Tuesday, June 28, 2016

Algebra II Common Core question 20 (my apologies to the "non-math" readers)

Print Friendly and PDF Here is a question from the Algebra II (Common Core) regents Exam from New York in June 2016. This question struck me as soon as I saw it. My comments are below.

Firstly, my immediate reaction was to recognize that there were three visible places where the tangent is horizontal, which is the max for a polynomial of degree 4, so, in essence, the graph could only zoom down and down in both directions were it continued. For an even degree polynomial, this is only possible with a negative leading coefficient.

I did a little canoodling with calculus and GeoGebra and obtained a function with a graph pretty close to the question in hand:

How many Algebra II students have a solid grounding in derivative calculus? Probably, like, none of them? So my reasoning process is no good (even though it is correct).

At this point something hit me: a graph of a pH-based function can not be equal to a polynomial. Polynomials have domains covering all the real numbers (the entire x-axis, if you wish), but pH values only range from 0 to 14. Also, since pH values can be less than 6 and more than 10, for the function to even have a degree 4 polynomial as a good approximation , the oxygen consumption of the snails would have to negative, meaning that the snails actually created oxygen instead of consuming it. If that were the case, load up the Mars mission with lots of snails in some very basic (or acidic) compartments!

I still cannot see how an Algebra II student would have any comfort (or understanding) of this question.

But, aha! It is multiple choice. Choice 1 is given (degree 4), choice 3 can be seen (2 humps), and choice 4 can be seen (two pieces where it descends left-to-right), so it ca only be choice 2 that is incorrect.

This question does give more evidence to the idea that one of the latest trends has been to go "real world examples" and risk losing touch with mathematics. Especially aggravating when the mathematics of the solution has absolutely nothing to do with pH values. The content amounts to built-in obfuscation 

Also, the graph takes an immediate jump from x = 0 to x = 6 without using any of the accepted symbolic notations (such as zig-zag or "squiggle").

How is an Algebra II student supposed to reason this question without falling into the "there's only one choice left" scenario?

1 comment:

Anonymous said...

If the leading coefficient were positive, the graph would open upward instead of downward. Yes, it's that simple-minded.