My favorite bad exam target: Math B (and a puzzle)
June 23, 2009 am30 8:35 am
I don’t like high stakes tests (I think necessary testing can be done in a way to reduce the stakes, and lots of testing is not necessary). And I don’t like bad math. And, if you read this blog you know, I hate Math B. How much? Take a look at some of these old posts:
Challenge problem. Go to the NY State Regents Exams and open the June 2004 Math B exam. Answer the circle problem (#33) using the arcs/angles. Now solve it again, using the relationships between the segments. They contradict, right?
Now, the challenge. Are the numbers they supplied possible, or impossible? Explain.
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Is there a posting of yesterday’s Math B June 2009 regents anywhere online? Hope so – wanted to look at the exam. I understand the cut-off conversion raw score is 47.
(Not been around for a while, busy – sorry to dig up an old post!)
Anyway. I don’t understand you. I’m looking at the circle problem, about the “machine part”. I’m not familiar with the notation in the first half of the last line, but I assume it’s telling me the ratio between arcs TA, AR and RT – which allows me to position T, A and R on a circle of arbitrary size. The only other information I’m given is RA (which allows me to size the circle) and AP (which allows me to position P given the size of the circle and the positions or R and A). Unless I’m missing something, which is definitely possible as tired as I am, I need all of this information to specify the problem – so how can I solve it using only part of it? How can there be a contradiction?
All I can think is that you want me to assume PT’s a tangent at T, but it doesn’t say so.
Doubtless I’m being dumb. Please advise.
You’ve nailed it, of course.
New York State assumed they were giving the kids a tangent. But the angles and the lengths support a non-tangent segment, with much harder math involved than they intended.
Ah, OK. Does your rubric allow you to assume that a line meeting at T is tangential?
If not, it’s actually worse (because I did think, wow, that seems like a pretty tough question – but I don’t know the metric here :)). A weaker kid will assume it’s a tangent and get full credit for getting it wrong, and – worse – a stronger kid won’t, and will get it right, and very likely get it marked as wrong!
Bah.
Unrelatedly, I’m very glad to see you back posting regularly and more on math :).