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  1.  
  2. <h3>Examples of interactive exercises under OEF format</h3>
  3.  
  4. Here are some exampls of interactive exercises one can create by Createxo.
  5. <ol>
  6.  
  7. <li> <hr style="width:50%"/><b>Length of vector 2D</b>, a simple computation of the length of
  8. a vector in the plane. Here is the complete source of this exercise.
  9.  
  10. <pre>
  11. \title{Norm of vector 2D}
  12. \language{en}
  13. \computeanswer{no}
  14. \format{html}
  15.  
  16. \integer{x=random(-10..10)}
  17. \integer{y=random(-10..10)}
  18. \real{norm=sqrt((\x)^2+(\y)^2)}
  19. \statement{What is the length of the vector (\x,\y) in R<sup>2</sup>?}
  20.  
  21. \hint{The length of a vector  (x,y) is equal to
  22. sqrt(x^2+y^2).}
  23. \answer{The length}{\norm}
  24. </pre>
  25.  
  26. In this exercise, one has defined 2 random integers, x et y, who are the
  27. coordinates of the vector. Then a third parameter, this time real, is defined
  28. by the formula of the length. The exercise takes a freestyle reply under the
  29. name of ``the length'', and the good reply should be the value of the third
  30. parameter``norm''. A hint is prepared in the exercise, which recalls the
  31. formula of the length. <p>
  32. You can
  33. !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= $
  34. !href cmd=reply&mode=guided&$parm load this example into the menu
  35.  to test it. (You can also copy the source into the menu under raw mode.)
  36.  
  37.  
  38. </li><li> <hr style="width:50%"/>
  39. <b>Trace of matrix 2x2</b>, computes the trace of a matrix. The question
  40.  is formatted by TeX, for a better presentation of the matrix. Here is
  41.  the complete source of the exercise.
  42. <pre>
  43. \title{Trace of matrix 2x2}
  44. \language{en}
  45. \computeanswer{yes}
  46. \format{html}
  47.  
  48. \integer{range=20}
  49. \integer{a=random(-\range..\range)}
  50. \integer{b=random(-\range..\range)}
  51. \integer{c=random(-\range..\range)}
  52. \integer{d=random(-\range..\range)}
  53. \integer{trace=(\a)+(\d)}
  54. \statement{Compute the trace of the matrix
  55. \([\a,\b;\c,\d]\).}
  56.  
  57. \answer{The trace}{\trace}
  58. </pre>
  59. We have first defined an integer ``range'', to be used to bound the
  60. random values a,b,c,d which are the elements of the matrix. And the trace is
  61. of course defined by the sum of the elements on the diagonal. Please take
  62. care to the definition <span class="tt">trace=(\a)+(\d)</span>: the pairs of parentheses
  63. are necessary, for the substitution is literary. If you define
  64. <span class="tt">trace=\a+\d</span> and if a and d take the values of 3 and -15 respectively,
  65. you woule have <span class="tt">trace=3+-15</span>, a bad mathematical expression. <p>
  66. Remark that in this exercise, the non-computed replies are admitted
  67. (such as 2+15 or 3*105). <p>
  68. You can
  69. !set parm=oef_answercnt=1&oef_choicecnt=0&oef_title=Trace of matrix 2x2&oef_format=html&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 \\([\a,\b;\c,\d]\\).&ansprompt1=The trace&ansgood1=%5Ctrace&oef_hint= &oef_solution= $
  70. !href cmd=reply&mode=guided&$parm load this example into the menu
  71.  to test it. (You can also copy the source into the menu under raw mode.)
  72.  
  73. </li>
  74. </ol>
  75.  
  76.