Date: Oct 2, 2012 1:27 PM
Author: Robert Hansen
Subject: Re: An Algebra 2 Test

On Oct 2, 2012, at 11:51 AM, "Dave L. Renfro" <renfr1dl@cmich.edu> wrote:

> 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.

Actually, I forgot to add series and composite functions.

Binomial Expansion Problem...

What are the first 4 terms of (1 + 2x)^6?

How many terms does the binomial expansion of (x2 + 2 y3 )20 contain?

Conic Sections...

The graph of (x/2)^2 - (y/3)^2 = 1 is a hyperbola. Which set of equations represents the asymptotes of the hyperbola?s graph?

What is the standard form of the conic section given by 4x^2 ? 5y^2 ? 16x ? 30y ? 9 = 0?

Combinatorics...

A train is made up of a locomotive, 7 different cars, and a caboose. If the locomotive must be first, and the caboose must be last, how many different ways can the train be ordered?

Logarithms...

Solve log5(2x2 ?3x+1)?log5(x?1)+log5 125=6 (this one actually asks to identify the incorrect step).

Series...

What is the sum of 1/2+1/4+1/8+...

Composite Functions...

Given that f x = 3x2 ?4 and g x = 2x?6, what is g( f (2))?

Complex Numbers...

If i=Sqrt(-1) and a and b are non-zero real numbers, what is 1 / (a+bi)?

A student is considered proficient if they get 60% of the exam correct, advanced if they get 80% of the exam correct.

We didn't have precalculus as I recall, maybe I will try to ask one of my former teachers. Also, as I recall, at least in the school I went, there wasn't an Algebra 2 and an honors Algebra 2. But I took it before high school so maybe I didn't see the split. Obviously, 8th grade algebra 2 would probably just be honors. There wasn't any trig on this exam. We did it both in algebra 2 and in geometry.

Obviously, students that take the competitive exams must be taking these topics (I was disappointed that we didn't do more combinatorics in my class). If this is MUCH too much algebra for the typical student then this would explain the failings in high school physics, the students aren't even getting through algebra.

Bob Hansen