Scale

The score assigned to a copy is the sum of the scores obtained for each question. AMC can also be configured to calculate a final score, for example, on a scale from 0 to 20.

The scale used to assign a score to each question is indicated in the MCQ source file, which can be done in several places. A scale is made up of a set of values given to directives, each with a specific role. These directives are described in Directives.

Question scale

Simple question

In the case of a simple question (a single correct answer), you can indicate the score assigned to a correct answer using the b directive, and the score assigned to a wrong answer using the m directive, as in the following example, where a correct answer will be assigned a score of 2 and a wrong answer a negative score of -0.5:

AMC-TXT

*{b=2,m=-0.5} What is the capital city of Cameroon?
+ Yaoundé
- Douala
- Kribi

LaTeX

\begin{question}{Cameroon}\scoring{b=2,m=-0.5}
  What is the capital city of Cameroon?
  \begin{choices}
    \correctchoice{Yaoundé}
    \wrongchoice{Douala}
    \wrongchoice{Abou-Dabi}
  \end{choices}
\end{question}

Multiple question

For a multiple question, the question score is the sum of the scores obtained for each answer.

For a well-processed answer, i.e. a correct answer ticked or an incorrect answer unticked, the value of the b directive (default 1) is used.
For a wrongly processed answer, i.e. a correct answer that has not been ticked or a wrong answer that has been ticked, the value of m (default 0) is used.

Consider the following example, for which we have specified a question scale with b=2,m=-0.5:

AMC-TXT

**{b=2,m=-0.5} Which of the following words begin with the letter A?
+ Anyway
- Olive
+ Aim
- Enemy

LaTeX

\begin{questionmult}{firstletter}\scoring{b=2,m=-0.5}
  Which of the following words begin with the letter A?
  \begin{choices}
    \correctchoice{Anyway}
    \wrongchoice{Olive}
    \correctchoice{Aim}
    \wrongchoice{Enemy}
  \end{choices}
\end{question}

What score will the following copy achieve?

Anyway
Olive
Aim
Enemy

The first two answers are well processed, so they are assigned a score of b, which equals 2.
The last two answers are incorrectly processed, so they are assigned a score of m, which equals -0.5.

The score for this question is therefore 2+2-0.5-0.5=3. If all the questions had been well answered, the score would have been 2+2+2+2=8. AMC will therefore give this question a score of 3/8 for this copy.

Scale for a choice

You can also assign a value to a scale directive for a given choice.

Simple question

To assign a negative score (-2 in this case) to an answer considered very bad for a simple question, we use a special syntax with no directive name:

AMC-TXT

* What is the capital city of USA?
+ Washington, D.C.
- New York
-{-2} Ouagadougou

LaTeX

\begin{question}{USA}
  What is the capital city of USA?
  \begin{choices}
    \correctchoice{Washington, D.C.}
    \wrongchoice{New York}
    \wrongchoice{Ouagadougou}\scoring{-2}
  \end{choices}
\end{question}

Multiple question

The syntax without a directive name is not valid for a multiple question, but you can specify the value of a directive for a given answer, as in the following example, where the answer Enemy is not penalized if you don’t treat it well, and the answer Olive is valued less than the others:

AMC-TXT

**{b=2,m=-0.5} Which of the following words begin with the letter A?
+ Anyway
-{b=1} Olive
+ Aim
-{m=0} Enemy

LaTeX

\begin{questionmult}{debutmot}\scoring{b=2,m=-0.5}
  Which of the following words begin with the letter A?
  \begin{choices}
    \correctchoice{Anyway}
    \wrongchoice{Olive}\scoring{b=1}
    \correctchoice{Aim}
    \wrongchoice{Enemy}\scoring{m=0}
  \end{choices}
\end{question}

What score will the following copy achieve?

Anyway
Olive
Aim
Enemy

The calculation becomes 2+1-0.5+0=2.5, whereas a perfect copy would have obtained 2+1+2+2=7. AMC will therefore give this question a score of 2.5/7 for this copy.

Default scale

If you wish to use the same scale for all questions, you can define a default scale b=2,m=-0.5 for all single questions, and a default scale b=0.5,m=-0.1 for all multiple questions as follows:

AMC-TXT

DefaultScoringS: b=2,m=-1
DefaultScoringM: b=0.5,m=-0.1

LaTeX

% Right after \begin{document}
\scoringDefaultS{b=2,m=-1}
\scoringDefaultM{b=0.5,m=-0.1}

Directives

Some directives only make sense in certain contexts. Here, SQA is used to indicate a directive that can be used for simple questions, both for the question and for an answer (only ? is used if it can only be used for the question, and only the box if it can only be used for a choice), and MQA is used to indicate a directive that can be used for multiple questions, both for the question and for a choice.

e : score assigned if answers are inconsistent, i.e. if several boxes are ticked for a single question, or, for a multiple question, if the box “none of these answers is correct” is ticked at the same time as another box.
v : score assigned in case of non-response (no box checked).
d : an offset, i.e. a value added to all notes that do not fall within the cases corresponding to parameters e and v.
p : a floor score. If the calculation of the score obtained for the question results in a value lower than the floor value, the score is set to the floor value.
P : a ceiling score. If the calculation of the score obtained for the question results in a value higher than the ceiling value, the score is reduced to the ceiling value.
b : points to be awarded for the correct answer to a simple question, or for a well-answered choice to a multiple question.
m : points to be awarded for a wrong answer to a single question, or for an incorrectly answered choice from multiple question.
Value without directive name : number of points to be awarded if the student has ticked this answer (see Simple question).
auto : with this parameter, the value of answer number i will be auto+i-1. This option is mainly used with \QuestionIndicative (see Indicative question for LaTeX sources or Questions options for AMC-TXT sources).
mz : this parameter imposes a “maximum or zero” scale. The student must tick all the right answers to get the mz mark. Otherwise, the mark will be zero.
haut : by giving this parameter a value of n, the score awarded to a perfect answer will be n, and one point will be deducted for each incorrectly processed choice. haut=n is in fact rewritten as d=n-N,p=0.
MAX : gives the maximum value assigned to the question (for a “question graded out of 5”, MAX=5). Enter this only if it does not correspond to the score obtained by entering all the correct answers. For example, if you enter MAX=3 for a question with a possible score of 4 points, a student could obtain a score of 4/3 for this question (and, if he/she gives perfect answers to the other questions, he/she could possibly obtain an overall mark higher than 20/20).

Formula

More complex scales can be obtained by using a formula given by formula and possibly using other directives among the following:

formula : gives the question score directly, often via a formula involving certain variables (see Variables), without taking into account the values of b and m.

If the formula contains commas, enclose it in quotation marks, e.g. formula="max(0,NBC-NMC)".
set.XXX : gives a specific value to the variable named XXX, which can then be used by formula. In the context of an answer, the value is assigned only if the box is checked. Special case: if the INVALID variable is given a non-zero value in this way, the answers will be declared inconsistent and the score will be that given by the e parameter.
setglobal.XXX : gives a value to the variable XXX for all the questions that follow it in the lexicographical order of identifiers.

default.XXX : gives a value to the variable XXX if no checked box has already given one via set.XXX.

You can assign to b and m the values of the variable declared with default.XXX:

AMC-TXT

**{default.CONF=1,m=-CONF,b=CONF} Question text.
...

LaTeX

\begin{questionmult}{id}\scoring{default.CONF=1,m=-CONF,b=CONF}
...

requires.XXX : Indicates an inconsistent entry (i.e. application of the score given by the value of e) in the case where no value has been given to the variable XXX if no ticked box has already given one via set.XXX.

Variables

In addition to the variables defined by set.XXX and setglobal.XXX, the following variables can be used in the formula provided by formula:

N is the number of proposed answers, excluding the answer automatically added by the completemulti option.
NB is the number of correct answers to the question (regardless of whether the box is checked or not).
NBC is the number of correct choices that have been ticked.
NM is the number of wrong answers to the question (regardless of whether the box is checked or not).
NMC is the number of wrong choices that have been ticked.
IS is 1 if the question is simple and 0 otherwise.
IMULT is 1 if the question is multiple and 0 otherwise.

Operators and functions

The following operators and functions can be used in the formula:

addition +, subtraction -, multiplication *, division /, power **.
test ( test ? value if true : value if false ), where the test can use the equality ==, difference !=, comparison >, >=, <, <= operators.
max(a,b) and min(a,b) functions to calculate the maximum or minimum value.

Global instructions

A scale can also be specified outside the question, with two specific directives:

SUF=x is used to give a total of points sufficient to obtain the maximum mark: if we set the maximum mark at 20, for example, a copy with a total of points of 12 using SUF=15 will be given a mark of 12/15×20=16, whatever the total of a copy with all the correct answers.
allowempty=n allows the student to leave n questions unanswered. Of the questions left unanswered by the student, n (or less if there are fewer) will be cancelled (i.e. not taken into account in calculating the total score).

For instance:

AMC-TXT

LaTeX-BeginDocument: \scoring{SUF=12}

LaTeX

% Right after \begin{document}
\scoring{SUF=12}