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% jzexam — LaTeX Exam Package v0.9 (2026-06-12)
% Author: Jorge I. Zuluaga (C) 2026-present
% Repository: https://github.com/seap-udea/jzexam
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% EXAM PACKAGE
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% Optional: hide answers (student version)
%\usepackage[noanswers]{jzexam}
% Show answers (answer-key / instructor version)
\usepackage[answers]{jzexam}
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% OTHER PACKAGES
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\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{amsmath}
\setlength\parindent{0pt}
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% EXAM HEADER CONFIGURATION
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\examinfo
{Exam Template — Course X}
{Department of Physics — University Y\\Course: General Topic\\Semester 2026-1}
% Customizing the student fill-in fields:
% - \examfield[0.5]{...} uses 50% of the line width (two fields per row)
% - \examfield[1]{...} uses 100% of the line width (one field per row)
% - \examfield{...} auto-width (shares remaining space equally)
\setexamheaderfields{%
\examfield[0.5]{Name}%
\examfield{ID Number}%
\examfield{Programme}%
}
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\begin{document}
\makeexamheader
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% PROBLEMS
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\begin{examproblems}
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% PROBLEM
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%\problempage
\problempage[header]
\begin{problem}{Generic Problem in Relativistic Mechanics}[30]
State the general context of the problem here.
\begin{questions}
%===========================
% QUESTION
%===========================
\question Derive a symbolic expression for a physical quantity of interest.
\begin{solution}
This is a sample solution. Replace this text with the actual derivation.
\end{solution}
%===========================
% QUESTION (example of \hidequestion)
%===========================
% Use \hidequestion instead of commenting out a sub-question to temporarily
% suppress it. Neither the question text nor its solution will appear in the PDF.
\hidequestion Discuss the physical interpretation of the previous result and its limiting cases.
\begin{solution}
Include a brief interpretation and a discussion of limiting cases here.
\end{solution}
\end{questions}
\end{problem}
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% PROBLEM
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\problempage[header]
\begin{problem}{Generic Problem in Electromagnetic Fields}[40]
Consider a scenario with fields \(\vec{E}\) and \(\vec{B}\) under a Lorentz transformation.
\begin{questions}
%===========================
% QUESTION
%===========================
\question Calculate an invariant quantity associated with the field tensor.
\begin{solution}
Include the invariant expression and the main derivation steps here.
\end{solution}
%===========================
% QUESTION
%===========================
\question Determine the fields in a moving reference frame and compare with the original frame.
\begin{solution}
Write the transformation equations and a qualitative comparison of results here.
\end{solution}
\end{questions}
\end{problem}
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% PROBLEM: MULTIPLE CHOICE
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%\problempage[header]
\begin{problem}{Single-Answer and Multiple-Answer Questions}[30]
Select the correct option(s) and provide a brief justification.
\begin{questions}
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% QUESTION: SINGLE CHOICE
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\singlechoicequestion{For a free particle, the conserved quantity associated with time-translation symmetry is:}
\begin{choices}[2]
\choice{The total angular momentum.}
\correctchoice{The total energy.}
\choice{The effective electric charge.}
\choice{The local scalar curvature.}
\end{choices}
%===========================
% QUESTION: MULTIPLE CHOICE
%===========================
\multiplechoicequestion{In special relativity, which of the following statements are correct?}
\begin{choices}[2]
\correctchoice{The speed of light in vacuum is invariant.}
\choice{Proper time is the same for all inertial observers.}
\correctchoice{Events simultaneous in one frame may not be simultaneous in another.}
\choice{Rest mass depends on the reference frame.}
\end{choices}
\end{questions}
\end{problem}
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% SHORT CONCEPTUAL QUESTIONS
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%\problempage[header]
\begin{problem}{Short Conceptual Questions}[30]
Answer briefly and with justification.
\begin{questions}
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% SUBSECTION: CONCEPTS
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\questionsection{General Concepts}
Describe in two or three sentences the difference between invariant quantities and observer-dependent quantities.
\begin{solution}
An invariant keeps its value under Lorentz transformations, whereas an observer-dependent quantity changes with the reference frame.
\end{solution}
%===========================
% SUBSECTION: APPLICATION
%===========================
\questionsection{Application}
Propose an example where the choice of reference frame simplifies the analysis of a problem.
\begin{solution}
A typical example is working in the centre-of-mass frame for relativistic collisions, which simplifies the conservation of energy and momentum.
\end{solution}
\end{questions}
\end{problem}
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% END OF PROBLEMS
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\end{examproblems}
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% FORMULA SHEET (optional)
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% Use this environment to generate a formula page at the end of the exam.
\begin{formulasheet}
\item Euler--Lagrange equations: $\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{q}_i}\right) - \frac{\partial L}{\partial q_i} = 0$
\item Lagrange--Jacobi identity and Virial theorem: $\dot{G}=2 K+U$, $2\langle K\rangle=-\langle U\rangle$
\item Lorentz transformations (1D): $x' = \gamma (x - vt), \quad t' = \gamma \left(t - \frac{vx}{c^2}\right)$
\end{formulasheet}
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% END OF DOCUMENT
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\end{document}
