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[math-fun] California Math Exit Exam
by Henry Baker 18 May '06

18 May '06

Here's another question to add to the California Exit Exam for high school students in mathematics: If there are 80 questions on this test, and each of the 80 questions has 4 choices, what is the probability that someone could pass (>= 55%) [oops, first answer the question of how many questions out of a total of 80 questions 55% is] the test, if for each question he chose one of the 4 answers at random (p=25% for each answer). Alternatively, assuming that the test preparers aren't insane, what is the probability that someone could pass the test by always choosing the "A" answer for each question? Extra credit: using this probability, estimate the number of times one should take the test to raise the probability of passing it at least once to 80%.

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Re: [math-fun] big numbers and how they're made
by dasimov＠earthlink.net 17 May '06

17 May '06

Have you tried 2600 ? --Dan << I bought this book, "Identification Numbers and Check Digit Schemes" in the hopes that it would describe the ID number / checksum / hashing schemes actually used in some real applications. I'd like to give a talk on the subject to a general audience. http://www.amazon.com/gp/product/0883857200/104-8328046-6239112?v=glance&n=… However, this book left me unsatisfied. Ideally, I'd like to know, for example, how to distinguish between a valid UPS tracking number and an invalid one, or (say) a valid US twenty dollar bill serial number and an invalid one. UPS tracking#: 1Z9999999999999999 US $20 bill, Series 2004: EB 42994244 D Such schemes are presumably often proprietary / unpublished, for security reasons, although the "there is no security through obscurity" maxim would seem to apply. Googling hasn't turned up much, except in a few unsavory hacking resources (mostly how to forge a valid credit card number) Anyone know a good resource? >>

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[math-fun] Don't hire authoritarian programmers
by R. William Gosper 17 May '06

17 May '06

This quick and not at all dirty one liner to draw an orthoscheme, block([o:[0,0,0],a:[1,0,0],b:[0,1,0],c:[0,1,1]],plotfaces(combinations([o,a,b,c],3))) was thwarted by the previous incarnation of this line of code in Macsyma\Macsyma2\share\set2 : /*if not %set=setify(%set) then "Some a&&hole thinks you should be screwed with error(\"First argument to subpowerset must be a set.)",*/ --rwg PS, It can't be news to serious sudokulists, but making the rounds of Mountain View High School is gosper.org/sud5.PNG, a quincunx of overlapping 9x9s with clues in four concentric rings.

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RE: [math-fun] California Math Exit Exam
by dasimov＠earthlink.net 16 May '06

16 May '06

<< > The radius of the earth's orbit is 150,000,000,000 meters. What is > this number in scientific notation? > A 1.5x10^-11 > B 1.5x10^11 > C 15x10^10 > D 150x10^9 > > [The last time I looked, the Earth's orbit was ~ elliptical, so it > has a semimajor & semiminor axis...] B, C, and D are all correct. Is scientific notation supposed to be normalized, making B the only correct answer >> Yes, that's the way it's usually taught in school. --Dan

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RE: [math-fun] California Math Exit Exam
by Marc LeBrun 16 May '06

16 May '06

>=Cordwell, William R > so a student with knowledge at only the 40% level (whatever that means) Speaking as a product of the California public school system myself: If it's indeed true, as I've heard, that the math portion only involves curriculum material at or below the 8th grade level, and the English at or below 10th grade level, then that means, let's see, 3rd or 4th grade level, right? Do I pass?

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Re: [math-fun] California Math Exit Exam
by Henry Baker 16 May '06

16 May '06

I seem to recall someone once advertising butter by the "tub", but 45 gallons of butter would be a pretty big tub... Also 60 lbs of tea: http://www.new-york-lawyer.ws/law-dictionary/tribute.htm At 05:37 AM 5/16/2006, dasimov(a)earthlink.net wrote: >Don't people know that "tub" means a largish pail, not just a bathtub? > >--Dan

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Re: [math-fun] California Math Exit Exam
by dasimov＠earthlink.net 16 May '06

16 May '06

Don't people know that "tub" means a largish pail, not just a bathtub? --Dan

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RE: [math-fun] California Math Exit Exam
by Russ Cox 16 May '06

16 May '06

> Tina is filling a 45 gallon tub at a rate of 1.5 gallons of water per minute. At this rate, how long will it take to fill the tub? > > A 30.0 minutes > B 43.5 minutes > C 46.5 minutes > D 67.5 minutes > > [What's a "tub" ? Is that like a bathtub? ] 45 gallons would be a very small bathtub. Russ

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RE: [math-fun] California Math Exit Exam
by Cordwell, William R 15 May '06

15 May '06

However, a student who knew only 32 out of 80 questions could guess randomly on the remaining 48 questions, and expect to come very close to the required 44 correct answers; so a student with knowledge at only the 40% level (whatever that means) might expect to pass, as long as there is no penalty for incorrect answers. -----Original Message----- From: math-fun-bounces+cordwell=sandia.gov(a)mailman.xmission.com [mailto:math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com]On Behalf Of Henry Baker Sent: Monday, May 15, 2006 3:07 PM To: math-fun Subject: Re: [math-fun] California Math Exit Exam I didn't really set up this posting correctly. In California, we now (are supposed to) have an "exit exam" for high school students which sets standards for graduation. http://www.cde.ca.gov/ta/tg/hs/ The math portion of the test is approx. 80 questions, each of which is multiple choice with 4 choices. A radio talk show host here in Los Angeles was carrying on about how easy it should be to pass this examination, since it required only a 55% score to pass. If I've done _my_ math correctly, a completely random answer sheet with 20 questions would pass with a probability of ~ 1/254; with 40 questions would pass with a probability of ~ 1/20560, with 60 questions would pass with a probability of ~ 1/1467711, and with 80 questions would pass with a probability of ~ 10^-8. So, our random student would have to take the test on the order of 10 million times to have a good probability of passing it. So monkeys with typewriters probably aren't going to pass. At 08:42 PM 5/14/2006, Henry Baker wrote: >Here's another question to add to the California Exit Exam for >high school students in mathematics: > >If there are 80 questions on this test, and each of the 80 questions >has 4 choices, what is the probability that someone could pass >(>= 55%) [oops, first answer the question of how many questions out >of a total of 80 questions 55% is] the test, if for each question >he chose one of the 4 answers at random (p=25% for each answer). > >Alternatively, assuming that the test preparers aren't insane, >what is the probability that someone could pass the test by always >choosing the "A" answer for each question? > >Extra credit: using this probability, estimate the number of times >one should take the test to raise the probability of passing it at >least once to 80%. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] eta as theta
by R. William Gosper 12 May '06

12 May '06

oo pi 1/6 /===\ Theta (--, q ) 1/24 | | k 2 6 eta(q) := q | | (1 - q ) = ---------------- . | | sqrt(3) k = 1 This can't be new. Why isn't it more prevalent? Instead I've been using a bletcherous Thetaprime_1(0,sqrt(q)) for (q;q)_oo in the q-Gamma/q-factorial reflection (and q-sin) formulae. --rwg

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