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

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

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

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

<ol>

<ol>

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

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

<p><pre>

<p><pre>

\title{Norm of vector 2D}

\title{Norm of vector 2D}

\language{en}

\language{en}

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

\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

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

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

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

\answer{The length}{\norm}

\answer{The length}{\norm}

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

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

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

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

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

formula of the length. <p>

formula of the length. <p>

You can

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= $

!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

!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.)

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

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

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

 the complete source of the exercise.

 the complete source of the exercise.

\title{Trace of matrix 2x2}

\title{Trace of matrix 2x2}

\language{en}

\language{en}

\computeanswer{yes}

\computeanswer{yes}

\format{tex}

\format{tex}

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

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

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

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

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

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

\statement{Compute the trace of the matrix

\statement{Compute the trace of the matrix

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

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

\answer{The trace}{\trace}

\answer{The trace}{\trace}

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

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

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

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

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

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

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

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

You can

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= $

!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

!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.)

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

</ol>

</ol>