The June 2008 Math B exam is fairly typical – and that includes too many problematic questions.

Format: the exam is made up of 20 2-point multiple choice questions, 6 2-point free response questions, 6 4-point free response questions, and 2 6-point free response questions (yes, 88 points, scaled so that 46 this year is passing)

I chose several questions I think are bad: one multiple choice, 2 2-point free response, 3 4-point free response, and both 6-point free response.

#18 (multiple choice) A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB = 20 feet. What is the length of arc AC, in feet?

Diagram (omitted) is normal. Whole question is normal. Except lawn care companies don’t measure angles in radians. And math-y folks measure angles in multiples of π radians. Look folks, artificial, contrived context is confusing and weighs problems down. Don’t do it.

(more below the fold)

#21 (2 point free response) The entire graph of f(x) is symmetric with respect to the origin. If the accompanying graph represents f(x) for x ≥ 0, sketch, on the same axes, the graph of f(x) for x ≤ 0.

Leave aside the duplicated value of x. The diagram looks like $f(x) = +\sqrt{x}$ . Reasonable? I don’t think so. This “symmetric with respect to the origin” bothers me as a sort of vocab-trivia question. What do you think?

#31 (4 point free response) The engineering office in the village of Whitesboro has a map of the village that is laid out on a rectangular coordinate system. A traffic circle located on the map is represented by the equation $(x+4)^2 + (y-2)^2 = 81$. The village planning commission asks that the transformation $D_2$ be applied to produce a new traffic circle, where the center of the dilation is at the origin.

Find the coordinates of the new center of the traffic circle.

Find the length of the radius of the new traffic circle.

Where to begin? The transformation may be a bit confusing. All the regular NYS texts dilate 95% of the time about the origin, and usually do not state as much. Someone caught this, corrected the language, but leaves the students with a clarifying detail they are not used to reading. Further, the dilation is written as $D_2$, and then repeated in words. I don’t think I like that. Confusing, not clarifying. And not parallel, since the words state the center, and the symbols don’t.

But more. Context? Could you get more artificial? Bizarre? Village laid out in a rectangle, ok. But x-y equation for a street feature? Arbitrary transformation of a traffic circle? And the result, I’m glad they didn’t give the kids a graph to plot this one on, one traffic circle entirely enclosing the other???

3 more problems, coming soon.

1. June 22, 2008 am30 8:08 am 8:08 am

I think the dilation is the most egregious. What does D_2 mean, is this some sort of New York terminology. Is the math equivalent of “ring ding”.

2. June 22, 2008 am30 8:18 am 8:18 am

$D_2$ is a dilation by a factor of 2, center of dilation unspecified. The notation is neither obscure, I have seen it in text books, nor universal (there are entire books on transformations that don’t use that notation). In NY State it is ubiquitous. And most teachers here are unaware that the notation is not universal.

The radian problem would have been far better without the context, and with a multiple of pi radians, or with degrees.

3. June 22, 2008 pm30 4:56 pm 4:56 pm

How about this for a problem with the lawn care problem. Why would this company be interested in arc-length anyway. It seems much more natural to be interested in the area that you have watered not the length of the edge.

4. June 22, 2008 pm30 6:43 pm 6:43 pm

Matt, I agree. To make the problem realistic would require a more complicated model. Better to drop the artificial context altogether.

I grew up learning math in math class, and using math in science classes. I don’t know how I can be comfortable, how we can be comfortable, doing the modeling where the skill acquisition is supposed to be taking place.

5. June 22, 2008 pm30 10:45 pm 10:45 pm

I have no problem with artificial context, to be honest. It’s there to test if they can pick the relevant parts out of a question, which is surely a testable skill?

The first problem you posted, I agree that the context is daft – because it’s too brief to present any sort of challenge to reading and comprehension, rather than because it doesn’t make sense in itself. All sorts of things in the real world make no sense but still happen, after all! I don’t have a problem with “1 radian” – the assertion that mathy people measure angles in multiples of pi holds true only when they’re *nice* multiples of pi.

Next question: whatever “symmetric with respect to the origin” is supposed to mean, it probably shouldn’t. I couldn’t begin to guess. Do the mean symmetric in the x axis? y? both? rotational symmetry, and if so of what order?

Third question: if “D_2” means “enlargement* with scale factor 2 about the origin”, then the wording is redundant. If it means “enlargement with scale factor 2” then it’s a bad piece of notation as it doesn’t describe a transformation without further information. Either way I really don’t like this sort of unglossed semi-standard notation stuff.

* we brits say “enlargement” rather than “dilation”

6. June 22, 2008 pm30 11:06 pm 11:06 pm

Addendum to previous: I guess they’re talking point symmetry? Yuck.

7. June 22, 2008 pm30 11:22 pm 11:22 pm

Point symmetry – yes.
Yuck – yes.

August 7, 2008 pm31 9:11 pm 9:11 pm

i hate this regent, there are a lot of problem that i dont even get, its very confusing, i mean i almost fail it, i did do a lot of practices