Subversion Repositories wimsdev

<center><h3>Examples of interactive exercises under OEF format</h3></center> <p>

Here are some exampls of interactive exercises one can create by Createxo.

<ol>

<li>

<hr style="width:50%"/>

<b>Length of vector 2D</b>, a simple computation of the length of

a vector in the plane. Here is the complete source of this exercise.

<p><pre>

\title{Norm of vector 2D}

\language{en}

\computeanswer{no}

\format{html}

\integer{x=random(-10..10)}

\integer{y=random(-10..10)}

\real{norm=sqrt((\x)^2+(\y)^2)}

\statement{What is the length of the vector (\x,\y) in R<sup>2</sup>?}

\hint{The length of a vector  (x,y) is equal to

sqrt(x^2+y^2).}

\answer{The length}{\norm}

</pre>

In this exercise, one has defined 2 random integers, x et y, who are the

coordinates of the vector. Then a third parameter, this time real, is defined

by the formula of the length. The exercise takes a freestyle reply under the

name of ``the length'', and the good reply should be the value of the third

parameter``norm''. A hint is prepared in the exercise, which recalls the

formula of the length. <p>

You can

!set parm=oef_answercnt=1&oef_choicecnt=0&oef_title=Norm of vector 2D&oef_format=html&oef_computeanswer=no&level=2&oef_parms=%5Cinteger%7Bx%3Drandom%28-10..10%29%7D%0D%0A%5Cinteger%7By%3Drandom%28-10..10%29%7D%0D%0A%5Creal%7Bnorm%3Dsqrt%28%28%5Cx%29%5E2%2B%28%5Cy%29%5E2%29%7D&oef_statement=What is the length of the vector %28%5Cx%2C%5Cy%29 in R%3Csup%3E2%3C%2Fsup%3E%3F&ansprompt1=The length&ansgood1=%5Cnorm&oef_hint=The length f a vector %28x%2Cy%29 is equal to %0D%0Asqrt%28x%5E2%2By%5E2%29.&oef_solution= $

!href cmd=reply&mode=guided&$parm load this example into the menu

 to test it. (You can also copy the source into the menu under raw mode.)

</p>

</li>

<li> <hr style="width:50%"/>

<b>Trace of matrix 2x2</b>, computes the trace of a matrix. The question

 is formatted by TeX, for a better presentation of the matrix. Here is

 the complete source of the exercise.

<pre>

\title{Trace of matrix 2x2}

\language{en}

\computeanswer{yes}

\format{tex}

\integer{range=20}

\integer{a=random(-\range..\range)}

\integer{b=random(-\range..\range)}

\integer{c=random(-\range..\range)}

\integer{d=random(-\range..\range)}

\integer{trace=(\a)+(\d)}

\statement{Compute the trace of the matrix

$$\pmatrix{\a&\b\cr \c&\d}$$.}

\answer{The trace}{\trace}

</pre>

We have first defined an integer ``range'', to be used to bound the

random values a,b,c,d which are the elements of the matrix. And the trace is

of course defined by the sum of the elements on the diagonal. Please take

care to the definition <span class="tt">trace=(\a)+(\d)</span>: the pairs of parentheses

are necessary, for the substitution is literary. If you define

<span class="tt">trace=\a+\d</span> and if a and d take the values of 3 and -15 respectively,

you woule have <span class="tt">trace=3+-15</span>, a bad mathematical expression. <p>

Remark that in this exercise, the non-computed replies are admitted

(such as 2+15 or 3*105). <p>

You can

!set parm=oef_answercnt=1&oef_choicecnt=0&oef_title=Trace of matrix 2x2&oef_format=tex&oef_computeanswer=yes&level=2&oef_parms=%5Cinteger%7Brange%3D20%7D%0D%0A%5Cinteger%7Ba%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bb%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bc%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bd%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Btrace%3D%28%5Ca%29%2B%28%5Cd%29%7D&oef_statement=Compute the trace of the matrix%0D%0A%24%5Cpmatrix%7B%5Ca%26%5Cb%5Ccr %5Cc%26%5Cd%7D%24.&ansprompt1=The trace&ansgood1=%5Ctrace&oef_hint= &oef_solution= $

!href cmd=reply&mode=guided&$parm load this example into the menu

 to test it. (You can also copy the source into the menu under raw mode.)

</li>

</ol>