I had the opportunity today to proctor a Regents algebra test at John Jay high school today. I am not allowed to read during administrating these tests, as they are 'very serious', and we have to be on the constant alert so the students can't cheat.
(These are NY statewide exams, all given at the same time all over the state at each school.)
Because of a long story, I luckily ended up with a class of only 5 students, who had other tests to take right after, so were allowed to leave when finished, (which is not usually the case). So, when I was whittled down to 2 students left, I took the opportunity to glance down at the test questions every once and awhile to see if I could do them. ( I had 3 completed tests in front of me, and on most answers, all 3 were different. :) )
I was happy to say I could do most, but I came up with one I was stumped on. I tried to ask dad when I got home tonight, but he is too involved in IBM's own math and engineering troubles to even hear mine. He plans on working all evening. (PS- a fellow IBMer named Peppy who was top level and used to work a lot with dad was layed off yesterday. Dad said he was one of the smartest guys he knew.)
so: if anyone can help me with this problem, I would love it.
There are 64 volleyball teams, and 1/2 of them get eliminated after each round.
let t = how many teams are left, and r = rounds.
find the equation. these are the 4 answers in the multiple choice question:
a- 64(r) to the .05power ( I don't know how to type that)
b- 64(-0.5) to the r ( r is the exponent)
c- 64(1.5) to the r "
d- 64(0.5) to the r "
I am going to go figure it out by just substituting in figures, but I was not sure how to do that without guessing.
4 comments:
t = 54(.5)^r
There isn't a wrong or right way to do it. It's just a word problem. they arn't asking you to compute anything.
I don't understand what you are asking per say. They are just testing the students knowledge of equations and the use of the distibutive property of multiplication using power notation.
64(.5 * .5 * .5 * .5) = 64(.5)^4
If you were smart enough to work backwards and use substitution then you understood enough about equations and the distributive propery of exponents to answer correctly. Theres nothing worng with that, but it would be faster to just think that every round cuts the number of teams in half, therfore a power of .5 could represent the number of rounds.
that's what I thought! oh good. I still have it!!!!
thanks!
Hey, even Jarek got it right - though I think he guessed it more than work it out in his head. The equation should be:
t = 64 * (.5^r)
The students could easily figure it out by writing it out. e.g. the first round they know there are only 32 left and the second, 16. So plug those numbers into t and r and the only one that works is d. Fun brain age problem for us - thanks for sharing.
good job Jarek! you know high school math !
It was fun to see how many questions I knew. I always enjoy using my brain.
I like to think hard, and I like to be challenged, esp. in math.
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