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23 | reyssat | 1 | |
2 | <center><h3>Examples of interactive exercises under OEF format</h3></center> <p> |
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3 | |||
4 | Here are some exampls of interactive exercises one can create by Createxo. |
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5 | <ol> |
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1004 | bpr | 6 | <p><hr width="50%"> <p> |
23 | reyssat | 7 | <li> <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. |
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9 | |||
10 | <p><pre> |
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11 | \title{Norm of vector 2D} |
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12 | \language{en} |
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13 | \computeanswer{no} |
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14 | \format{html} |
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15 | |||
16 | \integer{x=random(-10..10)} |
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17 | \integer{y=random(-10..10)} |
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18 | \real{norm=sqrt((\x)^2+(\y)^2)} |
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19 | \statement{What is the length of the vector (\x,\y) in R<sup>2</sup>?} |
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20 | |||
21 | \hint{The length of a vector (x,y) is equal to |
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22 | sqrt(x^2+y^2).} |
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23 | \answer{The length}{\norm} |
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24 | </pre> <p> |
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25 | |||
26 | In this exercise, one has defined 2 random integers, x et y, who are the |
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27 | coordinates of the vector. Then a third parameter, this time real, is defined |
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28 | by the formula of the length. The exercise takes a freestyle reply under the |
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29 | name of ``the length'', and the good reply should be the value of the third |
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30 | parameter``norm''. A hint is prepared in the exercise, which recalls the |
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31 | formula of the length. <p> |
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32 | You can |
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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= $ |
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34 | !href cmd=reply&mode=guided&$parm load this example into the menu |
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35 | to test it. (You can also copy the source into the menu under raw mode.) |
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36 | |||
1004 | bpr | 37 | <p><hr width="50%"> <p> |
23 | reyssat | 38 | <li> <b>Trace of matrix 2x2</b>, computes the trace of a matrix. The question |
39 | is formatted by TeX, for a better presentation of the matrix. Here is |
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40 | the complete source of the exercise. |
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41 | <p><pre> |
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42 | \title{Trace of matrix 2x2} |
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43 | \language{en} |
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44 | \computeanswer{yes} |
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45 | \format{tex} |
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46 | |||
47 | \integer{range=20} |
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48 | \integer{a=random(-\range..\range)} |
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49 | \integer{b=random(-\range..\range)} |
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50 | \integer{c=random(-\range..\range)} |
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51 | \integer{d=random(-\range..\range)} |
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52 | \integer{trace=(\a)+(\d)} |
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53 | \statement{Compute the trace of the matrix |
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54 | $$\pmatrix{\a&\b\cr \c&\d}$$.} |
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55 | |||
56 | \answer{The trace}{\trace} |
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57 | </pre> <p> |
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58 | We have first defined an integer ``range'', to be used to bound the |
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59 | random values a,b,c,d which are the elements of the matrix. And the trace is |
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60 | of course defined by the sum of the elements on the diagonal. Please take |
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61 | care to the definition <tt>trace=(\a)+(\d)</tt>: the pairs of parentheses |
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62 | are necessary, for the substitution is literary. If you define |
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63 | <tt>trace=\a+\d</tt> and if a and d take the values of 3 and -15 respectively, |
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64 | you woule have <tt>trace=3+-15</tt>, a bad mathematical expression. <p> |
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65 | Remark that in this exercise, the non-computed replies are admitted |
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66 | (such as 2+15 or 3*105). <p> |
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67 | You can |
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68 | !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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69 | !href cmd=reply&mode=guided&$parm load this example into the menu |
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70 | to test it. (You can also copy the source into the menu under raw mode.) |
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71 | |||
72 | |||
73 | </ol> |
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74 |