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| {{Question de type Formules}}
| | #REDIRECT [[Types_de_questions_tiers]] |
| {{Traduction}}
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| =Chiffres significatifs=
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| ''"Le nombre de chiffres significatifs indique la précision d'une mesure physique."'' (Référence: https://fr.wikipedia.org/wiki/Chiffre_significatif).
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| La question Formules n'a pas de fonction intégrée pour afficher des valeurs avec un nombre donné de chiffres significatifs. Cependant, il est facile de définir cette fonction comme l'affectation de variable suivante qui fonctionne avec n'importe quel nombre réel::
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| <pre style="font-size:113%;width: 98%;">
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| xr=x==0?x:round(x*pow(10,nsf-1-floor(log10(abs(x)))),0)*pow(10,-nsf+1+floor(log10(abs(x))));
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| </pre>
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| où <span style="font-family: monospace;font-size:113%;">x</span> est le nombre qu'on veut arrondir, <span style="font-family: monospace;font-size:113%;">nsf</span> le nombre de chiffres significatifs qu'on veut garder et <span style="font-family: monospace;font-size:113%;">xr</span> la valeur arrondie résultante.
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| <div style="border:1px solid #bce8f1;border-radius:4px;padding: 0px 15px 0px; margin:30px 0 25px;">
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| <div style="font-family:Lucida Sans Unicode;font-size:150%;color:#f98012;margin:10px 0 10px;>Exemple</div>
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| Cet exemple traite de l'affichage des réponses correctes avec différents nombres de chiffres significatifs.
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| La question Formules devrait ressembler à ceci :
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| [[File:Formulas201712310126.png|680px]]
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| <div style="margin:20px 0 20px;">
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| [http://35.193.77.29/mod/quiz/view.php?id=153<span style="background-color:#f98012;box-shadow: 0 5px 10px #cbcbcb;border: none;color:white;padding: 8px 16px;text-align:center;text-decoration: none;cursor:pointer;">À vous de jouer</span>] [[Question_de_type_Formules#Exemples|Info connexion ↗]] ''(Ouvrir dans un nouvel onglet : Ctrl+Maj+Clic)''
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| </div>
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| </div>
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| <div style="border:1px solid #bce8f1;border-radius:4px;padding: 0px 15px 0px; margin:35px 0 25px;">
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| <div style="font-family:Lucida Sans Unicode;font-size:150%;color:#f98012;margin:10px 0 10px;>Exemple</div>
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| Cet exemple est un exercice de chiffres significatifs.
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| <pre style="font-size:113%;width: 98%;">
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| Généraux
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| Nom de question! Exercice de chiffres significatifs
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| Variables
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| Variables au hasard # a signe plus ou moins
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| # b exposant variant de -4 to 4 par pas de 0.01
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| # rnsf nombre aléatoire de chiffres significatifs : 1, 2, 3, or 4
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| a={-1,1};
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| b={-4:4.01:0.01};
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| rnsf={1,2,3,4};
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| Variables globales # nx nombre x = ± 10^b
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| nx=a*pow(10,b);
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| # Routine d'arrondissement :
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| # x nombre à arrondir
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| # nsf nombre de chiffres significatifs
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| # xr valeur arrondie de x
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| x=nx;
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| nsf=rnsf;
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| xr=x==0?x:round(x*pow(10,nsf-1-floor(log10(abs(x)))),0)*pow(10,-nsf+1+floor(log10(abs(x))));
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| Question principale
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| Texte de la question! Exercice de chiffres significatifs
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| Partie 1
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| Note de la partie* 1
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| Type de réponse Nombre
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| Réponse* xr
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| Critère de notation* Erreur relative < 0.0001
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| Texte de la partie Nombre à arrondir : {nx}
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| Nombre de chiffres significatifs à garder : {ncs}
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| Nombre arrondi : {_0}
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| Feedback combiné
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| Pour toute réponse correcte
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| La réponse correcte est : {xr}
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| Pour toute réponse incorrecte
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| La réponse correcte est : {xr}
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| </pre>
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| In the Variables fields (random, global and local), lines starting with # are treated as comments.
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| <div style="background-color:#d3ffd3;
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| border:1px solid #abdaac;
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| border-radius:4px;
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| color:#4f691a;
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| padding:5px 15px 10px;
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| margin: 15px 0 15px;
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| ">
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| C'est toujours une bonne idée de documenter son travail en utilisant des commentaires dans les champs '''Variables'''.</div>
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| In this example, values to be rounded range from -10 000 to +10 000. In order to have the same number of values in each order of magnitude, hence a more interesting exercise, the random variable <span style="font-family:monospace;font-size:113%;">b</span> is used as a power of 10. By letting:
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| <div style="margin-left:50px;font-family:monospace;font-size:113%;">x = ± 10<sup>b</sup></div>
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| with <span style="font-family:monospace;font-size:113%;">b</span> ranging from -4 to +4 in steps of 0.01, there are one hundred random values in each order of magnitude (0.000 1 to 0.001, 0.001 to 0.01, 0.01 to 0.1, 0.1 to 1, 1 to 10, 10 to 100, 100 to 1 000 and 1 000 to 10 000), both positive and negative.
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| '''Au total, cet exemple génère 6 408 questions aléatoires différentes :'''
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| <div style="margin-left:50px;">2 (a={-1,1}) × 801 (b={-4:4.01:0.01}) × 4 (rnsf={1,2,3,4}) = 6 408</div>
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| La question Formules devrait ressembler à ceci :
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| [[File:Formulas201712301427.png|680px]]
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| <div style="margin:20px 0 20px;">
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| [http://35.193.77.29/mod/quiz/view.php?id=152<span style="background-color:#f98012;box-shadow: 0 5px 10px #cbcbcb;border: none;color:white;padding: 8px 16px;text-align:center;text-decoration: none;cursor:pointer;">À vous de jouer</span>] [[Question_de_type_Formules#Exemples|Info connexion ↗]] ''(Ouvrir dans un nouvel onglet : Ctrl+Maj+Clic)''
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| </div>
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| </div>
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| =Factoriel=
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| "In mathematics, the factorial of a non-negative integer <span style="vertical-align:1px;"><math>n</math></span>, denoted by <span style="vertical-align:3px;"><math>n!</math></span>, is the product of all positive integers less than or equal to <span style="vertical-align:1px;"><math>n</math></span>. For example,
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| <div style="margin-left:50px;vertical-align:40px;"><math>5!=5\times4\times3\times2\times1=120.</math></div>
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| The value of <span style="vertical-align:3px;"><math>0!</math></span> is <span style="vertical-align:3px;"><math>1</math></span>, according to the convention for an empty product." (Reference: https://en.wikipedia.org/wiki/Factorial).
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| With the built-in function <span style="font-family: monospace;font-size:113%;">fact()</span>, the Formulas question calculates factorial values up to <span style="vertical-align:3px;"><math>170!=7.26\rm{E}306</math></span> (which would correspond to the largest number that can be handled by PHP). For larger values of <span style="vertical-align:1px;"><math>n</math></span>, <span style="font-family: monospace;font-size:113%;">fact()</span> returns <span style="font-family: monospace;font-size:113%;">INF</span> for the value of <span style="vertical-align:4px;"><math>n!</math></span>.
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| However input (with <span style="font-family: monospace;font-size:113%;">{_0}</span>, <span style="font-family: monospace;font-size:113%;">{_1}</span>, etc.) is limited to a maximum value corresponding to <span style="vertical-align:4px;"><math>102!=9.61\rm{E}161</math></span>.<sup>(Explain why)</sup>
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| ===References===
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| * Factorials can readily be evaluated up to 170! on Google built-in calculator, under 64-bit Windows and Android: [https://www.google.ca/search?&q=%3D170! 170!]
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| * For larger factorials, see WolframAlpha: [https://www.wolframalpha.com/input/?i=1000! 1000!] [https://www.wolframalpha.com/input/?i=(10%5E100)! 10<sup>100</sup>!]
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| <div style="border:1px solid #bce8f1;border-radius:4px;padding: 0px 15px 0px; margin:30px 0 25px;">
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| <div style="font-family:Lucida Sans Unicode;font-size:150%;color:#f98012;margin:10px 0 10px;>Example</div>
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| This simple example illustrates the use of the <span style="font-family: monospace;font-size:113%;">fact()</span> function.
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| <pre style="font-size:113%;width: 98%;">
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| General
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| Question name! Factorial - example 1
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| Variables
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| Random variables n = {2:8};
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| m = {2:8};
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| Global variables x = fact(n)*fact(m);
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| Main question
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| Question text! Factorial - example 1
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| Part 1
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| Part's mark* 1
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| Answer type Number
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| Answer* x
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| Grading criteria* Absolute error == 0
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| Part's text Calculate:
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| {n}! x {m}! = {_0} (enter value using integer format)
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| Combined feedback
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| For any correct response
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| The correct answer is: {x}
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| For any incorrect response
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| The correct answer is: {x}
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| </pre>
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| The Formulas question should look like this:
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| [[File:Formulas201801021122.png|680px]]
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| <div style="margin:20px 0 20px;">
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| [http://35.193.77.29/mod/quiz/view.php?id=173<span style="background-color:#f98012;box-shadow: 0 5px 10px #cbcbcb;border: none;color:white;padding: 8px 16px;text-align:center;text-decoration: none;cursor:pointer;">Play it</span>] [[Formulas_question_type#Examples|Login info]] ''(Open in new tab: Ctrl+Shift+Click)''
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| </div>
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| </div>
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| <div style="border:1px solid #bce8f1;border-radius:4px;padding: 0px 15px 0px; margin:35px 0 25px;">
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| <div style="font-family:Lucida Sans Unicode;font-size:150%;color:#f98012;margin:10px 0 10px;>Example</div>
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| This slightly more elaborate example shows that the <span style="font-family: monospace;font-size:113%;">fact()</span> function can handle large factorials and also that calculations with factorials can easily be performed using the <span style="font-family: monospace;font-size:113%;">fact()</span> function.
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| <pre style="font-size:113%;width: 98%;">
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| General
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| Question name! Factorial - example 2
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| Variables
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| Random variables n = {0:171:1};
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| nn = {12:171:1};
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| na = {1:10};
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| m = {0:103:1};
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| Global variables x=fact(m);
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| Main question
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| Question text! Factorial - example 2
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| Part 1
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| Part's mark* 1
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| Answer type Number
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| Answer* x
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| Grading criteria* Relative error < 0.01
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| Part's text 1. Calculate:
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| {m}! = {_0} (use scientific notation for large numbers)
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| 2. It can easily be shown that {nn}! / {=nn-na}! = {=fact(nn)/fact(nn-na)}.
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| Combined feedback
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| For any correct response
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| The correct answer is: {x}
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| For any incorrect response
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| The correct answer is: {x}
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| </pre>
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| The Formulas question should look like this:
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| [[File:Formulas201801020347.png|680px]]
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| <div style="margin:20px 0 20px;">
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| [http://35.193.77.29/mod/quiz/view.php?id=172<span style="background-color:#f98012;box-shadow: 0 5px 10px #cbcbcb;border: none;color:white;padding: 8px 16px;text-align:center;text-decoration: none;cursor:pointer;">Play it</span>] [[Formulas_question_type#Examples|Login info]] ''(Open in new tab: Ctrl+Shift+Click)''
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| </div>
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| </div>
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| [[#top|Accéder au haut de la page]]
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| [[Question de type Formules|← QUESTION DE TYPE FORMULES]]
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| =Autres langues=
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| [https://docs.moodle.org/33/en/Formulas:_More_examples English]<br>
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| [https://docs.moodle.org/all/es/F%C3%B3rmulas:_M%C3%A1s_ejemplos Español]
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