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<center><h3>Examples of interactive exercises under OEF format</h3></center> <p>
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Here are some exampls of interactive exercises one can create by Createxo.
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<ol>
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<p><hr width="50%"> <p>
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<li> <b>Length of vector 2D</b>, a simple computation of the length of
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a vector in the plane. Here is the complete source of this exercise.
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<p><pre>
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\title{Norm of vector 2D}
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\language{en}
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\computeanswer{no}
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\format{html}
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\integer{x=random(-10..10)}
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\integer{y=random(-10..10)}
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\real{norm=sqrt((\x)^2+(\y)^2)}
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\statement{What is the length of the vector (\x,\y) in R<sup>2</sup>?}
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\hint{The length of a vector  (x,y) is equal to
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sqrt(x^2+y^2).}
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\answer{The length}{\norm}
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</pre> <p>
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In this exercise, one has defined 2 random integers, x et y, who are the
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coordinates of the vector. Then a third parameter, this time real, is defined
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by the formula of the length. The exercise takes a freestyle reply under the
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name of ``the length'', and the good reply should be the value of the third
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parameter``norm''. A hint is prepared in the exercise, which recalls the
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formula of the length. <p>
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You can
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!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= $
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!!provisoire --to translate
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!href cmd=reply&mode=guided&$parm load this example into the menu
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 to test it. (You can also copy the source into the menu under raw mode.)
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<p><hr width="50%"> <p>
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<li> <b>Trace of matrix 2x2</b>, computes the trace of a matrix. The question
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 is formatted by TeX, for a better presentation of the matrix. Here is
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 the complete source of the exercise.
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<p><pre>
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\title{Trace of matrix 2x2}
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\language{en}
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\computeanswer{yes}
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\format{tex}
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\integer{range=20}
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\integer{a=random(-\range..\range)}
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\integer{b=random(-\range..\range)}
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\integer{c=random(-\range..\range)}
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\integer{d=random(-\range..\range)}
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\integer{trace=(\a)+(\d)}
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\statement{Compute the trace of the matrix
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$$\pmatrix{\a&\b\cr \c&\d}$$.}
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\answer{The trace}{\trace}
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</pre> <p>
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We have first defined an integer ``range'', to be used to bound the
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random values a,b,c,d which are the elements of the matrix. And the trace is
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of course defined by the sum of the elements on the diagonal. Please take
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care to the definition <tt>trace=(\a)+(\d)</tt>: the pairs of parentheses
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are necessary, for the substitution is literary. If you define
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<tt>trace=\a+\d</tt> and if a and d take the values of 3 and -15 respectively,
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you woule have <tt>trace=3+-15</tt>, a bad mathematical expression. <p>
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Remark that in this exercise, the non-computed replies are admitted
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(such as 2+15 or 3*105). <p>
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You can
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!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= $
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!changeto help/en/examples.phtml
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!href cmd=reply&mode=guided&$parm load this example into the menu
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 to test it. (You can also copy the source into the menu under raw mode.)
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</ol>
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