Inserting graphics into homework problems and other documents.
A diagram, drawing or picture is sometimes needed to help explain a concept or motivate a problem, and the MCtools and latextools package has words to make this relatively easy to do. You can use
addpic
from the MCtools package to add your drawings to documents. Maple has two packages of drawing words you can use:
plots
and
plottools
. The Visual Problem Solving Handbook has lots of sample work to show how to draw diagrams. We will concentrate here on giving examples of homework problems which have problems. First, we will load the four packages we may need words from.
| > |
with(MCtools);with(latextools):
|
| > |
with(plots):with(plottools):
|
Addpic is the principal word for inserting a diagram into a document. Here is the help for it.
addpic(pic,name) saves a plotstucture pic to name.gif in the
current directory and writes an img src into the source worksheet, unless
LATEX_=yes or Latex=yes. In that case, pic is saved to name.eps and an
includegraphics is written into the source worksheet.
addpic(name) writes an img src or includegraphics into the source worksheet,
and checks to see if name.Format exists in the current directory.
Options:
Latex = no Change to yes for a latex file.
Format=gif Change to eps,jpg,bmp,pcx as desired. If Latex or LATEX_ = yes,
jpeg and jpg is automatically converted to eps by jpeg2ps by Thomas Mertz, if you have it.
and have set Convertjpg=yes
Height=120 units are points
Width=160 units are points
Write=yes Change to no to reuse a previously stored file
Hfill=no Change to before, after, both to put an hfill in those locations
Center=no Change to yes to center the picture
Plotoptions="" Change this only if you must. This replaces the string used by plotsetup which is constructed
by addpic.
To show how addpic works in mathclass homework, make a header for a sample homework, so we can post it later.
| > |
currentdir("c:/tmp/addpicandragit");
|
So let us make a diagram of a triangle using textplot from plots and polygon from plottools.
| > |
pic:=display(textplot([0,-.5,10]),textplot([-2.6,3,6]),
textplot([2.6,3,6]),polygon([[-5,0],[5,0],[0,5]],color=yellow),
axes=none,scaling=constrained):pic;
|
![[Maple Plot]](images/worksheet38.gif)
When we export this worksheet to html, the above image is saved to a numbered gif file. The simplest way to insert a diagram into a homework problem is to just include the name of the structure (in this case 'pic') in the tagit line. We can refer to this as the
visual method
. For example,
| > |
ragit("Classify the triangle shown below.",brak(),pic,as_(["isosceles","right","equiangular"]));
|
QM_[.05;isosceles]
AH_[0]
Classify the triangle shown below.
_brk_
![[Maple Plot]](images/worksheet39.gif)
AS_[isosceles;right;equiangular]
SKIP_
The latex version of this would look like this:
| > |
LATEX_:=yes:
ragit("Classify the triangle shown below.",brak(),pic,as_(["isosceles","right","equiangular"]));
LATEX_:=no:
|
_LATEX
\item \
Classify the triangle shown below.
\par
![[Maple Plot]](images/worksheet40.gif)
$\!$
\begin{tabular}{lll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ isosceles & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ right & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ equiangular\\
& &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $1$ \\
\end{tabular}
_YEK
Pros and cons of the visual method.
One disadvantage of the visual method of inserting diagrams into problems is that you have to resize (usually shrink) the graphic after it is generated in the problem the first time. If you re-execute the tagit line, the worksheet remembers the dimensions you set. Resizing by hand involves grabbing a corner of the graphic with your cursor and then pushing in to make the dimensions smaller. With practice, this works very well generally.
A big advantage of the method is that it is easier to keep track of the graphic. Another advantage is that each time you export the worksheet to html or latex the grahic is exported also.
Using addpic.
The procedure addpic will save your graphic to the worksheet directory and put an html or latex instruction into the worksheet for including the graphic either in a mathclass homework or a latex homework. It is a little harder to keep track of the graphic if you use the addpic method rather than the visual method. First, you have to make sure you are in the homework directory before you execute the tagit line. addpic will warn you if the target directory is the default Maple directory, but otherwise you are on your own to monitor this.
| > |
currentdir("c:/tmp/addpicandragit");
|
| > |
ragit("Classify the triangle shown below.",as_(["isosceles","right","equiangular"],randomize=yes),addpic(pic,"isosceles"));
|
QM_[.05;isosceles]
AH_[0]
Classify the triangle shown below.
AS_[equiangular;isosceles;right]
lt_img src="isosceles.gif" alt="MaplePlot" /gt_
SKIP_
Here is the same problem in latex.
| > |
LATEX_:=yes:
ragit("Classify the triangle shown below.",brak(),
as_(["isosceles","right","equiangular"],randomize=yes),addpic(pic,"isosceles"));
LATEX_:=no:
|
_LATEX
\item \
Classify the triangle shown below.
\par
\begin{tabular}{lll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ isosceles & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ equiangular & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ right\\
& &\\
\end{tabular}
\includegraphics[width=160pt,height=120pt]{isosceles.eps}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $1$ \\
\end{tabular}
_YEK
Here is an example of a problem which has an external jpg you want to add to a problem. In order for this to work right you must have the jpg in
the current directory.
| > |
ragit("Estimate the age of the person in the picture below.",as_(["40-49","50-59",["60-69"],"70-79","80-89","90-99"]),
brak(),addpic("carl3",Format=jpg));
|
QM_[.05;60-69]
AH_[0]
Estimate the age of the person in the picture below.
AS_[40-49;50-59;60-69;70-79;80-89;90-99]
_brk_
lt_img src="carl3.jpg" alt="MaplePlot" /gt_
SKIP_
To use the jpg
| > |
LATEX_:=yes:
ragit("Estimate the age of the person in the picture below.",brak(),as_(["40-49","50-59",["60-69"],"70-79","80-89","90-99"]),brak(),
addpic("carl3",Format=jpg,Height=120,Width=125));
LATEX_:=no:
|
_LATEX
\item \
Estimate the age of the person in the picture below.
\par
\begin{tabular}{llllll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ 40-49 & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ 50-59 & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ 60-69 & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ 70-79 & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ 80-89 & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ 90-99\\
& & & & &\\
\end{tabular}
\par
\includegraphics[width=125pt,height=120pt]{carl3.eps}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $3$ \\
\end{tabular}
_YEK
| > |
ragit("Find the area of the isosceles triangle shown below. Answer:",
ac_(evalf(5*sqrt(11),5)),addpic(pic,"atriangle"));
|
QM_[.05;16.583]
AH_[0]
Find the area of the isosceles triangle shown below. Answer:
AC_[15]
lt_img src="atriangle.gif" alt="MaplePlot" /gt_
SKIP_
| > |
LATEX_:=yes:
ragit("Find the area of the isosceles triangle shown below. Answer:",
ac_(evalf(5*sqrt(11),5)),brak(),addpic(pic,"atriangle"));
LATEX_:=no:
|
_LATEX
\item \
Find the area of the isosceles triangle shown below. Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\par
\includegraphics[width=160pt,height=120pt]{atriangle.eps}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$ 16.583$\\
\end{tabular}
_YEK
Let's make up a calculus problem. Find the area between the curves
and
. Let's draw a picture for the problem.
| > |
pic2:=display(GP(llcorner=[-1,-1],wide=6,height=6,font=[TIMES,ROMAN,4]),plot({1/4*x^2,x},x=-1..5,thickness=3),view=[-1..5,-1..5],axesfont=[TIMES,ROMAN,10]): pic2;
|
![[Maple Plot]](images/worksheet44.gif)
| > |
ragit(precision=`.01`,"Find the area between the graphs of ",y=1/4*x^2," and ",y=x,", for ",ltlt(0,leq,x,leq,4),
" shown below.",brak()," Answer:",ac_(int(x-1/4*x^2,x=0..4)), addpic(pic2,"twofuns"));
|
QM_[.01;8/3]
AH_[0]
Find the area between the graphs of `y = (1)/(4)\ x^(2)` and `y = x`, for `0 <= x <= 4` shown below.
_brk_
Answer:
AC_[15]
lt_img src="twofuns.gif" alt="MaplePlot" /gt_
SKIP_
Here is the problem in latex
| > |
LATEX_:=yes:
ragit("Find the area between the graphs of ",y=1/4*x^2," and ",y=x,", for ",ltlt(0,leq,x,leq,4),
" shown below.",brak()," Answer:",ac_(int(x-1/4*x^2,x=0..4)), addpic(pic2,"twofuns"));
LATEX_:=no:
|
_LATEX
\item \
Find the area between the graphs of $y = \frac{1}{4}\,x^{2}$ and $y = x$, for
$0\leq x\leq 4$ shown below.
\par
Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\includegraphics[width=160pt,height=120pt]{twofuns.eps}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$\frac{8}{3}$\\
\end{tabular}
_YEK
more use of addpic
| > |
#print(rlprint);rlprint(Help);
|
| > |
geo := proc(m,n,r,clrs)
local bord,nails;
bord:=plottools[polygon]([[0,0],[n,0],[n,m],[0,m]],color=clrs[1]):
nails := plots[display]( seq(seq(plottools[disk]([i,j],r,color=clrs[2]),i=0..n),j=0..m)):
plots[display](nails,bord,scaling=constrained,axes=none);
end:
|
| > |
#geo(5,6,.05,[yellow,red]);
|
| > |
band := proc(lst,clr)
plot(lst,color=clr) end:
|
| > |
pic:=(n,m)->plots[display](geo(n,m,.05,[turquoise,red])):
|
acew_(lst::listlist) constructs an array of strings, expressions, and answer formats ac_,an_,af_,ae_,ai_,aw_
Options:
Help=no acew_(Help) will retrieve this help
Numcols=1 increase as needed
Tableopts="" replace with an appropriate format string
Cellopts="" replace with a format such as "color=\"yellow\"" for all cells or a list of
| > |
ragit("For each rectangle below, count the number B of boundary nails, the number I of interior nails, and also compute the area of the rectangle, assuming that adjacent horizontal or vertical pairs of nails are 1 unit apart.",brak(),
acew_([["`B= `",ac_(12),"`I= `",ac_(3),"`Area = `",ac_(8),(addpic(pic(2,4),"pic1"))],
["`B= `",ac_(14),"`I= `",ac_(6),"`Area = `",ac_(12),(addpic(pic(3,4),"pic2"))],
["`B= `",ac_(18),"`I= `",ac_(10),"`Area = `",ac_(18),(addpic(pic(3,6),"pic3"))]]),brak());
LATEX_:=yes:
ab:=op([ansbox=[Height=.2,Width=.3,Fill="",Placement="c"]]):
|
| > |
ragit("For each rectangle below, count the number B of boundary nails, the number I of interior nails, and also compute the area of the rectangle, assuming that adjacent horizontal or vertical pairs of nails are 1 unit apart.",brak(),
acew_([["$B= $",ac_(12,ansbox=[Height=.2,Width=.3,Fill="",Placement="c"]),"$I= $",ac_(3,ab),"$Area = $",ac_(8,ab),(addpic(pic(2,4),"pic1",Height=30,Width=40))],
["$B= $",ac_(14,ab),"$I= $",ac_(6,ab),"$Area = $",ac_(12,ab),(addpic(pic(3,4),"pic2",Height=30,Width=40))],
["$B= $",ac_(18,ab),"$I= $",ac_(10,ab),"$Area = $",ac_(18,ab),(addpic(pic(3,6),"pic3",Height=30,Width=40))]],Numcols=7));
LATEX_:=no:
|
QM_[.05;12;3;8;14;6;12;18;10;18]
AH_[0]
For each rectangle below, count the number B of boundary nails, the number I of interior nails, and also compute the area of the rectangle, assuming that adjacent horizontal or vertical pairs of nails are 1 unit apart.
_brk_
lt_table gt_
lt_tr gt_
lt_td gt_
`B= `
lt_/td gt_
lt_td gt_
AC_[15]
AH_[0]
lt_/td gt_
lt_td gt_
`I= `
lt_/td gt_
lt_td gt_
AC_[15]
AH_[0]
lt_/td gt_
lt_td gt_
`Area = `
lt_/td gt_
lt_td gt_
AC_[15]
AH_[0]
lt_/td gt_
lt_td gt_
lt_img src="pic1.gif" alt="MaplePlot" /gt_
lt_/td gt_
lt_/tr gt_
lt_tr gt_
lt_td gt_
`B= `
lt_/td gt_
lt_td gt_
AC_[15]
AH_[0]
lt_/td gt_
lt_td gt_
`I= `
lt_/td gt_
lt_td gt_
AC_[15]
AH_[0]
lt_/td gt_
lt_td gt_
`Area = `
lt_/td gt_
lt_td gt_
AC_[15]
AH_[0]
lt_/td gt_
lt_td gt_
lt_img src="pic2.gif" alt="MaplePlot" /gt_
lt_/td gt_
lt_/tr gt_
lt_tr gt_
lt_td gt_
`B= `
lt_/td gt_
lt_td gt_
AC_[15]
AH_[0]
lt_/td gt_
lt_td gt_
`I= `
lt_/td gt_
lt_td gt_
AC_[15]
AH_[0]
lt_/td gt_
lt_td gt_
`Area = `
lt_/td gt_
lt_td gt_
AC_[15]
lt_/td gt_
lt_td gt_
lt_img src="pic3.gif" alt="MaplePlot" /gt_
lt_/td gt_
lt_/tr gt_
lt_/table gt_
_brk_
SKIP_
_LATEX
\item \
For each rectangle below, count the number B of boundary nails, the number I of interior nails, and also compute the area of the rectangle, assuming that adjacent horizontal or vertical pairs of nails are 1 unit apart.
\par
\begin{tabular}{lllllll}
$B= $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & $I= $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & $Area = $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & \includegraphics[width=40pt,height=30pt]{pic1.eps}\\
& & & & & &\\
$B= $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & $I= $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & $Area = $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & \includegraphics[width=40pt,height=30pt]{pic2.eps}\\
& & & & & &\\
$B= $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & $I= $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & $Area = $ & $\ \fbox{\parbox[c][.2in][c]{.3in}{\hfill}}$ & \includegraphics[width=40pt,height=30pt]{pic3.eps}\\
& & & & & &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$12$\\
$\diamond$\hspace{2mm}$3$\\
$\diamond$\hspace{2mm}$8$\\
$\diamond$\hspace{2mm}$14$\\
$\diamond$\hspace{2mm}$6$\\
$\diamond$\hspace{2mm}$12$\\
$\diamond$\hspace{2mm}$18$\\
$\diamond$\hspace{2mm}$10$\\
$\diamond$\hspace{2mm}$18$\\
\end{tabular}
_YEK
problem generators
One of the main advantages of using Maple to format problems is that it gives you the ability to create problem generators, that is, procedures which when executed will return problems which are essentially the same, except some numbers in the problem are different.
In order to create such a problem generator, you can start with any problem and parameterize it: Choose one or more things (usually numbers, but not always) in the problem which you want to allow to be different. For example, take a problem using the ac_ format:
| > |
i:='i':ragit("Compute: ",Sum(i,i=1..25),". Answer:",ac_(sum(i,i=1..25)));
|
QM_[.05;325]
AH_[0]
Compute: ` sum_(i = 1)^(25)i`. Answer:
AC_[15]
SKIP_
One parameter in this problem is the number of terms, say n, that are being summed: So a simple parameterization of this problem would be
| > |
prob:=proc(n)
global LATEX_; # This is needed if you want the latex version of the problem.
local i;
ragit("Compute: ",Sum(i,i=1..n),". Answer:",ac_(sum(i,i=1..n)));
LATEX_:=yes: # ragit returns latex version when LATEX_ = yes
ragit("Compute: ",Sum(i,i=1..n),". Answer:",ac_(sum(i,i=1..n)));
LATEX_:=no: # ragit returns html version when LATEX_ <> yes
NULL:
end:
|
Note we are making this generator spit out both an html and a latex version. If you want a latex version version of your problem available, you always need to include the 3 lines which have LATEX_ in them. If you only want an html version, omit those lines and make only one call to ragit in the generator.
QM_[.05;1275]
AH_[0]
Compute: ` sum_(i = 1)^(50)i`. Answer:
AC_[15]
SKIP_
_LATEX
\item \
Compute: $\displaystyle\sum_{i = 1}^{50}i$. Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$1275$\\
\end{tabular}
_YEK
We can now create as many versions of this problem as we want, simply by executing the line prob(n); for as many values of n that we need.
We can put another parameter in this problem, namely the summand f(i) (currently f(i)=i). So, copy down the problem generator to a new input line and modify it. For example, we could have f(i)=a*i+b, for various values of a and b.
| > |
prob:=proc(n,a,b)
global LATEX_;
local i;
ragit("Compute: ",Sum(a*i+b,i=1..n),". Answer:",ac_(sum(a*i+b,i=1..n)));
LATEX_:=yes:
ragit("Compute: ",Sum(a*i+b,i=1..n),". Answer:",ac_(sum(a*i+b,i=1..n)));
LATEX_:=no:
NULL:
end:
|
QM_[.05;1025]
AH_[0]
Compute: ` sum_(i = 1)^(25)3\ i + 2`. Answer:
AC_[15]
SKIP_
_LATEX
\item \
Compute: $\displaystyle\sum_{i = 1}^{25}3\,i + 2$. Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$1025$\\
\end{tabular}
_YEK
Of course, the problems above can be solved by brute force. We could modify this problem to test the students knowledge of summing arithmetic sequences in general, simply by changing the answer format from ac_ to ae_. Then they will need to type in an expression, using Maple syntax. This is close to calculator syntax and you should make a description of it available to your students.
| > |
prob:=proc(n,a,b)
global LATEX_;
local i;
ragit("Compute: ",Sum(a*i+b,i=1..n),". Answer:",ae_(sum(a*i+b,i=1..n)));
LATEX_:=yes:
ragit("Compute: ",Sum(a*i+b,i=1..n),". Answer:",ae_(sum(a*i+b,i=1..n)));
LATEX_:=no:
NULL:
end:
|
QM_[.05;25*s+325*r]
AH_[0]
Compute: ` sum_(i = 1)^(25)r\ i + s`. Answer:
AE_[15;2;r;s;25;.1;1;.1;1]
SKIP_
_LATEX
\item \
Compute: $\displaystyle\sum_{i = 1}^{25}r\,i + s$. Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$25\,s + 325\,r$\\
\end{tabular}
_YEK
Paramvals
As it turns out, it is convenient to have a procedure that we can use in ragit to generate a set of values for our parameters in a problem. This makes it easier to generate problems. What you do is restrict each parameter to a small set of values and have the procedure then randomly select values from those ranges. The procedure is called paramvals. Here is it's help page.
paramvals([args],ls1) where args is the sequence of arguments to the problem generator,
and ls1 is a list of lists of parameter names
and range specifications suitable for assignvals (See assignvals(Help=yes) below).
Note: this was written to be used in a problem generator.
Usually, you will call something like paramvals([args],[[a,{2,3,1}],...])
Then when the generator is called with just a version number, the list which is printed
can be pasted back into the call to get the same inputs in case maintainance is needed.
Help for assignvals
assignvals(exprseq) takes a exprseq of ['X',range] or ['X',d,m..n] or ['X',perm,list]
or ['X',mat,list] or ['X',struct,command],and assigns X a random value chosen thusly:
1. for ['X',range] X is assigned a value in range, where range can be an integer range m..n,
or a set or list of values
2. for ['X',d,m..n] d is a positive integer, m..n is an integer range and X is assigned a random floating point with d significant digits between m/10^d and n/10^d.
3. for ['X',perm,list] X is assigned a random permuation of the elements in the list.
4. for ['X',list,listofvalues] X is assigned the listofvalues
5. for ['X',mat,list] X is assigned a random list of lists using list as the argument to LinearAlgebra[RandomMatrix].
Example: ['c',mat,[2,3,generator=rand(1..4),density=.8] assigns c a
2 by 3 list of lists of 20% zeros, 80% random numbers between 1 and 4.
6. for ['X',struct,command] X is assigned the output of the maple command.
Example: ['b',struct,plot(x^2,x=0..4)] assigns b the plot structure for the graph of x^2.
Note: no variable can depend on a variable assigned in that call to assignvals.
Example:
illegal assignvals(['A',2..5],['B',{"t",b,c,1}],['C',[A,A,A,B]]);
legal assignvals(['A',2..5],['B',{"t",b,c,1}]): assignvals(['C',[A,A,A,B]]);
Options:
Help=no change to yes to get this message.
To illustrate, if we want to employ this method to generate numerical values for n, a, and b in example above, we would take the parameters out of the line proc(n,a,b) and make them local. Then, we can invoke getparams to assign values to n, a and b. Note that we have restricted the range considerably in the problem. This tends to make the problems comparable in difficulty. As it stands, there will be 3^3 = 27 different possible versions of this problem. It is customary to have only 5 actual versions of a problem, one for the common version and 4 to choose from in the personal versions. Generally speaking when generating problems in this 'random' manner it is a good idea to look at the problems as you generate them to see if they are suitable. If they are, you can go ahead and past the current inputs into the problem line to fix the problem. This is useful for homework maintenance. Sometimes you need to make a change in a problem after you have posted the homework. If this occurs you would like to be able to repost the problem with the same inputs.
| > |
prob:=proc()
global LATEX_;
local i,n,a,b; #all parameter names should go in this line.
paramvals([args],[[n,[25,30,35]],[a,[2,3,4]],[b,[10,15,20]]]);
ragit("Compute: ",Sum(a*i+b,i=1..n),". Answer:",ac_(sum(a*i+b,i=1..n)));
LATEX_:=yes:
ragit("Compute: ",Sum(a*i+b,i=1..n),". Answer:",ac_(sum(a*i+b,i=1..n)));
LATEX_:=no:
NULL:
end:
|
current inputs are (1,[30,2,20])
QM_[.05;1530]
AH_[0]
Compute: ` sum_(i = 1)^(30)2\ i + 20`. Answer:
AC_[15]
SKIP_
_LATEX
\item \
Compute: $\displaystyle\sum_{i = 1}^{30}2\,i + 20$. Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$1530$\\
\end{tabular}
_YEK
Now often you might have two parameters you want to come from the same range but you want them to have different values. Use the perm assignment. To illustrate, suppose we wanted to choose which of two numbers is larger.
| > |
prob:=proc()
global LATEX_;
local i,p; #p is to be a permutation of the numbers in.
paramvals([args],[[p,perm,[293828,2281883,3030392,2292929,2200229]]]);
ragit("Which of the numbers ",p[1]," and ",p[2]," is larger? Answer:",ac_(max(p[1],p[2])));
LATEX_:=yes:
ragit("Which of the numbers ",p[1]," and ",p[2]," is larger? Answer:",ac_(max(p[1],p[2])));
LATEX_:=no:
NULL:
end:
|
| > |
prob (1,[[2281883, 2200229, 3030392, 293828, 2292929]]);
|
current inputs are (1,[[2281883, 2200229, 3030392, 293828, 2292929]])
QM_[.05;2281883]
AH_[0]
Which of the numbers `2281883` and `2200229` is larger? Answer:
AC_[15]
SKIP_
_LATEX
\item \
Which of the numbers $2281883$ and $2200229$ is larger? Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$2281883$\\
\end{tabular}
_YEK
Problem generators using paramvals
Here is an example of a problem generator which
| > |
prob1 := proc()
global LATEX_:
local a,b;
paramvals([args],[[a,perm,[1,2,3,4,5]],[b,struct,LinearAlgebra[RandomMatrix](5,5)]]);
ragit("What is the value of the cell in row ",a[1]," and column,",a[2]," of ",Mat(b),"? ",ac_(b[a[1],a[2]])):
LATEX_:=yes:
ragit("What is the value of the cell in row ",a[1]," and column,",a[2]," of ",Mat(b),"? ",ac_(b[a[1],a[2]])):
LATEX_:=no: end:
|
| > |
prob1 (1,[[1, 3, 5, 2, 4],Matrix(5, 5, [[78,-2,33,-58,98],[-8,-69,-17,75,5],[-90,17,58,-31,-23],[-81,-87,-21,-30,19],[-43,37,15,-50,-93]])]);
|
current inputs are (1,[[1, 3, 5, 2, 4],Matrix(5, 5, [[78,-2,33,-58,98],[-8,-69,-17,75,5],[-90,17,58,-31,-23],[-81,-87,-21,-30,19],[-43,37,15,-50,-93]])])
QM_[.05;33]
AH_[0]
What is the value of the cell in row `1` and column,`3` of `((78 , -2 , 33 , -58 , 98),(-8 , -69 , -17 , 75 , 5),(-90 , 17 , 58 , -31 , -23),(-81 , -87 , -21 , -30 , 19),(-43 , 37 , 15 , -50 , -93))`?
AC_[15]
SKIP_
_LATEX
\item \
What is the value of the cell in row $1$ and column,$3$ of $\left(\begin{array}{ccccc} 78 & -2 & 33 & -58 & 98 \\-8 & -69 & -17 & 75 & 5 \\-90 & 17 & 58 & -31 & -23 \\-81 & -87 & -21 & -30 & 19 \\-43 & 37 & 15 & -50 & -93 \end{array}\right)$?
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$33$\\
\end{tabular}
_YEK
evaluate and make judgement
Here is another problem generator made using ragit and paramvals.
| > |
prob := proc()
global LATEX_:
local a,b,c,d,e,i,f,funcs1,dom1;
paramvals([args],[[a,[seq(i,i=1..6)]],[b,[seq(i,i=1..6)]],[c,[seq(i,i=2..8)]],[d,[1,2,3]],[e,[1,2,3]]]);
funcs1:=[f(x,y)=sqrt(a*x+b*exp(y)+c),f(x,y)=b*ln(x^2+c*y^2+c),f(x,y)=a/(b*x^2+exp(c*y))];
dom1:=["increasing","neither","decreasing"];
ragit("Evaluate the function ",funcs1[d]," at ",Pnt([x,y]) = Pnt(1,1/2),ac_(subs({x=1,y=1/2},rhs(funcs1[d]))),brak(),
"Consider the function ",f(1,y)," of ",y,": Decide if it is increasing, decreasing or neither over its natural domain.",as_(dom1,Rightone=d) );
LATEX_:=yes:
ragit("Evaluate the function ",funcs1[d]," at ",Pnt([x,y]) = Pnt(1,1/2),ac_(subs({x=1,y=1/2},rhs(funcs1[d]))),brak(),
"Consider the function ",f(1,y)," of ",y,": Decide if it is increasing, decreasing or neither over its natural domain.",as_(dom1,Rightone=d) );
LATEX_:=no: NULL: end:
|
current inputs are (1,[1,3,8,2,1])
QM_[.05;3*ln(11);neither]
AH_[0]
Evaluate the function `f(x,y) = 3\ text(ln)(x^(2) + 8\ y^(2) + 8)` at `(x,y) = (1,(1)/(2))`
AC_[15]
AH_[0]
_brk_
Consider the function `f(1,y)` of `y`: Decide if it is increasing, decreasing or neither over its natural domain.
AS_[increasing;neither;decreasing]
SKIP_
_LATEX
\item \
Evaluate the function $f \left( x,y \right) = 3\,\ln(x^{2} + 8\,y^{2} + 8)$ at $(x, y) = (1, \frac{1}{2})$
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\par
Consider the function $f \left( 1,y \right) $ of $y$: Decide if it is increasing, decreasing or neither over its natural domain.
\begin{tabular}{lll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ increasing & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ neither & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ decreasing\\
& &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$3\,\ln(11)$\\
$\diamond$\hspace{2mm} $2$ \\
\end{tabular}
_YEK
as_(l) returns a list from which to circle
the correct answer (listed first or enclosed in square brackets)if LATEX_=yes, else it returns an AS format for tagit, taking the same arguments the tagit format does.
Options:
Shuffle=no, or =yes or =[3,2,1] to reverse the order of 3 alternatives
Rightone=1 Change if the correct answer is not the first answer.)
prob12
Here is a trig problem generator using arq_. (the old tbuttons) It always generates the same problem, only the order of the answers changes. We widened the table in html to 40% for readability.
| > |
prob := proc()
global LATEX_:
local ans;
ans:=[3/2*pi,0,pi/3,pi/2,pi,5/4*pi,"All reals","No solution"];
ragit("Solve for ",theta,", ",theta," in [0,",2*pi,"): ", 2*sin(theta)^2 - sin(theta) = 3,
arq_(ans,Numcols=4,Tableopts="width=\"40\%\""));
LATEX_:=yes:
ragit("Solve for ",theta,", ",theta," in [0,",(2*pi),"): ", 2*sin(theta)^2 - sin(theta) = 3,
arq_(ans,Numcols=4));
LATEX_:=no:
NULL: end:
|
QM_[.05;1]
AH_[0]
Solve for `\theta`, `\theta` in [0,`2\ \pi`): `2\ (text(sin)(\theta))^(2) - text(sin)(\theta) = 3`
lt_table width="40%" gt_
lt_tr gt_
lt_td gt_
AR_[-2500;1]
`(3)/(2)\ \pi`
lt_/td gt_
lt_td gt_
AR_[-2500;1]
`0`
lt_/td gt_
lt_td gt_
AR_[-2500;1]
`(1)/(3)\ \pi`
lt_/td gt_
lt_td gt_
AR_[-2500;1]
`(1)/(2)\ \pi`
lt_/td gt_
lt_/tr gt_
lt_tr gt_
lt_td gt_
AR_[-2500;1]
`\pi`
lt_/td gt_
lt_td gt_
AR_[-2500;1]
`(5)/(4)\ \pi`
lt_/td gt_
lt_td gt_
AR_[-2500;1]
All reals
lt_/td gt_
lt_td gt_
AR_[-2500;1]
No solution
lt_/td gt_
lt_/tr gt_
lt_/table gt_
SKIP_
_LATEX
\item \
Solve for $\theta$, $\theta$ in [0,$2\,\pi$): $2\,{\sin(\theta)}^{2} - \sin(\theta) = 3$
\begin{tabular}{llll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{3}{2}\,\pi$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{1}{3}\,\pi$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{1}{2}\,\pi$\\
& & &\\
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\pi$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{5}{4}\,\pi$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ All reals & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ No solution\\
& & &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $1$ \\
\end{tabular}
_YEK
Here is the same problem, only with labels stuck in and a permutation of the alternatives so that we can recover a particular permutation for problem maintenance. Also, when using arq_ or acew_ in a homework which requires maintenance, you should make the identifier a parameter so you can use it again on re-execution.
| > |
2*sin(3*Pi/2)^2-sin(3*Pi/2);
|
| > |
prob12 := proc()
global LATEX_:
local ans,labels,p,i,id;
ans:=[[3/2*pi],[0],[pi/3],[pi/2],[pi],[5/4*pi],["All reals"],["No solution"]];
paramvals([args],[[p,perm,[seq(i,i=1..nops(ans))]],[id,[seq(rand(10001..19999)(),i=1..1)]]]);
ragit("Solve for ",theta,", ",theta," in [0,",2*pi,"): ", 2*sin(theta)^2 - sin(theta) = 3,
arq_(ans,Numcols=4,Labels=2,Shuffle=p,Tableopts="width=\"50\%\"",Id=-id));
LATEX_:=yes:
ragit("Solve for ",theta,", ",theta," in [0,",2*pi," ): ", 2*sin(theta)^2 - sin(theta) = 3,
arq_(ans,Numcols=4,Labels="",Shuffle=p,Tableopts="width=\"50\%\""));
LATEX_:=no:
end:
|
| > |
prob12 (1,[[4, 8, 6, 5, 3, 1, 2, 7],15124]);
|
current inputs are (1,[[4, 8, 6, 5, 3, 1, 2, 7],15124])
QM_[.05;6]
AH_[0]
Solve for `\theta`, `\theta` in [0,`2\,\pi`): `2\,{\sin(\theta)}^{2} - \sin(\theta) = 3`
lt_table width="50%" gt_
lt_tr gt_
lt_td gt_
AR_[-15124;1]
lt_font color="red" gt_lt_b gt_A) lt_/b gt_ lt_/font gt_
`\frac{1}{2}\,\pi`
lt_/td gt_
lt_td gt_
AR_[-15124;1]
lt_font color="red" gt_lt_b gt_B) lt_/b gt_ lt_/font gt_
No solution
lt_/td gt_
lt_td gt_
AR_[-15124;1]
lt_font color="red" gt_lt_b gt_C) lt_/b gt_ lt_/font gt_
`\frac{5}{4}\,\pi`
lt_/td gt_
lt_td gt_
AR_[-15124;1]
lt_font color="red" gt_lt_b gt_D) lt_/b gt_ lt_/font gt_
`\pi`
lt_/td gt_
lt_/tr gt_
lt_tr gt_
lt_td gt_
AR_[-15124;1]
lt_font color="red" gt_lt_b gt_E) lt_/b gt_ lt_/font gt_
`\frac{1}{3}\,\pi`
lt_/td gt_
lt_td gt_
AR_[-15124;1]
lt_font color="red" gt_lt_b gt_F) lt_/b gt_ lt_/font gt_
`\frac{3}{2}\,\pi`
lt_/td gt_
lt_td gt_
AR_[-15124;1]
lt_font color="red" gt_lt_b gt_G) lt_/b gt_ lt_/font gt_
`0`
lt_/td gt_
lt_td gt_
AR_[-15124;1]
lt_font color="red" gt_lt_b gt_H) lt_/b gt_ lt_/font gt_
All reals
lt_/td gt_
lt_/tr gt_
lt_/table gt_
SKIP_
_LATEX
\item \
Solve for $\theta$, $\theta$ in [0,$2\,\pi$ ): $2\,{\sin(\theta)}^{2} - \sin(\theta) = 3$
\begin{tabular}[t]{llll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{1}{2}\,\pi$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ No solution & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{5}{4}\,\pi$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\pi$\\
& & &\\
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{1}{3}\,\pi$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{3}{2}\,\pi$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ All reals\\
& & &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $6$ \\
\end{tabular}
_YEK
The multiple choice format as_ : selection box answers
This is a selection box multiple choice answer format, for simple unformatted choices.
The format is as_(answers) where answers is a list of alternative answers with the correct answer first. If the first alternative is not correct, put brackets around the correct one.
| > |
ragit("Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours. How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other? Select the most nearly correct answer.",as_([1.875,2.125,4,"None of the others"]));
LATEX_:=yes:
ragit("Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours. How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other? Select the most nearly correct answer.", as_([1.875,2.125,4,"None of the others"]));
LATEX_:=no:
|
QM_[.05;1.875]
AH_[0]
Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours. How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other? Select the most nearly correct answer.
AS_[1.875;2.125;4;None of the others]
SKIP_
_LATEX
\item \
Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours. How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other? Select the most nearly correct answer.
\begin{tabular}{llll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $ 1.875$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $ 2.125$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $4$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ None of the others\\
& & &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $1$ \\
\end{tabular}
_YEK
By default the first alternative in the list of alternatives is assumed the right answer. You can change this by setting the rightanswers option to the correct answer, or by enclosing the right answer in square brackets. You can also fix the order of the alternatives in the list to be the one given by setting the
randomize=
option to no.
| > |
ragit("Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours. How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other?",brak()," Select the most nearly correct answer.",brak(),as_([2.125,[1.875],4,"None of the others"],randomize=no));
LATEX_:=yes:
ragit("Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours. How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other?",brak()," Select the most nearly correct answer.",brak(),as_([2.125,[1.875],4,"None of the others"],randomize=no));
LATEX_:=no:
|
QM_[.05;1.875]
AH_[0]
Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours. How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other?
_brk_
Select the most nearly correct answer.
_brk_
AS_[2.125;1.875;4;None of the others]
SKIP_
_LATEX
\item \
Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours. How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other?
\par
Select the most nearly correct answer.
\par
\begin{tabular}{llll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $ 2.125$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $ 1.875$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $4$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ None of the others\\
& & &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $2$ \\
\end{tabular}
_YEK
tr and special symbols
There is a large vocabulary of special math symbols in both latex and ascimath. tr will process many of these as latex or html depending on whether LATEX_ = yes. The vocabulary will be enlarged as time permits.
The help is
tr(a1,a2,...) returns a string formatted either with $ (if LATEX_=yes) or `. The ai's can be regular expressions, strings, or the terms leq,lt,geq,gt,neq,xx,`-:`,cup,cap,sub,elt,`-=`,pm,int,oint,del,grad, infty,empty,aleph,angle,cdots,cdot,tri,perp.
Here are some sample problems:
| > |
prob:=proc()
global LATEX_:
local a,b,alts,w;
#w:="amp_8734":
paramvals([args],[[a,[3,4,5]],[b,[-9,-11,-7]]]);
alts:=[cat(w,"/-",w)," 0/0 ",cat(" 0^0 "),cat(" ",w,"^",w," ")];
alts:=[cat("1. ",tr(infty,"/-",infty)),cat("2. ",tr(0,"/",0)),cat("3. ",tr(0,"^",0)),cat("4. ",tr(infty,"^",infty))];
ragit("Classify the indeterminancy type of the following limits:",brak(),
"i) ",Lim((a*x+b)/(a+b*x),x=infinity),as_(alts),brak(),
"ii) ",Lim((x^2-4)/(x-2),x=infinity),as_(alts,Rightone=2));
LATEX_:=yes:
alts:=[tr("\\frac{",infinity,"}{-",infinity,"}"),tr(0,"/",0),tr(0,"^",0),tr(infinity,"^",infinity)];
ragit("Classify the indeterminancy type of the following limits:",brak(),
"i) ",Lim((a*x+b)/(a+b*x),x=infinity),as_(alts),brak(),
"ii) ",Lim((x^2-4)/(x-2),x=infinity),as_(alts,Rightone=2));
LATEX_:=no:
NULL
end:
|
current inputs are (1,[4,-11])
QM_[.05;1. `\amp_#8734;/-\amp_#8734;`;2. `0/0`]
AH_[0]
Classify the indeterminancy type of the following limits:
_brk_
i) `lim_(x to \infty )\ (-4\ x + 11)/(-4 + 11\ x)`
AS_[1. `\amp_#8734;/-\amp_#8734;`;2. `0/0`;3. `0^0`;4. `\amp_#8734;^\amp_#8734;`]
AH_[0]
_brk_
ii) `lim_(x to \infty )\ (x^(2) - 4)/(x - 2)`
AS_[1. `\amp_#8734;/-\amp_#8734;`;2. `0/0`;3. `0^0`;4. `\amp_#8734;^\amp_#8734;`]
SKIP_
_LATEX
\item \
Classify the indeterminancy type of the following limits:
\par
i) $\displaystyle\lim_{x\rightarrow \infty }\,\frac{-4\,x + 11}{-4 + 11\,x}$
\begin{tabular}[t]{llll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{\infty }{-\infty }$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0/0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0^0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\infty ^\infty $\\
& & &\\
\end{tabular}
\par
ii) $\displaystyle\lim_{x\rightarrow \infty }\,\frac{x^{2} - 4}{x - 2}$
\begin{tabular}[t]{llll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{\infty }{-\infty }$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0/0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0^0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\infty ^\infty $\\
& & &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $1$ \\
$\diamond$\hspace{2mm} $2$ \\
\end{tabular}
_YEK
| > |
prob:=proc()
global LATEX_:
local a,b,alts,w;
paramvals([args],[[a,[3,4,5]],[b,[-9,-11,-7]]]);
alts:=["1. `infty/-infty`","2. `0/0`","3. `0^0`","4. `infty^infty`","`infty/infty`"];
ragit("Classify the indeterminancy type of the following limits:",brak(),
"i) ",Lim((a*x+b)/(a+b*x),x=infinity),as_(alts),brak(),
"ii) ",Lim((x^2-4)/(x-2),x=infinity),as_(alts,Rightone=2));
LATEX_:=yes:
alts:=[tr("\\frac{",infinity,"}{-",infinity,"}"),tr(0,"/",0),tr(0,"^",0),tr(infinity,"^",infinity),tr(infty,"/",infty)];
ragit("Classify the indeterminancy type of the following limits:",brak(),
"i) ",Lim((a*x+b)/(a+b*x),x=infinity),as_(alts),brak(),
"ii) ",Lim((x^2-4)/(x-2),x=infinity),as_(alts,Rightone=2));
LATEX_:=no:
NULL
end:
|
current inputs are (1,[3,-9])
QM_[.05;1. `infty/-infty`;2. `0/0`]
AH_[0]
Classify the indeterminancy type of the following limits:
_brk_
i) `lim_(x to \infty )\ (-1\ x + 3)/(-1 + 3\ x)`
AS_[1. `infty/-infty`;2. `0/0`;3. `0^0`;4. `infty^infty`;`infty/infty`]
AH_[0]
_brk_
ii) `lim_(x to \infty )\ (x^(2) - 4)/(x - 2)`
AS_[1. `infty/-infty`;2. `0/0`;3. `0^0`;4. `infty^infty`;`infty/infty`]
SKIP_
_LATEX
\item \
Classify the indeterminancy type of the following limits:
\par
i) $\displaystyle\lim_{x\rightarrow \infty }\,\frac{-1\,x + 3}{-1 + 3\,x}$
\begin{tabular}[t]{lllll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{\infty }{-\infty }$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0/0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0^0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\infty ^\infty $ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\infty /\infty $\\
& & & &\\
\end{tabular}
\par
ii) $\displaystyle\lim_{x\rightarrow \infty }\,\frac{x^{2} - 4}{x - 2}$
\begin{tabular}[t]{lllll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{\infty }{-\infty }$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0/0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0^0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\infty ^\infty $ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\infty /\infty $\\
& & & &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $1$ \\
$\diamond$\hspace{2mm} $2$ \\
\end{tabular}
_YEK
tr and special symbols
There is a large vocabulary of special math symbols in both latex and ascimath. tr will process many of these as latex or html depending on whether LATEX_ = yes. The vocabulary will be enlarged as time permits.
The help is
| > |
prob:=proc()
global LATEX_:
local a,b,alts;
paramvals([args],[[a,[3,4,5]],[b,[-9,-11,-7]]]);
alts:=[tr(infinity,"/-",infinity),tr(0,"/",0),tr(0,"^",0),tr(infinity,"^",infinity)];
alts:=[tr(infinity,"/-",infinity),tr(0,"/",0),tr(0,"^",0),tr(infinity,"^",infinity)];
ragit("Classify the indeterminancy type of the following limits:",brak(),
"i) ",Lim((a*x+b)/(a+b*x),x=infinity),as_(alts),brak(),
"ii) ",Lim((x^2-4)/(x-2),x=infinity),as_(alts,Rightone=2));
LATEX_:=yes:
alts:=[tr("\\frac{",infinity,"}{-",infinity,"}"),tr(0,"/",0),tr(0,"^",0),tr(infinity,"^",infinity)];
ragit("Classify the indeterminancy type of the following limits:",brak(),
"i) ",Lim((a*x+b)/(a+b*x),x=infinity),as_(alts),brak(),
"ii) ",Lim((x^2-4)/(x-2),x=infinity),as_(alts,Rightone=2));
LATEX_:=no:
NULL
end:
|
current inputs are (1,[5,-7])
QM_[.05;`\infty /-\infty `;`0/0`]
AH_[0]
Classify the indeterminancy type of the following limits:
_brk_
i) `lim_(x to \infty )\ (-5\ x + 7)/(-5 + 7\ x)`
AS_[`\infty /-\infty `;`0/0`;`0^0`;`\infty ^\infty `]
AH_[0]
_brk_
ii) `lim_(x to \infty )\ (x^(2) - 4)/(x - 2)`
AS_[`\infty /-\infty `;`0/0`;`0^0`;`\infty ^\infty `]
SKIP_
_LATEX
\item \
Classify the indeterminancy type of the following limits:
\par
i) $\displaystyle\lim_{x\rightarrow \infty }\,\frac{-5\,x + 7}{-5 + 7\,x}$
\begin{tabular}[t]{llll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{\infty }{-\infty }$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0/0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0^0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\infty ^\infty $\\
& & &\\
\end{tabular}
\par
ii) $\displaystyle\lim_{x\rightarrow \infty }\,\frac{x^{2} - 4}{x - 2}$
\begin{tabular}[t]{llll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\frac{\infty }{-\infty }$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0/0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $0^0$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ $\infty ^\infty $\\
& & &\\
\end{tabular}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $1$ \\
$\diamond$\hspace{2mm} $2$ \\
\end{tabular}
_YEK
tr(a1,a2,...) returns a string formatted either with $ (if LATEX_=yes) or `. The ai's can be regular expressions, strings, or the terms leq,lt,geq,gt,neq,xx,`-:`,cup,cap,sub,elt,`-=`,pm,int,oint,del,grad, infty,empty,aleph,angle,cdots,cdot,tri,perp.
Here are some sample problems:
| > |
prob:=proc()
global LATEX_;
local a,b,c,ans,A,B;
paramvals([args],[[a,[{1,2,3},{4,5,7},{1,4,9}]],[b,[{6,10,3},{14,5,17},{21,4,9}]],[c,[2,3,4]]]);
ragit("Given ",A=a,", ",B=b,".",brak(),
"a) How many members in ",tr(A, cup, B),"? Answer:",ac_(nops(a union b)),brak(),
"b) How many members in ",tr(A, cap, B),"? Answer:",ac_(nops(a intersect b)),brak(),
"c) How many members in ",tr(A, xx, B),"? Answer:",ac_(nops(a)*nops( b)));
LATEX_:=yes:
ragit("Given ",A=a,", ",B=b,".",brak(),
"a) How many members in ",tr(A, cup, B),"? Answer:",ac_(nops(a union b)),brak(),
"b) How many members in ",tr(A, cap, B),"? Answer:",ac_(nops(a intersect b)),brak(),
"c) How many members in ",tr(A, xx, B),"? Answer:",ac_(nops(a)*nops( b)));
LATEX_:=no:
NULL:
end:
|
current inputs are (1,[{1, 2, 3},{5, 14, 17},4])
QM_[.05;6;0;9]
AH_[0]
Given `A = {1,2,3}`, `B = {5,14,17}`.
_brk_
a) How many members in `A uu B`? Answer:
AC_[15]
AH_[0]
_brk_
b) How many members in `A nn B`? Answer:
AC_[15]
AH_[0]
_brk_
c) How many members in `A xx B`? Answer:
AC_[15]
SKIP_
_LATEX
\item \
Given $A = \{1,2,3\}$, $B = \{5,14,17\}$.
\par
a) How many members in $A\cup B$? Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\par
b) How many members in $A\cap B$? Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\par
c) How many members in $A \times B$? Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$6$\\
$\diamond$\hspace{2mm}$0$\\
$\diamond$\hspace{2mm}$9$\\
\end{tabular}
_YEK
| > |
prob:=proc()
global LATEX_;
local a,b,c,ans,A,B;
paramvals([args],[[a,[{1,2,3,4},{4,5,7,11},{1,4,9,10}]],[b,[{6,10,3},{14,5,17},{21,4,9}]],[c,[2,3,4]]]);
ragit("Given ",A=a,", ",B=b union a,".",brak(),
"a) Is ",tr(A, sub, B),"? Answer:",as_([yes,no]),brak(),
"b) Is ",tr(c,elt,A),"? Answer:",as_([member(c,a),not member(c,a)]),brak(),
"c) How many members in ",tr("(",A, xx, B,")",cup,"(",B, xx,A,")"),"? Answer:",ac_(2*nops(a)*nops( b)));
LATEX_:=yes:
ragit("Given ",A=a,", ",B=b,".",brak(),
"a) Is ",tr(A, sub, B),"? Answer:",as_([yes,no]),brak(),
"b) Is ",tr(c,elt,A),"? Answer:",as_([member(c,a),not member(c,a)]),brak(),
"c) How many members in ",tr("(",A, xx, B,")",cup,"(",B, xx,A,")"),"? Answer:",ac_(2*nops(a)*nops( b)));
LATEX_:=no:
NULL:
end:
|
current inputs are (1,[{4, 5, 7, 11},{5, 14, 17},3])
QM_[.05;yes;false;24]
AH_[0]
Given `A = {4,5,7,11}`, `B = {4,5,7,11,14,17}`.
_brk_
a) Is `A sub B`? Answer:
AS_[yes;no]
AH_[0]
_brk_
b) Is `3 in A`? Answer:
AS_[false;true]
AH_[0]
_brk_
c) How many members in `(A xx B) uu (B xx A)`? Answer:
AC_[15]
SKIP_
_LATEX
\item \
Given $A = \{4,5,7,11\}$, $B = \{5,14,17\}$.
\par
a) Is $A\subset B$? Answer:
\begin{tabular}{ll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ ${\it yes}$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ ${\it no}$\\
&\\
\end{tabular}
\par
b) Is $3\in A$? Answer:
\begin{tabular}{ll}
\ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ ${\it false}$ & \ \fbox{\parbox[c][.1in][c]{.1in}{\hfill}}\ ${\it true}$\\
&\\
\end{tabular}
\par
c) How many members in $(A \times B)\cup (B \times A)$? Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm} $1$ \\
$\diamond$\hspace{2mm} $1$ \\
$\diamond$\hspace{2mm}$24$\\
\end{tabular}
_YEK
| > |
prob:=proc()
global LATEX_;
local a,b,c,ans,A,B,x;
paramvals([args],[[a,[12,14,16]],[b,[3,4,5]],[c,[2,3,4]]]);
ragit("From the given information about the arithmetic sequence ",tr(x[1],",",x[2],",",x[3],cdots,x[n],cdots),", find its ",n^th," term.",brak(),
"a) ",x[1]=a,", ",x[2]=a+b,". ",tr(x[n]," = "),ae_(a+(n-1)*b),brak(),
"b) ",x[4]=a,", ",x[6]=a+b,". ",tr(x[n]," = "),ae_(a-3/2*b+(n-1)/2*b),brak(),
"c) For some fixed positive integer ",A,", ",x[A]=a,", ",x[A+1]=a+b,". ",tr(x[n]," = "),ae_(a-(A-1)*b+(n-1)*b)):
LATEX_:=yes:
ragit("From the given information about the arithmetic sequence ",tr(x[1],",",x[2],",",x[3],cdots,x[n],cdots),", find its ",n^th," term.",brak(),
"a) ",x[1]=a,", ",x[2]=a+b,". ",tr(x[n]," = "),ae_(a+(n-1)*b),brak(),
"b) ",x[4]=a,", ",x[6]=a+b,". ",tr(x[n]," = "),ae_(a-3/2*b+(n-1)/2*b),brak(),
"c) For some fixed positive integer ",A,", ",x[A]=a,", ",x[A+1]=a+b,". ",tr(x[n]," = "),ae_(a-(A-1)*b+(n-1)*b)):
LATEX_:=no:
NULL:
end:
|
current inputs are (1,[12,4,4])
QM_[.05;8+4*n;4+2*n;12-4*A+4*n]
AH_[0]
From the given information about the arithmetic sequence `x_(1),x_(2),x_(3) cdots x_(n) cdots `, find its `n^(th)` term.
_brk_
a) `x_(1) = 12`, `x_(2) = 16`. `x_(n) = `
AF_[15;n;6;.1;1]
AH_[0]
_brk_
b) `x_(4) = 12`, `x_(6) = 16`. `x_(n) = `
AF_[15;n;6;.1;1]
AH_[0]
_brk_
c) For some fixed positive integer `A`, `x_(A) = 12`, `x_(A+1) = 16`. `x_(n) = `
AE_[15;2;A;n;25;.1;1;.1;1]
SKIP_
_LATEX
\item \
From the given information about the arithmetic sequence $x_{1},x_{2},x_{3}\cdots x_{n}\cdots $, find its $n^{{\it th}}$ term.
\par
a) $x_{1} = 12$, $x_{2} = 16$. $x_{n} = $
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\par
b) $x_{4} = 12$, $x_{6} = 16$. $x_{n} = $
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\par
c) For some fixed positive integer $A$, $x_{A} = 12$, $x_{A+1} = 16$. $x_{n} = $
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$8 + 4\,n$\\
$\diamond$\hspace{2mm}$4 + 2\,n$\\
$\diamond$\hspace{2mm}$12 - 4\,A + 4\,n$\\
\end{tabular}
_YEK
| > |
prob:=proc()
global LATEX_;
local a,b,c;
paramvals([args],[[a,[seq(10*i,i=1..5)]],[b,[seq(10*i+rand(2..6)(),i=1..5)]],[c,[4,6,8,3,5]]]);
ragit("Calculate:",tr("(",a,`-:`,b,")+(",c,`-:`,a,") = "),ac_(a/b+c/a)):
LATEX_:=yes:
ragit("Calculate:",tr("(",a,`-:`,b,")+(",c,`-:`,a,") = "),ac_(a/b+c/a)):
LATEX_:=no:
NULL:
end:
|
current inputs are (1,[40,35,6])
QM_[.05;181/140]
AH_[0]
Calculate:`(40 -: 35)+(6 -: 40) = `
AC_[15]
SKIP_
_LATEX
\item \
Calculate:$(40 \div 35)+(6 \div 40) = $
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$\frac{181}{140}$\\
\end{tabular}
_YEK
| > |
prob:=proc()
global LATEX_;
local a,b,c,x,y;
paramvals([args],[[a,[seq(10*i,i=1..5)]],[b,[seq(10*i+rand(2..6)(),i=1..5)]],[c,[4,6,8,3,5]]]);
ragit("Calculate:",tr("(",a,cdot,b,")+(",c,`-:`,x,") = "),af_(a*b+c/x)):
LATEX_:=yes:
ragit("Calculate:",tr("(",a,cdot,b,")+(",c,`-:`,x,") = "),af_(a*b+c/x)):
LATEX_:=no:
NULL:
end:
|
current inputs are (1,[30,13,8])
QM_[.05;390+8/x]
AH_[0]
Calculate:`(30 * 13)+(8 -: x) = `
AF_[15;x;6;.1;1]
SKIP_
_LATEX
\item \
Calculate:$(30\cdot 13)+(8 \div x) = $
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$\frac{390\,x + 8}{x}$\\
\end{tabular}
_YEK
| > |
prob:=proc()
global LATEX_;
local a,b,c,x,y;
paramvals([args],[[a,[seq(10*i,i=1..5)]],[b,[seq(10*i+rand(2..6)(),i=1..5)]],[c,[4,6,8,3,5]]]);
ragit("a) Calculate: ",Lim(x^2/b+c,x=a),ac_(a^2/b+c),brak(),
"b) Calculate: ",Pdiff(x^3*sin(y*z)+y^4*x+ln(z),x^2,y)," Answer: ",ae_(diff(x^3*sin(y*z)+y^4*x+ln(z),x,x,y))):
LATEX_:=yes:
ragit("a) Calculate: ",Lim((1/b*x^2+c),x=a),ac_(a^2/b+c),brak(),
"b) Calculate: ",Pdiff(x^3*sin(y*z)+y^4*x+ln(z),x^2,y)," Answer: ",ae_(diff(x^3*sin(y*z)+y^4*x+ln(z),x,x,y))):
LATEX_:=no:
NULL:
end:
|
current inputs are (1,[40,34,6])
QM_[.05;902/17;6*x*cos(y*z)*z]
AH_[0]
a) Calculate: `lim_(x to 40)\ (1)/(34)\ x^(2) + 6`
AC_[15]
AH_[0]
_brk_
b) Calculate: `\frac{del^(3)}{ del x^(2) del y}\ (x^(3)\ text(sin)(y\ z) + y^(4)\ x + text(ln)(z))` Answer:
AE_[15;3;x;y;z;25;.1;1;.1;1;.1;1]
SKIP_
_LATEX
\item \
a) Calculate: $\displaystyle\lim_{x\rightarrow 40}\,\frac{1}{34}\,x^{2} + 6$
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\par
b) Calculate: $\frac{\partial^{3}}{\partial x^{2}\partial y}\ (x^{3}\,\sin(y\,z) + y^{4}\,x + \ln(z))$ Answer:
\ \fbox{\parbox[c][.4in][c]{1in}{\hfill}}
\vspace{12pt}
_XETAL
_KEY
\begin{tabular}[t]{l}
$\diamond$\hspace{2mm}$\frac{902}{17}$\\
$\diamond$\hspace{2mm}$6\,x\,\cos(y\,z)\,z$\\
\end{tabular}
_YEK
After we get the problems that we want, we will export to html and then create homework zipfile using the following zipit line.
| > |
zipit("addpicandragit","c:/tmp/addpicandragit");
|
version 4/2/2009
Tue 04/07/2009
10:23 PM
Have you saved the source worksheet lately?
Files in c:\tmp\addpicandragit will go in homework zipfile.
Have you saved the source worksheet lately?
You are using zipit with the option Mathml=yes. You should put
a note at the top of the homework that IE6 and the Mathplayer plugin
(or special fonts for Mozilla) are needed to view the homework.
A zipfile addpicandragitkde.zip has been created in c:/tmp.
Now install the homework via mathclass
When we export the file to tex, we can use latexit to make a hardcopy mirror of the file, as shown below.
| > |
latexit("addpicandragit","c://tmp/addpicandragit");
|
index words duplicated
addpicandragitwhs.tex created
addpicandragitwhs.dvi created.
fixed eps files (removed their borders and recolored if Color=yes is set)
addpicandragitwhs.ps created sucessfully.
finished
But actually if we want a hardcopy version of the homework problems, we can use makexam as shown below.
| > |
makexam("addpicandragit","c:/tmp/addpicandragit",
Version=[[1],[seq(i,i=1..40)],[seq(i,i=1..40)]],
Cover=cat("\\textbf{\\Large Math Test with pictures}\\hfill Jan 31, 2009 \\hfill \\textbf{Name:}\\rule[-.01in]{1in}{.01in}\\\\\\bigskip"),
Spacing=[seq(vf,i=1..40)],
ExtraPreamble=cat("\\raggedright\n\\textheight=9.3in\\topmargin=-.5in"));;
|
The addpicandragit eps files are already recolorized.
addpicandragitv1_la.tex created: 36 problems
index words duplicated
addpicandragitv1_lawhs.tex created
addpicandragitv1_lawhs.dvi created.
fixed eps files (removed their borders and recolored if Color=yes is set)
addpicandragitv1_lawhs.ps created sucessfully.
finished
![g := F -> [F, MCtools:-ac_(subs(x = 2,F)), MCtools:-ac_(int(F,x = 0 .. 1)), MCtools:-af_(diff(F,x))]](images/worksheet31.gif)
![[sin(x), _AC(sin(2)), _AC(1-cos(1)), _AF(cos(x))]](images/worksheet32.gif){kind=small}