Let's make mathematics great again...

This is a magical question from the New York Regents Exam in Geometry (Common Core) of June 2016. Based on a NYSED decision, both (1) and (3) are accepted as correct, which means that item III is both always true and not always true. Magic!!!

For the visually-motivated. here is a quick GeoGebra file based on this question.. Unfortunately, due to space limitations, I had to put limits on the dilation scale factor and the translation components (computers do not like to accept infinity as a number!)

This question was one of 3 in this exam in which multiple answers were deemed acceptable (after initial scoring, grading, and graduations were all over.)

I have two concerns over this fiasco:

1. A student seriously confused by question 14 (not be the mathematics) might have, in following the directions to indicate the BEST choice, left the answer blank. That would have been correct, as there cannot be multiple BEST answers. They would get no credit, yet a student who was clueless and put down a random selection would get credit.
2. Many teachers use old regents exams as study/review/practice for exam time. What will NYSED do to ensure that future use of these exams is predicated on information regarding these mess-ups? It is now three questions (14, 22, and 24) on this exam that have been acknowledged as invalid.

Be aware that on question 14 two answer selections are accepted as correct, on question 22 all 4 answer selections are being accepted as correct, and on question 24 all 4 answers plus a blank are being accepted as correct. See these links: question 24, questions 14 and 22

Cavalieri's What?

Here is question 27 from the New York State Geometry Regents exam of June 2016.

One thing specifically stands out in this question. Cavalieri's Principle.

Students in New York do not have to remember the quadratic formula, how many feet in a mile, or even the Pythagorean Theorem. Those items are all on the Common Core High School Math Reference Sheet with which each student is supplied. 

But Cavalieri's Principle? That stands out. After all, everyone should know the main success of Felix Cavalieri, lead singer of the Lovin' Spoonful.

Oh, sorry, Wrong Cavalieri.

This Cavalieri is actually the gentleman who proved the formula for the volume of a general prism (which can be found on the reference sheet). 

I will admit that when I first read this question, I said to myself "what the heck is Cavalieri's Principle?" After a little research I was reminded that I had confronted it somewhere in my mathematical meanderings.

It does please me that NY has risen its standards and now expects students to remember and be able to apply Cavalieri's Principle. Now if they could only do that with the other items on the reference sheet...

New York has to make better tests!

The above is the first section of a question from the January 2017 New York State regents exam in Algebra II (Common Core).

I believe the question needs the word "tsunami" rather than "tidal".  The presence of the word "tidal" in this context illustrates the need for improved "proofreading" in the creation of these exams.

Continuing on, here is question 24 from the New York State Geometry (Common Core) regents exam:

I suspect that the word "cone" here should read "inverted cone". When used by itself, the word "cone" refers to this:

Rarely have I seen a water cup used "point up". Let me correct myself: I have never seen a cup used that way.  Should a student solve the question as written, they could be perfectly correct and get an answer not listed. That situation should be avoided at all costs on a state exam.

Let's look at question 8 from the January 2017 NY regents exam in Algebra I (Common Core):

I found this question misleading, since the USPS charges 49 cents for up to 1 ounce and 21 cents for each extra ounce or fraction of an ounce. The best mathematical model would be 

\({\rm{Cost}} = 49 + 21(w - 1)\)

where w is the weight of the letter in ounces and the costs are measured in cents.

I suspect the question writer was trying to come up with a "real world' application of recursive functions. My advice would be to look again. Question 20 on this test would have made a much better model, as postage must take into account portions of an ounce but mp3 sales would not.

Now comes question 14 from the same Algebra I exam;

The mathematics in this question is basically asking "Which of the following is equal to 6(16)^t ?" The rest of the verbiage is due to the attempt to make the problem "real world".

Can't we just ask math questions to test math knowledge?