[LON-CAPA-users] square roots in formula response
Justin Gray
lon-capa-users@mail.lon-capa.org
Mon, 3 Sep 2007 17:53:39 -0800
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Hi Peter,
Are you sure that Maxima does not simplify expressions when comparing them?
I was under the impression that Maxima tries to simplify the difference of
two equivalent expressions and verify that it is zero. Consider the
following problem.
<problem>
<startouttext />
Simplify: <p></p>
<m display =3D jsmath>$\Large{\frac{x^3 - 3x^2 + 3x - 9}{x^4 - 81}} =3D $</=
m>
<endouttext />
<formularesponse answer=3D"(x^2 + 3)/((x + 3)(x^2 + 9))">
<textline readonly=3D"no" size=3D"40" />
</formularesponse>
</problem>
This appears to accept the LHS as a correct answer.
Thanks,
Justin
On 9/3/07, Justin Gray <jgray@math.sfu.ca> wrote:
>
> Many thanks, Peter. This is exactly what I was looking for.
>
> Justin
>
> On 9/3/07, Peter Riegler <p.riegler@fh-wolfenbuettel.de > wrote:
> >
> > Hi Justin,
> >
> > does "elegant" include two seperate input fields, for demoninator and
> > numerator? Or did you come up with two input fields because otherwise
> > the lhs (i.e. non-rationalized) would be accepted if using sampling?
> > If so, I would suggest something like
> > <formularesponse answer=3D"(m - 4)*(sqrt(m) + 4)/(m-16)">
> >
> > (I would prefer the students enter sqrt(m) rather than sqrtm).
> >
> > What the above does is to ask maxima
> > is( STUDENTSRESPONSE =3D (m - 4)*(sqrt(m) + 4)/(m-16));
> >
> > The important point here is that a student's reponse
> > (m-4)/(sqrt(m)-4)
> > would return false. The reason is, maxima does not simplify before
> > comparison.
> >
> > Hope this will help.
> >
> > Peter
> >
> > Justin Gray wrote:
> >
> > > Does anyone know a more elegant way to write the problem below?
> > >
> > > Thanks,
> > > Justin
> > >
> > > <problem>
> > > <startouttext />Rationalize the denominator and
> > simplify:<p></p><br></br>
> > > Use sqrtm for <m display =3D jsmath>$\sqrt{m}</m>.<p></p>
> > > <table>
> > >
> > > <tr>
> > > <td><m display=3D"jsMath">\, \, \, \, $m - 4$</m></td> <td></td>
> > > <td><endouttext />
> > > <formularesponse samples=3D"m,sqrtm@-3,-3:3,3#5" answer=3D"(m - 4)(sq=
rtm +
> >
> > > 4)" id=3D"11">
> > >
> > > <textline readonly=3D"no" size=3D"20" />
> > >
> > > </formularesponse><startouttext /></td>
> > > </tr>
> > > <tr>
> > > <td><hr width=3D"60"></hr></td> <td><m display=3D"jsMath">$\mbox{=
} =3D
> > > \mbox{ }$</m></td> <td><hr width=3D"140"></hr></td>
> > > </tr>
> > > <tr>
> > > <td><m display=3D"jsMath">$\sqrt{m} - 4$</m></td> <td></td>
> > > <td><endouttext />
> > > <formularesponse samples=3D"m@-3:3#5" answer=3D"m - 16" id=3D"12">
> > >
> > > <textline readonly=3D"no" size=3D"20" />
> > >
> > > </formularesponse><startouttext /></td>
> > > </tr>
> > > </table><p></p><endouttext />
> > > </problem>
> > >
> > >
> > > --
> > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> > > Justin Gray Tel.
> > > 778-782-4237
> > > Dept. of Mathematics Fax.
> > 778-782-4947
> > > Simon Fraser University
> > > 8888 University Drive
> > > Burnaby, B.C. V5A 1S6
> > > Canada
> > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> >
> > --
> > Peter Riegler
> > Fachhochschule Braunschweig/Wolfenb=FCttel
> > Salzdahlumer Str. 46/48, 38302 Wolfenb=FCttel
> > Tel. +49 5331 939 6314, Fax. +49 5331 939 6002
> > email: p.riegler@fh-wolfenbuettel.de
> > http://public.rz.fh-wolfenbuettel.de/~riegler<http://public.rz.fh-wolfe=
nbuettel.de/%7Eriegler>
> > _______________________________________________
> > LON-CAPA-users mailing list
> > LON-CAPA-users@mail.lon-capa.org
> > http://mail.lon-capa.org/mailman/listinfo/lon-capa-users
> >
>
>
>
> --
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Justin Gray Tel.
> 778-782-4237
> Dept. of Mathematics Fax. 778-782-4947
> Simon Fraser University
> 8888 University Drive
> Burnaby, B.C. V5A 1S6
> Canada
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
--=20
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Justin Gray Tel.
778-782-4237
Dept. of Mathematics Fax. 778-782-4947
Simon Fraser University
8888 University Drive
Burnaby, B.C. V5A 1S6
Canada
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Hi Peter,<br><br>Are you sure that Maxima does not simplify expressions whe=
n comparing them? I was under the impression that Maxima tries to simplify =
the difference of two equivalent expressions and verify that it is zero. Co=
nsider the following problem.
<br><br><problem> <br> <startouttext />=
;<br>Simplify: <p></p><br><br><m display =3D jsmath>$\Lar=
ge{\frac{x^3 - 3x^2 + 3x - 9}{x^4 - 81}} =3D $</m><br> &nb=
sp; <endouttext /><br><br> <formularesponse answ=
er=3D"(x^2 + 3)/((x + 3)(x^2 + 9))">
<br> <textline readonly=3D&quo=
t;no" size=3D"40" /> <br> &n=
bsp; </formularesponse><br></problem><br><br>This appears to ac=
cept the LHS as a correct answer.<br><br>Thanks,<br>Justin<br><br>
<div><span class=3D"gmail_quote">On 9/3/07, <b class=3D"gmail_sendername">J=
ustin Gray</b> <<a href=3D"mailto:jgray@math.sfu.ca">jgray@math.sfu.ca</=
a>> wrote:</span><blockquote class=3D"gmail_quote" style=3D"border-left:=
1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex=
;">
Many thanks, Peter. This is exactly what I was looking for.<br><span class=
=3D"sg"><br>Justin</span><div><span class=3D"q" id=3D"q_114cd9381ef54c6d_2"=
><br><br><div><span class=3D"gmail_quote">On 9/3/07, <b class=3D"gmail_send=
ername">
Peter Riegler</b> <<a href=3D"mailto:p.riegler@fh-wolfenbuettel.de" targ=
et=3D"_blank" onclick=3D"return top.js.OpenExtLink(window,event,this)">p.ri=
egler@fh-wolfenbuettel.de
</a>> wrote:</span><blockquote class=3D"gmail_quote" style=3D"border-lef=
t: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1=
ex;">Hi Justin,<br><br>does "elegant" include two seperate input =
fields, for demoninator and
<br>numerator? Or did you come up with two input fields because otherwise<b=
r>the lhs (i.e. non-rationalized) would be accepted if using sampling?<br>I=
f so, I would suggest something like<br><formularesponse answer=3D"=
(m - 4)*(sqrt(m) + 4)/(m-16)">
<br><br>(I would prefer the students enter sqrt(m) rather than sqrtm).<br><=
br>What the above does is to ask maxima<br>is( STUDENTSRESPONSE =3D (m - 4)=
*(sqrt(m) + 4)/(m-16));<br><br>The important point here is that a student&#=
39;s reponse
<br>(m-4)/(sqrt(m)-4)<br>would return false. The reason is, maxima does not=
simplify before<br>comparison.<br><br>Hope this will help.<br><br>Peter<br=
><br>Justin Gray wrote:<br><br>> Does anyone know a more elegant way to =
write the problem below?
<br>><br>> Thanks,<br>> Justin<br>><br>> <problem><br>=
> <startouttext />Rationalize the denominator and simplify:<p&g=
t;</p><br></br><br>> Use sqrtm for <m display =3D j=
smath>$\sqrt{m}</m>.<p></p>
<br>> <table><br>><br>> <tr><br>> =
<td><m display=3D"jsMath">\, \, \, \, $m - 4$&=
lt;/m></td> <td></td><br>> <td><endouttext=
/><br>> <formularesponse samples=3D"m,sqrtm@-3,-3:3,3#5"=
; answer=3D"(m - 4)(sqrtm +
<br>> 4)" id=3D"11"><br>><br>> =
<textline readonly=3D"no" size=3D"20" /><b=
r>><br>> </formularesponse><startouttext /></td><br=
>> </tr><br>
> <tr>
<br>> <td><hr width=3D"60">=
;</hr></td> <td><m display=3D"jsMath">$\m=
box{ } =3D<br>> \mbox{ }$</m></td> <td><hr width=3D=
"140"></hr></td>
<br>> </tr><br>> <tr><br>> <=
;td><m display=3D"jsMath">$\sqrt{m} - 4$</m></t=
d> <td></td><br>> <td><endouttext /><br>> =
<formularesponse samples=3D"m@-3:3#5" answer=3D"m - 16&qu=
ot; id=3D"12">
<br>><br>> <textline readonly=3D"no&q=
uot; size=3D"20" /><br>><br>> </formularesponse>&l=
t;startouttext /></td><br>> </tr><br>> </table>&=
lt;p></p><endouttext />
<br>> </problem><br>><br>><br>> --<br>> ~~~~~~~~~~~~~~=
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<br>> Justin Gray &nb=
sp; =
&nb=
sp; =
Tel.<br>&=
gt; 778-782-4237<br>
> Dept. of Mathematics &n=
bsp;  =
; &n=
bsp; Fax. 778-782-4947
<br>> Simon Fraser University<br>> 8888 University Drive<br>> Burn=
aby, B.C. V5A 1S6<br>> Canada<br>> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=
~~~~~~~~~~~~~~~~~~~~~~~~~~<br><br>--<br>Peter Riegler<br>Fachhochschule Bra=
unschweig/Wolfenb=FCttel
<br>Salzdahlumer Str. 46/48, 38302 Wolfenb=FCttel<br>Tel. +49 5331 939 6314=
, Fax. +49 5331 939 6002<br>email: <a href=3D"mailto:p.riegler@fh-wolfenbue=
ttel.de" target=3D"_blank" onclick=3D"return top.js.OpenExtLink(window,even=
t,this)">
p.riegler@fh-wolfenbuettel.de</a><br><a href=3D"http://public.rz.fh-wolfenb=
uettel.de/%7Eriegler" target=3D"_blank" onclick=3D"return top.js.OpenExtLin=
k(window,event,this)">
http://public.rz.fh-wolfenbuettel.de/~riegler</a><br>______________________=
_________________________<br>LON-CAPA-users mailing list<br><a href=3D"mail=
to:LON-CAPA-users@mail.lon-capa.org" target=3D"_blank" onclick=3D"return to=
p.js.OpenExtLink(window,event,this)">
LON-CAPA-users@mail.lon-capa.org</a>
<br><a href=3D"http://mail.lon-capa.org/mailman/listinfo/lon-capa-users" ta=
rget=3D"_blank" onclick=3D"return top.js.OpenExtLink(window,event,this)">ht=
tp://mail.lon-capa.org/mailman/listinfo/lon-capa-users</a><br></blockquote>=
</div>
<br><br clear=3D"all"><br></span></div>-- <br>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
<div><span class=3D"e" id=3D"q_114cd9381ef54c6d_4"><br>Justin Gray &nb=
sp; =
&nb=
sp; =
Tel. 778-=
782-4237<br>Dept. of Mathematics &=
nbsp; &nbs=
p; &=
nbsp; Fax. 778-782-4947<br>Simon Fraser University
<br>8888 University Drive<br>Burnaby,=20
B.C. V5A 1S6<br>Canada<br>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=
~~~~~~~~~~~
</span></div></blockquote></div><br><br clear=3D"all"><br>-- <br>~~~~~~~~~~=
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<br>Justin Gray &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; Tel. 778-7=
82-4237<br>Dept. of Mathematics &n=
bsp;  =
; &n=
bsp; Fax. 778-782-4947
<br>Simon Fraser University<br>8888 University Drive<br>Burnaby, B.C. V5A 1=
S6<br>Canada<br>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=
~
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