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  1.  
  2. <center><h3>
  3. Voorbeelden van interactieve opgaven <br>
  4. in het OEF formaat</h3></center> <p>
  5.  
  6. Hier staan enkele voorbeelden van interactieve oefeningen gemaakt met Createxo
  7. <ol>
  8. <p><hr width="50%"> <p>
  9. <li> <b>Lengte van een 2D vector </b>,
  10. een simpele berekening van de lengte van een vector in het platte vlak.
  11. Hier is de broncode van deze oefening/opgave:
  12.  
  13. <p><pre>
  14. \title{Norm of vector 2D}
  15. \language{en}
  16. \computeanswer{no}
  17. \format{html}
  18.  
  19. \integer{x=random(-10..10)}
  20. \integer{y=random(-10..10)}
  21. \real{norm=sqrt((\x)^2+(\y)^2)}
  22. \statement{Wat is de lengte van de vector (\x,\y) in R<sup>2</sup>?}
  23.  
  24. \hint{de lengte van een vector  (x,y) is gelijk aan
  25. sqrt(x^2+y^2).}
  26. \answer{De lengte}{\norm}
  27. </pre> <p>
  28.  
  29.  
  30. In this exercise, one has defined 2 random integers, x and y, who are the
  31. coordinates of the vector. Then a third parameter, this time real, is defined
  32. by the formula of the length. The exercise takes a freestyle reply under the
  33. name of ``the length'', and the good reply should be the value of the third
  34. parameter``norm''. A hint is prepared in the exercise, which recalls the
  35. formula of the length. <p>
  36. You can
  37. !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= $
  38. !href cmd=reply&mode=guided&$parm load this example into the menu
  39.  to test it. (You can also copy the source into the menu under raw mode.)
  40.  
  41. <p><hr width="50%"> <p>
  42. <li> <b>Trace of matrix 2x2</b>, computes the trace of a matrix. The question
  43.  is formatted by TeX, for a better presentation of the matrix. Here is
  44.  the complete source of the exercise.
  45. <p><pre>
  46. \title{Trace of matrix 2x2}
  47. \language{en}
  48. \computeanswer{yes}
  49. \format{tex}
  50.  
  51. \integer{range=20}
  52. \integer{a=random(-\range..\range)}
  53. \integer{b=random(-\range..\range)}
  54. \integer{c=random(-\range..\range)}
  55. \integer{d=random(-\range..\range)}
  56. \integer{trace=(\a)+(\d)}
  57. \statement{Compute the trace of the matrix
  58. $$\pmatrix{\a&\b\cr \c&\d}$$.}
  59.  
  60. \answer{The trace}{\trace}
  61. </pre> <p>
  62. We have first defined an integer ``range'', to be used to bound the
  63. random values a,b,c,d which are the elements of the matrix. And the trace is
  64. of course defined by the sum of the elements on the diagonal. Please take
  65. care to the definition <tt>trace=(\a)+(\d)</tt>: the pairs of parentheses
  66. are necessary, for the substitution is literary. If you define
  67. <tt>trace=\a+\d</tt> and if a and d take the values of 3 and -15 respectively,
  68. you woule have <tt>trace=3+-15</tt>, a bad mathematical expression. <p>
  69. Remark that in this exercise, the non-computed replies are admitted
  70. (such as 2+15 or 3*105). <p>
  71. You can
  72. !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= $
  73. !href cmd=reply&mode=guided&$parm load this example into the menu
  74.  to test it. (You can also copy the source into the menu under raw mode.)
  75.  
  76.  
  77. </ol>
  78.  
  79.