Date: Oct 2, 2012 11:51 AM Author: Dave L. Renfro Subject: Re: An Algebra 2 Test Robert Hansen wrote (in part):

http://mathforum.org/kb/message.jspa?messageID=7899247

>> So here are released problems from the California CST

>> Algebra 2 exam...

>>

>> http://www.cde.ca.gov/ta/tg/sr/documents/rtqalg2.pdf

>>

>> From the standpoint of skills, these problems have good coverage.

>> Namely...

>>

>> Polynomial Arithmetic

>> Factoring and Simplification

>> Simultaneous Equations

>> Graphing

>> Probability

>> Conic Sections

>> Binomial Expansion

>> Logs and Exponents

>> Absolute Value and Radicals

>> Complex Numbers

>>

>> But from the standpoint of problems, this exam has hardly any

>> and of the few problems it does have, they are just direct

>> adaptations of the skills. For example, restating a simultaneous

>> equation directly into words...

GS Chandy wrote (in part):

http://mathforum.org/kb/message.jspa?messageID=7899316

> I've not checked through the problems - but the topic list

> posted by RH does seem - to my foreign eyes - pretty sound

> for an 'Algebra 2' exam (in fact, it's a bit more than we

> would expect in an 'Algebra 2' exam in India).

To me it seems MUCH more than I would expect in a typical

Algebra 2 class. In fact, it is roughly what was covered

in the last two years of high school math when I was in

school (my school didn't offer calculus). Also, I can

certainly tell you (from past teaching and current tutoring)

that very few college students taking Calculus have a

working knowledge of these topics. I wonder what is covered

in a Precalculus course if all this is to be covered in

Algebra 2? Rotations of coordinate systems and study of the

various invariants of 2-variable quadratic forms? Nontrivial

inequality work, such as arithmetic-geometric mean inequality

and other things one sees in contest level math? Binomial

probability distributions and the normal distribution?

Elementary complex variables, such as linear fractional

transformation mapping problems and formal manipulations

of trigonometric and exponential functions (and their inverses)

for complex number inputs? Working with vectors, including

dot, cross, and triple products and proving geometry

theorems by vector algebra methods?

I doubt it. My guess is that the Precalculus topics are

much that same as the above, maybe worded a little more

suggestively to indicate that more mastery of the topic is

expected, given what Robert Hansen said about the level of

the problems testing the material. I'm guessing that "binomial

expansion" means being able to expand (a + b)^2, (a + b)^3,

and *maybe* (a + b)^4, but no binomial theorem with C(n,k)

numbers (although perhaps Pascal's triangle, but in my mind

that's a Precalculus topic, not an Algebra 2 topic). Personally,

I'd do away with conics, logarithms, binomial expansions to begin

with. I'd have to know more of what is meant by "probability"

and "radicals" and "complex numbers" before going further,

as VERY basic introductions to these topics would probably

be fine.

The topics Robert Hansen posted would make for an excellent

honors Algebra 2 course, but not for a regular Algebra 2

course, especially given the push to have 50% or more of

the population take Algebra 2 (100% in some places, with

Algebra 2 being a graduation requirement).

Dave L. Renfro