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| {{Formulas question type}}
| | #REDIRECT [[Formulas_question_type]] |
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| For a subquestion to become valid, you must give a mark and define an answer for it. Also, grading criteria must be specified in order to check the correctness of a student answer.
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| ==Answer type==
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| This question supports four answer types. Each type will accept a particular set of numbers, operators, functions and possibly algebraic variables. Depending on the purpose of the quiz, some or all of these answer types may be used.
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| {| class="nicetable"
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| |-
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| ! Answer type
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| ! Description
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| | Number
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| | You can type in the standard scientific E notation such as: <span style="font-family:monospace;font-size:113%;">3.14</span>, <span style="font-family:monospace;font-size:113%;">6.626e-34</span>.
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| |-
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| | Numeric
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| | You can type in numbers and arithmetic operation <span style="font-family:monospace;font-size:113%;">+ - * / ^</span> and <span style="font-family:monospace;font-size:113%;">( )</span> and the constant π, such as <span style="font-family:monospace;font-size:113%;">5+1/2</span>, <span style="font-family:monospace;font-size:113%;">2^9</span>, <span style="font-family:monospace;font-size:113%;">3pi</span>.
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| | Numerical formula
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| | You can type in everything of numeric plus a set of single variable functions <span style="font-family:monospace;font-size:113%;">sin()</span>, <span style="font-family:monospace;font-size:113%;">cos()</span>, <span style="font-family:monospace;font-size:113%;">tan()</span>, <span style="font-family:monospace;font-size:113%;">asin()</span>, <span style="font-family:monospace;font-size:113%;">acos()</span>, <span style="font-family:monospace;font-size:113%;">atan()</span>, <span style="font-family:monospace;font-size:113%;">exp()</span>, <span style="font-family:monospace;font-size:113%;">log10()</span>, <span style="font-family:monospace;font-size:113%;">ln()</span>, <span style="font-family:monospace;font-size:113%;">sqrt()</span>, <span style="font-family:monospace;font-size:113%;">abs()</span>, <span style="font-family:monospace;font-size:113%;">ceil()</span>, <span style="font-family:monospace;font-size:113%;">floor()</span>, such as <span style="font-family:monospace;font-size:113%;">sin(pi/12)</span>, <span style="font-family:monospace;font-size:113%;">10 ln(2)</span>.
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| | Algebraic formula
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| | You can type in every numerical formula and any algebraic variables.
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| |}
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| Notes:
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| <ul>
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| <li>Students will also need to know these rules in order to input the answers correctly.</li>
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| <li>The possible inputs have the following relation: Number ⊆ Numeric ⊆ Numerical formula ⊆ Algebraic formula.</li>
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| <li>The answer requires a list of strings for Algebraic formula and a list of numbers for the other answer types.</li>
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| <li><span style="font-family:monospace;font-size:113%;">^</span> in the algebraic formula means "power", not "exclusive or".</li>
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| <li>Juxtaposition between numbers or symbols mean multiplication.</li>
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| <li>The format check in the quiz interface shows a warning sign when the format is wrong for the answer type. It does not give any information about the correctness of the answer.</li>
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| <li>All symbols are treated as algebraic variable in the answer type of algebraic formula. Hence, you may need to hint students what symbols should be used in the question.</li>
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| </ul>
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| ==Correct answer==
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| Depending on the answer type, the answer options will accept an expression that evaluates to either a list of numbers or a list of strings for Algebraic formula. The size of the list will determine how many input boxes for the part. If only one answer is required, you can specify a number or a string instead of a one element list.
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| For the answer type of Number, Numeric and Numerical formula, a list of numbers or a single number is required. Suppose the variables are defined, each line below is a possible answer:
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| <pre style="font-size:113%;width: 97%;">
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| pi()
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| [sin(pi()/2), cos(pi()/2)]
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| [ans[0], ans[1], ans[2]]
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| ans
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| </pre>
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| For the answer type of Algebraic formula, a list of strings or a single string is required. Suppose the variables are defined, each line below is a possible answer:
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| <pre style="font-size:113%;width: 97%;">
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| "exp(-a x)"
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| " a x^2 + b y^2"
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| ["a sin(x)", "b cos(x)"]
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| </pre>
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| Note that all algebraic variables must be defined in order to be usable in the answer. For the answers above to work, you need to define the following variables:
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| <pre style="font-size:113%;width: 97%;">
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| a = 2;
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| b = 3;
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| x = {-100:100:1};
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| y = {1:100:1};
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| </pre>
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| ==Grading criterion==
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| A grading criterion is required to determine the correctness of the student answer. It requires an expression evaluated to a number whose 0 value means false and 1 value means true. Typically, the expression is either the absolute error or the relative error with a tolerance level.
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| For a question with only one answer, the absolute error is simply the different between the correct answer and the student answer. Hence if the correct answer is 3.2 and the student answer is 3.1, then the absolute error is |3.2-3.1| = 0.1 You may want to limit the range of correct answers, say to 0.05. In this case, you should select <span style="font-family:monospace;font-size:113%;">Absolute error < 0.05</span>. The relative error is defined as the absolute error divided by the absolute value of correct answer. See <span style="font-family:monospace;font-size:113%;">_err</span> and <span style="font-family:monospace;font-size:113%;">_relerr</span> in Grading variables below for more details.
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| ==Grading variables==
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| Most of the time, the absolute error or the relative error satisfy the grading criterion. However, sometimes there is a need for other grading criteria.
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| The scope of Grading variables contains all local variables and the student answers. You can define your own grading criterion with the student answers. The information related to the student answers and correct answers is stored in a set of special variables that start with an underscore as shown below:
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| {| class="nicetable"
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| ! Variable name
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| ! Description
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| | <span style="font-family:monospace;font-size:113%;">_0</span>, <span style="font-family:monospace;font-size:113%;">_1</span>, <span style="font-family:monospace;font-size:113%;">_2</span>, ...
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| | The student answers. The first answer is <span style="font-family:monospace;font-size:113%;">_0</span> corresponding to the answer box <span style="font-family:monospace;font-size:113%;">{_0}</span> in the part, etc.
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| | <span style="font-family:monospace;font-size:113%;">_a</span>
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| | The list of target answers, as defined in the answer field.
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| | <span style="font-family:monospace;font-size:113%;">_r</span>
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| | The list of student answers with the same size as <span style="font-family:monospace;font-size:113%;">_a</span>. The 0<sup>th</sup> element is the same as <span style="font-family:monospace;font-size:113%;">_0</span>, etc.
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| | <span style="font-family:monospace;font-size:113%;">_d</span>
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| | The list of differences between each element, where <span style="font-family:monospace;font-size:113%;">_d = diff(_a,_r);</span>. See the Appendix for the function details.
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| | <span style="font-family:monospace;font-size:113%;">_err</span>
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| | The absolute error, using the Euclidean norm |a-r|, i.e. <span style="font-family:monospace;font-size:113%;">_err = sqrt(sum(map("*",_d,_d)));</span>.
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| | <span style="font-family:monospace;font-size:113%;">_relerr</span>
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| | The relative error, obtained by dividing the absolute error by the norm of the correct answerd |a-r|/|a| , i.e. <span style="font-family:monospace;font-size:113%;">_relerr = _err/sqrt(sum(map("*",_a,_a)));</span>.
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| |}
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| Notes:
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| <ul>
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| <li>The corresponding input boxes of <span style="font-family:monospace;font-size:113%;">_0</span>, <span style="font-family:monospace;font-size:113%;">_1</span>, ... can be specified as <span style="font-family:monospace;font-size:113%;">{_0}</span>, <span style="font-family:monospace;font-size:113%;">{_1}</span>, ... in the part's text.</li>
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| <li><span style="font-family:monospace;font-size:113%;">_relerr</span> is <i>not</i> defined for algebraic answers! So <span style="font-family:monospace;font-size:113%;">_err</span> should be used instead.</li>
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| <li> For non-algebraic answers, the student answer is rescaled towards the unit of the target answer. For example, if the target answer is 2 m and the student answer is 199 cm, then _a is [2] , _r is [1.99] and _0 is 1.99 . It has no effect if no unit is used.</li>
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| <li> When there are more than on answer, for example if _a = [100,100]; and == _r = [101,102];, then _relerr = sqrt(1*1+2*2)/sqrt(100*100+100*100) ≒ 0.0158
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| In this sense, the answer defined in the answer field is only a target answer because it may not be related directly to the correctness of the answer.</li>
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| </ul>
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| ==Manual grading criteria==
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| Other than true or false, the grading criterion can be any number between 0 (all incorrevt) and 1 (all correct). The value 1 means that the student gets the full mark for this par see Gng scheme). A fractional value represents the partial correctness of the student answer. Note that values less than 0 are treated as 0 and that values greater than 1 are treated as 1. The following examples illustrate cases where a manual grading criterion is required:
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| ===Multiple correct answers===
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| The possibility for a student to give any correct answer among several correct answers can be allowed by establishing manually the required '''Grading criteria'''.
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| <div style="background:#f2dede;color:#a94442;0px;padding:4px 8px 6px;border:1px solid #ebcccc;border-radius:4px;margin:10px 0;">
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| <p>
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| With site themes '''Clean''' and '''More''', the field for manual '''Grading Criteria''' is obtained by checking a box on the left hand side of the field. With the '''Boost''' theme, the check box does not display. [https://moodle.org/mod/forum/discuss.php?d=345283#p1392516 This bug has been reported] by Bernat Martinez a while ago, but has not yet been fixed.
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| </p>
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| <p>As a teacher, you can get the manual '''Grading criteria''' by changing the theme of the site to '''Clean''' or '''More''', but if you do not have access to the site theme, hang on, this bug should be fixed soon!
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| </p>
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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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| Give a number <i>x</i> that is a multiple of 7 and satisfies 40 < <i>x</i> < 50.
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| <pre style="font-size:113%;width: 97%;">
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| General
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| Question name! Multiples of 7
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| Main question
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| Question text! Give a number x that is a multiple of 7 and satisfies 40 < x < 50:
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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* 1
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| Grading criteria* _0 == 42 || _0 == 49
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| Part's text {_0}
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| </pre>
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| In Part 1, Answer is specified as 1 (or any other number) to indicate to the system that just one answer is expected. Grading criteria _0 == 42 || _0 == 49 means that the answer is correct if it is equal to 42 or equal to 49.
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| The Formulas question should look like this:
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| [[File:Formules201801212219.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=270<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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| ===Multiple criteria===
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| The above example uses only a fixed number, so how can you grade an answer with random variations? Suppose that you now ask questions with a variable range for each question a < <i>x</i>< <i>a</i> + 10. To determine the correctness, you need to check two criteria, type the following in the Grading Variables and Grading Criteria box respectively:
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| <pre style="font-size:113%;width: 97%;">
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| criterion1 = _0 % 7 == 0; # whether the remainder is 0. Note that true is 1 and false is 0.
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| criterion2 = a < _0 && _0 < a+10; # whether the response is in the desired range.
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| criterion1 && criterion2
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| </pre>
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| ===Mark for different accuracies===
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| Suppose you want to give different marks for the accuracy of the response, say full mark for 1% absolute error and half mark for 1% to 5% absolute error. The following criteria can be used:
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| <pre style="font-size:113%;width: 97%;">
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| case1 = _err < 0.01;
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| case2 = _err < 0.05;
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| max (case1, 0.5*case2)
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| </pre>
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| ==Trial mark sequence==
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| This option only apply to the adaptive mode of moodle quiz.
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| In the adaptive mode, students are allowed to submit answer to a particular question again and again. This field defines the mark sequence that a student can get for each resubmission. Note that it actually alter the default behavior of the adaptive mode.
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| The input is a list of numbers separated by comma. Each number represents a fraction of the maximum mark that a student can get in the first, second, third, etc. submission. Hence, if this field has value 1, the student can try it once only.
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| If the sequence is ended with a comma, infinite resubmission is allow. In this case, the mark that students can get in the following unlisted trial is decreased uniformly with the value equal to the difference of last two value. Note that the minimum mark is always zero (See grading scheme).
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| Trial mark sequence Maximum mark for each trial Description
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| 1 100% Only one trial is allowed
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| 1, 0.7, 0.3 100%, 70%, 30% Three trials are allowed
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| 1, 0.7, 0.3, 0 100%, 70%, 30%, 0% Four trials are allowed, but the last trial has no mark
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| 1, 0, 0, 0 100%, 0%, 0%, 0% Four trials are allowed, but only the first trial has non-zero mark
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| 1, 100%, 100%, 100%, ... Infinite trials. The difference is 0, which is repeated
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| 1, .9, 100%, 90%, 80%, 70%, 60%, ... Infinite trials. Difference between 1st and 2nd trial is 10%, which is repeated
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| 1, .6, 100%, 60%, 20%, 0%, 0%, ... Infinite trials. Difference between 1st and 2nd trial is 40%, which is repeated
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| 1, .5, .3, 100%, 50%, 30%, 10%, 0%, 0%, ... Infinite trials. Difference between 2nd and 3rd trial is 20%, which is repeated
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| ==Grading scheme==
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| The following is the grading formula used to grade a particular subquestion:
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| Symbol Description
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| c Correctness. It takes value between 0 and 1. Boolean false is treated as 0 and true is treated as 1. Other values may be possible if manual condition is used (see Grading criteria)
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| u Deduction for wrong unit (see Unit system). In the formula, it always takes value 0 if the unit is correct under Conversion rules
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| m Default mark of the subquestion.
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| r_n Maximum mark fraction of the n-th submission, for adaptive mode only (See Trial mark sequence)
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| f The computed final mark.
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| For non-adaptive mode:
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| f = m*c*(1-u)
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| For adaptive mode (see moodle documentation):
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| f = max(r_n*m*c*(1-u))
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| The maximum is taken over all submissions. From the above formula, even though a student get a low mark in the first attempt, it is still possible for them to get a higher mark in the following attempt.
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| ==Appendix==
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| ===Core function diff()===
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| This function depends on context variables in addition to the function parameters. It is also the core function to compare the students' response and model answer (see Grading variables). If input X and Y are a list of string, then X[i] and Y[i] are treated as algebraic formulas and all variables in them must be defined before the location of evaluation. For example,
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| <pre style="font-size:113%;width: 97%;">
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| a = 3;
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| x = {1:100};
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| d = diff(["a x"],["a x^2"]);
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| </pre>
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| Please note that the actual algebraic formulas should be "3 x" and "3 x^2" in the above case. In the above evaluation, the d will take a finite value but not close to zero because the algebraic formula are different. In general, any evaluation failure between two algebraic formula will result in a infinite value INF, so that the expression, say, sum(d) < 0.01 will always be false.
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| ===Idea of grading algebraic answer===
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| The evaluation will take place at N randomly selected points defined in all algebraic variables. The result of <span>diff("f(x,y)","f(x,y)")</span> will be the root mean square difference at all evaluation points (1/N)Σ<sub>i</sub>(f<sub>i</sub>-g<sub>i</sub>)<sup>2</sup>, which will converge when N tends to infinity. The N is 100 by default if it is not specified.
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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:_Respuestas_y_notaci%C3%B3n Español]<br>
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| [https://docs.moodle.org/3x/fr/Formules:_Réponses_et_notation Français]
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