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Topic: MIT Math Diagnostic for Physics Placement
Replies: 17   Last Post: Oct 24, 2012 12:51 PM

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Dave L. Renfro

Posts: 4,546
Registered: 12/3/04
Re: MIT Math Diagnostic for Physics Placement
Posted: Oct 22, 2012 2:06 PM
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Robert Hansen wrote:

http://mathforum.org/kb/message.jspa?messageID=7910476

> This is a practice exam...
>
> http://web.mit.edu/firstyear/2016/subjects/PracticeTest2008.pdf
>
> This is essentially a pre-calculus exam.


[...]

> It amazes me that MIT freshmen would have so much
> difficulty with this exam.


I too am rather amazed, but not because they're essentially
precalculus level, but because the difficulty level doesn't
seem to exceed what shows up on average level precalculus
tests. I can somewhat believe this now, but if you had shown
this to me when I was in high school, I would have thought
this was a joke (except the two or three "find the derivative"
questions, which could be a problem for someone whose high
school didn't offer calculus and who didn't have a college
campus within driving distance). I had this view (and still
do, but nowhere near as much) that those who got into places
like MIT, Pinceton, Harvard, etc. were geniuses who probably
could have learned calculus (and Russian, and molecular
biology, etc.) in middle school if they had the opportunity.
These were the 1500+ SAT people, the math olympiad people,
the people who entered projects in the Westinghouse Science
Talent Search, etc. ... the kinds of people who showed up
at a high school like mine maybe once a decade.

Now for the obligatory nitpicks of the problem statements.

Problem A1: They should say that k is an integer. Otherwise,
a correct answer would be (1/2) x 10^(log 2x), where x equals
the given numerical expression.

Problem B1: They should say that a and b are real numbers.
Otherwise, a correct answer would be a + 0*i, where a equals
the given expression(s).

Problem B2: Instead of saying "Find all possible values of x which
solve the equation x^4 - 13x^2 + 36 = 0", I would be less vague and
explicitly ask for all complex solutions.

Dave L. Renfro



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