In Statics and Dynamics, the one Mechanical Engineering class we had to take was MEE 225 first semester sophomore year in the Fall of 1982. Our professor, James Somerset, programmed his computer to generate unique exams for each student. There were 25 problems and you had to match them with answers in a 36 answer grid -- there were 11 extra answers. We all got our own data. For example, a _A__kg car is traveling at __B_m/s. We also got different As and Bs.
This promoted academic integrity as there was absolutely no way to cheat as we were all doing different problems!!
Saturday, September 29, 2012
Saturday, September 22, 2012
September 2012 Brain Teaser Solution
Q: When a four digit number wxyz is multiplied by 4, the digits are reversed and it becomes zyxw. All the digits are different. What is the number?
A: 2178
If the number is still 4 digits when multiplied by 4, then the number has to be less than 2500 (as 2500 x 4 = 10000 and you would then have 5 digits).
That makes w = 1 or 2
But when multiplying by 4, the last digit will never be 1 so when we reverse to zyxw, the w must be 2 so that the last digit will then be 2. The multiples of 4 that have a last digit of 2 are 3 x 4 and 8 x 4.
Since we are multiplying a number in the 2000s by 4, the number is becomes will start with an 8.
w = 2 and z = 8
The second digit x must be 4 or less as it says above, the number must be less than 2500.
Because 2250 x 4 = 9000, x must be 0 1 or 2
Through some trial and error, you can find that the number is 2178 and its reverse is 8712.
If the number is still 4 digits when multiplied by 4, then the number has to be less than 2500 (as 2500 x 4 = 10000 and you would then have 5 digits).
That makes w = 1 or 2
But when multiplying by 4, the last digit will never be 1 so when we reverse to zyxw, the w must be 2 so that the last digit will then be 2. The multiples of 4 that have a last digit of 2 are 3 x 4 and 8 x 4.
Since we are multiplying a number in the 2000s by 4, the number is becomes will start with an 8.
w = 2 and z = 8
The second digit x must be 4 or less as it says above, the number must be less than 2500.
Because 2250 x 4 = 9000, x must be 0 1 or 2
Through some trial and error, you can find that the number is 2178 and its reverse is 8712.
Friday, September 07, 2012
Regents Scoring and new 3 - 8 Math sample items
http://cityroom.blogs.nytimes.com/2012/09/06/at-a-new-school-a-math-lesson-from-the-mayor/#postComment
Jeff S is correct: if students get 30 points out of 87 (34%), it gets scaled up to a 65.
Here is the conversion chart for the most recent Integrated Algebra Regents -- it is still thankfully up on line as the actual exam ;)
http://www.nysedregents.org/IntegratedAlgebra/612/ialg62012-cc.pdf
Unfortunately, the latest 3 - 8 exams have not been posted due to the changeover to the Common Core. The latest exams for grades 3 - 8 are 2010: Here is an example: http://www.nysedregents.org/Grade5/Mathematics/home.html
However, there are new sample items for Grades 3 - 8 and they look more challenging than the old exams -- check them out:
http://www.p12.nysed.gov/assessment/common-core-sample-questions/ (scroll to the bottom)
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