Date: Oct 2, 2012 11:51 AM
Author: Dave L. Renfro
Subject: Re: An Algebra 2 Test

Robert Hansen wrote (in part):

>> So here are released problems from the California CST
>> Algebra 2 exam...
>> 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):

> 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