```Date: Sep 29, 2012 6:50 AM
Author: Robert Hansen
Subject: Re: An Algebra 2 Test

What can I say? I didn't know the "hidden trick".Bob HansenOn Sep 29, 2012, at 1:23 AM, Wayne Bishop <wbishop@calstatela.edu> wrote:> My guess is that the approach Dave had in mind was more obvious:> a^2 - (a-1)^2 = (a - (a-1)) (a + (a-1)) = (1)(2a - 1)> > Wayne> > At 08:36 PM 9/28/2012, Robert Hansen wrote:>> a^2 - (a-1)^2 = a^2 - (a^2 - 2a + 1) = 2a - 1 = 13.04822...>> >> This is a very good point, work the algebra FIRST. I wonder how many algebra teachers are even capable of concocting such a problem? Working backwards and making sure that 2*a doesn't require any more than single digit math (no digit greater than 4). I have to think about this. This works well with large integers as well, with the same condition on the digits.>> >> Lou, what do you say to problems like this with regards to our prior art discussion?>> >> Ha, calculators are allowed. Calculators with 70 digits of precision I suppose.:)>> >> Bob Hansen>> >> On Sep 28, 2012, at 5:51 PM, "Dave L. Renfro" <renfr1dl@cmich.edu> wrote:>> >> > Robert Hansen wrote:>> > >> > http://mathforum.org/kb/message.jspa?messageID=7897638>> > >> >> I want to try something different. I want everyone to contribute>> >> problems for a hypothetical algebra 2 exam. You can contribute>> >> just topics if you wish though I would like see examples as well.>> >> I am going with algebra 2 rather than algebra 1 because I think>> >> the line is more well defined.>> > >> > I only have a few moments before I need to leave to tutor>> > someone, but here's a somewhat silly one off the top of>> > my head:>> > >> > Determine the exact value of a^2 - b^2 if>> > >> > a = 7.0241132301442003123012230341430201>> > b = 6.0241132301442003123012230341430201>> > >> > Calculators are allowed.>> > >> > Dave L. Renfro
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