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| {{Formulas question type}}
| | #REDIRECT [[Formulas_question_type]] |
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| =Significant figures=
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| ''"The significant figures of a number are digits that carry meaning contributing to its measurement resolution."'' (Reference: https://en.wikipedia.org/wiki/Significant_figures).
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| The Formulas question has no built-in function to display values with a given number of significant figures. However, it is easy to work out this function as the following variable assignment which works with any real number:
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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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| where <span style="font-family: monospace;font-size:113%;">x</span> is the number to be rounded, <span style="font-family: monospace;font-size:113%;">nsf</span> the number of significant digits to keep and <span style="font-family: monospace;font-size:113%;">xr</span> the resulting rounded value.
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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 example deals with the display of the correct answers with different numbers of significant figures.
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| The Formulas question should look like this:
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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;">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 example is a significant figures drill.
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| <pre style="font-size:113%;width: 98%;">
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| General
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| Question name! Significant figures drill
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| Variables
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| Random variables # a plus or minus sign
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| # b exponent varying from -4 to 4 in steps of 0.01
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| # rnsf random number of significant figures: 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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| Global variables # nx number x = ± 10^b
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| nx=a*pow(10,b);
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| # Rounding routine:
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| # x number to round
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| # nsf number of significant figures
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| # xr rounded value of 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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| Main question
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| Question text! Significant figures drill
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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* xr
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| Grading criteria* Relative error < 0.0001
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| Part's text Number to round: {nx}
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| Number of significant digits to keep: {ncs}
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| Rounded number: {_0}
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| Combined feedback
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| For any correct response
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| The correct answer is: {xr}
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| For any incorrect response
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| The correct answer is: {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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| It is always a good idea to document your work using comments in the '''Variables''' fields.</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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| '''In total, this example generates 6 408 different random questions:'''
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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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| The Formulas question should look like this:
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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;">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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| =Factorial=
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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|Back to top of page]]
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| [[Formulas_question_type|← FORMULAS QUESTION TYPE]]
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| ===In other languages===
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| [https://docs.moodle.org/all/es/F%C3%B3rmulas:_M%C3%A1s_ejemplos Español]<br>
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| [https://docs.moodle.org/3x/fr/Formules:_Plus_d'exemples Français]
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