrewriting of expressions involving logarithms, and leavefor precalculus things like logarithm graphs and the basechange formula), perhaps do binomial expansions by relatingit to combinatorics (e.g. when expanding (x + y)^8, the numberof x^3*y^5 terms will be the number of times 3 x's and 5 y'sappear when you list all 8-term ordered sequences ########in which each # is an x or a y), perhaps restrict radicalequations to those that can be solved by squaring both sidesat most once, skip composite functions (I've always feltthat precalculus is where you make the transition fromnumbers and operations on numbers to functions and operationson functions), and only deal with complex numbers to the extentof adding, subtracting, multiplying, dividing, and graphingthem and using them in solving quadratic equations.I think including some material on sequences and series isfine, although in my opinion many books are way overly formulaoriented when dealing with arithmetic and geometric sequencesand series. For example, instead of using a formula todetermine how many terms are in the arithmetic sequence16, 23, 30, ..., 681, notice that subtracting 16 from eachof the terms doesn't change how many terms there are,which gives 0, 7, 14, ..., 665. Now notice that dividingeach term by 7 doesn't change how many terms there are,which gives 0, 1, 2, ..., 95. Finally, notice that adding1 to each term doesn't change how many terms there are,which gives 1, 2, 3, ..., 96. At this point it's obviousthere are 96 terms, since if you start counting them, thecount of the term is equal to the term. (Yes, this is likeyour "street fighting math" method you posted at [1].)You can also incorporate some elementary algebra inobtaining various sequences and series results, as illustratedin the handout "seq-and-series.pdf" that I posted at [2].[1] http://mathforum.org/kb/message.jspa?messageID=7873200[2] http://mathforum.org/kb/message.jspa?messageID=6544585Dave L. Renfro
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