qu.1.topic=Basic Algebra@

qu.1.1.mode=Matching@
qu.1.1.name=Matching  - simple algebra@
qu.1.1.comment=<p>In general, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>e</mi><mrow><mi>A</mi></mrow></msup><msup><mi>e</mi><mrow><mi>B</mi></mrow></msup><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi>e</mi><mrow><mi>A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>B</mi></mrow></msup></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>e</mi><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mi>A</mi></mrow></mfenced></mrow></msup><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>A</mi></mrow></mstyle></math>.</p>@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$f=range(0,1,1);
$Q=maple("
d:=2*(-1)^($f):
a1:=X+(d):
a2:=X-(d):
A:=($a1)*($a2):
A1:=MathML[ExportPresentation](A):
A0:=expand(A):
A2:=MathML[ExportPresentation](A0):
b1:=a1:
b2:=a2:
b3:=ln(b2):
B3:=MathML[ExportPresentation](b3):
b4:=exp((b1)*(b3)):
B4:=MathML[ExportPresentation](b4):
b5:=simplify(b4):
B5:=MathML[ExportPresentation](b5):
c1:=exp(a1):
c2:=exp(a2):
c3:=(c1)*(c2):
c4:=ln(c3):
C4:=MathML[ExportPresentation](c4):
C5:=MathML[ExportPresentation](2*X):
A1,A2,B4,B5,C4,C5
");
$A1=switch(0,$Q);
$A2=switch(1,$Q);
$B4=switch(2,$Q);
$B5=switch(3,$Q);
$C4=switch(4,$Q);
$C5=switch(5,$Q);@
qu.1.1.uid=73b93fd5-473f-49d5-8950-178628bcc8aa@
qu.1.1.info=  Course=Introductory Mathematical Economics;
  Topic=Simple Algebra;
  Sub-Topic=Polynomials, Exponential, Ln;
  Difficulty=Medium;
  Author=Asha Sadanand;
  Feature=Matching;
@
qu.1.1.format.columns=3@
qu.1.1.question=<p>Match each of the numbered items in the list with the numbers in the drop-down menus:</p>@
qu.1.1.term.1=$A1@
qu.1.1.term.1.def.1=$A2@
qu.1.1.term.2=$B4@
qu.1.1.term.2.def.1=$B5@
qu.1.1.term.3=$C4@
qu.1.1.term.3.def.1=$C5@

qu.1.2.mode=Multiple Choice@
qu.1.2.name=Rearranging Exponential@
qu.1.2.comment=<p>In general, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi>e</mi><mrow><mi>A</mi></mrow></msup><msup><mi>e</mi><mrow><mi>B</mi></mrow></msup><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi>e</mi><mrow><mi>A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>B</mi></mrow></msup></mrow></mstyle></math>.</p>@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$a=range(2,9);
$b=range(2,9);
$c=range(2,9);
$v=maple("
F:=$a*exp($c*X*Y+$b*X^2):
Fpretty:=MathML[ExportPresentation](F):
v1:=MathML[ExportPresentation]($a*exp($c*X*Y)*exp($b*X^2)):
v2:=MathML[ExportPresentation]($a*(exp($c*X*Y)+exp($b*X^2))):
v3:=MathML[ExportPresentation](exp($a*$c*X*Y)+exp($a*$b*X^2)):
v4:=MathML[ExportPresentation](eval($a*exp($c*X*Y)^($b*X^2))):
Fpretty,v1,v2,v3,v4
");
$Fpretty=switch(0,$v);
$ans1=switch(1,$v);
$ans2=switch(2,$v);
$ans3=switch(3,$v);
$ans4=switch(4,$v);@
qu.1.2.uid=d6b9f941-27f6-4d71-b34c-6af059b86676@
qu.1.2.info=  Course=Introductory Mathematical Economics;
  Topic=Simple Algebra;
  Sub-Topic=Distributive Law;
  Author=Asha Sadanand;
  Difficulty=Easy;
@
qu.1.2.question=<p>The expression $Fpretty is equal to</p>@
qu.1.2.answer=1@
qu.1.2.choice.1=$ans1@
qu.1.2.choice.2=$ans2@
qu.1.2.choice.3=$ans3@
qu.1.2.choice.4=$ans4@
qu.1.2.fixed=@

qu.1.3.mode=Multiple Choice@
qu.1.3.name=Division by Common Factor 2@
qu.1.3.comment=<p>In general, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mi>A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mi>B</mi></mrow></mrow><mrow><mi>C</mi></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mi>A</mi><mrow><mi>C</mi></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mi>B</mi><mrow><mi>C</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$a=range(2,9);
$b=range(2,9);
$c=range(2,9);
$F=($a*$c*X*Y+$a*$b*X^2)/($a*X);
$Fpretty=mathml($F);
$ans1=mathml($c*Y+$b*X);
$ans2=mathml($c*Y+$b*$a*X^2);
$ans3=mathml($a*$c*X*Y+$a*X);
$ans4=mathml($c*X*Y+$a*$b*X);@
qu.1.3.uid=7458f88a-a397-46fa-845a-ffe884e6b6bf@
qu.1.3.info=  Course=Introductory Mathematical Economics;
  Topic=Simple Algebra;
  Sub-Topic=Distributive Law;
  Author=Asha Sadanand;
  Difficulty=Easy;
@
qu.1.3.question=<p>The expression $Fpretty simplifies to</p>@
qu.1.3.answer=1@
qu.1.3.choice.1=$ans1@
qu.1.3.choice.2=$ans2@
qu.1.3.choice.3=$ans3@
qu.1.3.choice.4=$ans4@
qu.1.3.fixed=@

qu.1.4.mode=Matching@
qu.1.4.name=Simple algebra@
qu.1.4.comment=<p>In general, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mi>AB</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mi>A</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mi>B</mi></mrow></mfenced></mrow></mstyle></math>&nbsp;and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><msup><mi>A</mi><mrow><mi>B</mi></mrow></msup></mrow></mfenced><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>B</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>ln</mi><mfenced open='(' close=')' separators=','><mrow><mi>A</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>.</p>@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=$Z=maple("
A1:=MathML[ExportPresentation]((ln(a)+ln(b)+ln(c))*d):
B1:=MathML[ExportPresentation](ln((a^d)*(b^d)*(c^d))):
A2:=MathML[ExportPresentation](ln((a+b+c)^d)):
B21:=MathML[ExportPresentation](ln(a+b+c)):
B22:=MathML[ExportPresentation](d):
A3:=MathML[ExportPresentation](ln((a+b+c)*d)):
B3:=MathML[ExportPresentation](ln(a+b+c)+ln(d)):

A1,B1,A2,B21,B22,A3,B3
");
$A1=switch(0,$Z);
$B1=switch(1,$Z);
$A2=switch(2,$Z);
$B21=switch(3,$Z);
$B22=switch(4,$Z);
$A3=switch(5,$Z);
$B3=switch(6,$Z);@
qu.1.4.uid=b81e98fb-c2ed-45b7-bbfb-bc6460723bd6@
qu.1.4.format.columns=3@
qu.1.4.question=<p>Match each of the numbered items in the list with the numbers in the drop-down menus:</p>@
qu.1.4.term.1=$A1@
qu.1.4.term.1.def.1=$B1@
qu.1.4.term.2=$A3@
qu.1.4.term.2.def.1=$B3@
qu.1.4.term.3=$A2@
qu.1.4.term.3.def.1=($B21)*($B22)@

qu.1.5.mode=Multiple Choice@
qu.1.5.name=Distributive Law 1@
qu.1.5.comment=<p>In general, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi><mfenced open='(' close=')' separators=','><mrow><mi>B</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>AB</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>AC</mi></mrow></mstyle></math>.</p>@
qu.1.5.editing=useHTML@
qu.1.5.solution=@
qu.1.5.algorithm=$a=range(2,8);
$b=range(2,8);
$c=range(2,8);
$F=$a*X*($b+$c*Y);
$Fpretty=mathml($F);
$ans1=mathml($a*$b*X+$a*$c*X*Y);
$ans2=mathml($a*$b*X+$c*Y);
$ans3=mathml($a*$b*X+$a*$c*Y);
$ans4=mathml($a*$b+$c*X*Y);@
qu.1.5.uid=72f22382-700d-4081-99c7-465ff764acbd@
qu.1.5.info=  Course=Introductory Mathematical Economics;
  Topic=Simple Algebra;
  Sub-Topic=Distributive Law;
  Author=Asha Sadanand;
  Difficulty=Easy;
@
qu.1.5.question=<p>The expression $Fpretty simplifies to</p>@
qu.1.5.answer=1@
qu.1.5.choice.1=$ans1@
qu.1.5.choice.2=$ans2@
qu.1.5.choice.3=$ans3@
qu.1.5.choice.4=$ans4@
qu.1.5.fixed=@

qu.1.6.mode=Multiple Choice@
qu.1.6.name=Division by Common Factor 1@
qu.1.6.comment=<p>In general, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mi>A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>B</mi></mrow><mrow><mi>C</mi></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mi>A</mi><mrow><mi>C</mi></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mi>B</mi><mrow><mi>C</mi></mrow></mfrac></mrow></mrow></mstyle></math>.</p>@
qu.1.6.editing=useHTML@
qu.1.6.solution=@
qu.1.6.algorithm=$a=range(2,9);
$b=range(2,9);
$c=range(2,9);
$F=($a*$c*X*Y+$a*$b*X^2)/($a*Y);
$Fpretty=mathml($F);
$ans1=mathml($c*X+$b*X^2/Y);
$ans2=mathml($c*X+$b*$a*X^2);
$ans3=mathml($a*$c*X*Y+$a*X);
$ans4=mathml($c*X*Y+$a*$b*X^2/Y);@
qu.1.6.uid=1142d6b5-6241-47c8-943f-f7744dee6f18@
qu.1.6.info=  Course=Introductory Mathematical Economics;
  Topic=Simple Algebra;
  Sub-Topic=Distributive Law;
  Author=Asha Sadanand;
  Difficulty=Easy;
@
qu.1.6.question=<p>The expression $Fpretty simplifies to</p>@
qu.1.6.answer=1@
qu.1.6.choice.1=$ans1@
qu.1.6.choice.2=$ans2@
qu.1.6.choice.3=$ans3@
qu.1.6.choice.4=$ans4@
qu.1.6.fixed=@

qu.1.7.mode=Multiple Choice@
qu.1.7.name=Distributive Law 2@
qu.1.7.comment=<p>In general, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>A</mi><mfenced open='(' close=')' separators=','><mrow><mi>B</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>AB</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>AC</mi></mrow></mstyle></math>.</p>@
qu.1.7.editing=useHTML@
qu.1.7.solution=@
qu.1.7.algorithm=$a=range(2,9);
$b=range(2,9);
$c=range(2,9);
$F=$a*X*Y*($b/X+$c*Y);
$Fpretty=mathml($F);
$ans1=mathml($a*$b*Y+$a*$c*X*Y^2);
$ans2=mathml($a*$b*X*Y+$c*Y);
$ans3=mathml($a*$b*X+$a*$c*Y^2);
$ans4=mathml($a*$b+$c*X*Y);@
qu.1.7.uid=b4fdfb7d-78c4-44a8-9221-c22c96ffd3f1@
qu.1.7.info=  Course=Introductory Mathematical Economics;
  Topic=Simple Algebra;
  Sub-Topic=Distributive Law;
  Author=Asha Sadanand;
  Difficulty=Easy;
@
qu.1.7.question=<p>The expression $Fpretty simplifies to</p>@
qu.1.7.answer=1@
qu.1.7.choice.1=$ans1@
qu.1.7.choice.2=$ans2@
qu.1.7.choice.3=$ans3@
qu.1.7.choice.4=$ans4@
qu.1.7.fixed=@

