这可以看作是该问题的后续：使用 xsim 包正确定义问题和子问题
我还没有接受这个问题，因为我还在尝试将我的 tex 发行版更新到最新版本以全面测试答案。然而，从答案中我能够想出自己的解决方案，这让我想到了这个问题
背景
我想收集不同大学的微积分 1 历年考试题目，给它们贴上标签，然后将它们分成exercises和subquestions。这些exercises是主要的考试题目，看起来像这样
这subquestions是一个部分其中exercises能独立存在。想想“问题 1b”，其中“1b”不依赖于“1a”或其他信息（例如问题的介绍文本）。因此，可以混合搭配subquestions。
目标
我想exercises从这些考试中抽取不同的主题
理想情况下，我想采样 1-2 个关于积分、导数、微分方程和复数的问题。
问题
大约有 4 所大学提供这些课程，通常每年举行 2 次考试，每次考试约有 4-8 道题。我想从过去 5 年的考试中抽取一些题目。如果他们平均每次考试有 6 道题，那么我就可以大致250 exercises抽取一些题目了。
在下面的例子中，我仅包括了1每年每所大学的考试，1仅提供了 24 份exercises样本。
采样仅有的标记的问题integration给了我超过 58 个辅助文件。
为所有四个创建集合使问题更加严重。
编译时间大约需要一两分钟complex，当我将所有四个都包括在内时，30 分钟后仍未完成。
我不寒而栗当我考虑从全部 250 个问题中抽样完成编译需要多少周的时间时。
问题
有没有更好的方法来使用不同的标签进行抽样（随机挑选问题）？我是否必须为每个标签创建一个单独的唯一集合？
为什么要
xsim创建这么多aux文件？有没有什么办法可以让它平静下来？为什么编译时间需要永远当将数量增加到
exercises大约时，是否有一种方法可以使其在合理的时间内（例如几分钟）进行编译250？
代码
主文本
\documentclass{article}
\usepackage{amssymb,mathtools}
\usepackage[ISO]{diffcoeff}
\usepackage{tasks}
\usepackage{xsim}
\providecommand*\e{e}
\DeclareExerciseType{subquestion}{
exercise-env = question ,
solution-env = answer ,
exercise-name = Question ,
solution-name = Answer ,
exercise-template = item ,
solution-template = item
}
\DeclareExerciseTagging{year} % 1992, 2010, etc
\DeclareExerciseTagging{topic}
\DeclareExerciseTagging{semester} % V (Spring), H (Fall)
\DeclareExerciseTagging{exam} % O (ordinary), K (kont / re-sit exam), P (prøveeksamen)
\DeclareExerciseTagging{university} % UiO, UiB, UiT, etc
\DeclareExerciseProperty{title}
\DeclareExerciseTagging{type}
\DeclareExerciseEnvironmentTemplate{named}
{\subsection*{\GetExercisePropertyTF{title}{#1}{??}}}
{}
\DeclareExerciseEnvironmentTemplate{item}
{\item}
{}
\xsimsetup{
exercise/template = named,
exercise/begin-hook = \renewcommand\theenumi{\alph{enumi}},
}
\DeclareExerciseCollection{MAT}
\DeclareExerciseCollection{integral}
\DeclareExerciseCollection{derivative}
\DeclareExerciseCollection{complex}
\DeclareExerciseCollection{ODE}
\newcommand*\includeQuestion[1]{%
\XSIMexpandcode{\printexercise{subquestion}{\GetExerciseIdForProperty{ID}{#1}}}%
}
\newcommand*\includeProblem[1]{%
\XSIMexpandcode{\printexercise{exercise}{\GetExerciseIdForProperty{ID}{#1}}}%
}
\usepackage{csquotes}
\usepackage{multicol}
\begin{document}
% \collectexercises{integral}
% \xsimsetup{type=prob, topic=integral}
% \input{UiO/MAT1100/MAT1100-2015-2019}
% \input{UiB/MAT111/MAT111-2015-2019}
% \input{UiT/MAT-1001/MAT-1001-2015-2019}
% \input{UiS/MAT100/MAT111-2015-2019}
% \collectexercisesstop{integral}
% \collectexercises{derivative}
% \xsimsetup{type=prob, topic=derivative}
% \input{UiO/MAT1100/MAT1100-2015-2019}
% \input{UiB/MAT111/MAT111-2015-2019}
% \input{UiT/MAT-1001/MAT-1001-2015-2019}
% \input{UiS/MAT100/MAT111-2015-2019}
% \collectexercisesstop{derivative}
\collectexercises{complex}
\xsimsetup{type=prob}
\input{main-problems.tex}
% \input{UiO/MAT1100/MAT1100-2015-2019}
% \input{UiB/MAT111/MAT111-2015-2019}
% \input{UiT/MAT-1001/MAT-1001-2015-2019}
% \input{UiS/MAT100/MAT111-2015-2019}
\collectexercisesstop{complex}
% \collectexercises{ODE}
% \xsimsetup{type=prob, topic=ODE}
% \input{UiO/MAT1100/MAT1100-2015-2019}
% \input{UiB/MAT111/MAT111-2015-2019}
% \input{UiT/MAT-1001/MAT-1001-2015-2019}
% \input{UiS/MAT100/MAT111-2015-2019}
% \collectexercisesstop{ODE}
% \printcollection{MAT}
\printrandomexercises[collection=complex]{1}
% \printrandomexercises[collection=derivative]{1}
% \printrandomexercises[collection=integral]{1}
% \printrandomexercises[collection=ODE]{1}
\end{document}
主要问题.tex
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT-1001-2019-H-O-Problem-1-a,
university = {UiT},
topic = {complex, root}
]
Det komplekse tallet $z_1 = 1 + i \sqrt{2}$ er en løsning til annengradslikningen
\begin{equation*}
z^2 - 2z + 3 = 0.
\end{equation*}
Finn den andre løsningen $z_2$. Regn så ut tallet $z_1^2 + z_2^2$.
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT-1001-2019-H-O-Problem-1-b,
university = {UiT},
topic = {complex, root, figure}
]
Finn alle tre tredjegradsrøttene til $8$ på form $\rho e^{i\theta}$ og merk
dem av som punktet på en skisse av det komplekse planet. Pass på å merke av
enhetene $1$ og $i$ på aksene.
\end{question}
\begin{exercise}[
year=2019,semester=H,type={prob},exam=O,
topic={complex, root, figure},
ID=MAT-1001-2019-H-O-Problem-1,
university = {UiT},
title={Oppgave~1 (H19, UiT)}]
\begin{enumerate}
\includeQuestion{MAT-1001-2019-H-O-Problem-1-a}
\includeQuestion{MAT-1001-2019-H-O-Problem-1-b}
\end{enumerate}
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={concavity,monotonicity,limit},exam=O,
ID=MAT-1001-2019-H-O-Problem-1,
university = {UiT},
title={Oppgave~2 (H19, UiT)}]
En kontinuerlig funksjon $f\colon [0, \infty) \to \mathbb{R}$ er gitt ved
\begin{equation*}
f(x) = x^2 \log x, \qquad \text{når} > 0.
\end{equation*}
\begin{enumerate}
\item Avgjør hvor $f$ er voksende/avtagende på $(0, \infty)$.
\item Avgjør hvor $f$ er konveks/konkav på $(0, \infty)$.
\item Regn ut grensen
\begin{equation*}
\lim_{x \to 0^+} x^2 \log x
\end{equation*}
og finn funksjonsverdien $f(0)$. Hva er minimumsverdien til $f$?
\end{enumerate}
\end{exercise}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT-1001-2019-H-O-Problem-3-a,
university = {UiT},
topic = {ODE,2-order,homogeneous}
]
For differensiallikningen
\begin{equation*}
u''(x) - 5 u'(x) + 6 u(x) = 0,\phantom{e^x}
\end{equation*}
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT-1001-2019-H-O-Problem-3-b,
university = {UiT},
topic = {IVT,ODE,2-order,nonhomogeneous}
]
For differensiallikningen
\begin{equation*}
u''(x) - 5 u'(x) + 6 u(x) = 2e^x,
\end{equation*}
Løs startverdiproblemet $y(0)=y'(0)=0$.
\end{question}
\begin{exercise}[
year=2019,semester=H,type={prob},exam=O,
topic={IVT,ODE,2-order,nonhomogeneous,homogeneous},
ID=MAT-1001-2019-H-O-Problem-3,
university = {UiT},
title={Oppgave~3 (H19, UiT)}]
\begin{enumerate}
\includeQuestion{MAT-1001-2019-H-O-Problem-3-a}
\includeQuestion{MAT-1001-2019-H-O-Problem-3-b}
\end{enumerate}
\end{exercise}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT-1001-2019-H-O-Problem-4-a,
university = {UiT},
topic = {integral, IBP, substitution}
]
Regn ut integralene
\begin{equation*}
\int \frac{e^x + 1}{(e^x + 1)^2} \dl x
\quad \text{og} \quad
\int_1^e x \log^2(x) \dl x
\end{equation*}
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT-1001-2019-H-O-Problem-4-b,
university = {UiT},
topic = {integral, FTC, linear-approximation}
]
Integralet
\begin{equation*}
\int_0^{2\pi} \frac{\dl u}{5 + 3 \cos(u)} = \frac{\pi}{2}
\end{equation*}
er oppgitt. Finn for funksjonen
\begin{equation*}
F(x) = \int_0^{x} \frac{\dl u}{5 + 3 \cos(u)}
\end{equation*}
den beste lineære tilnærmingen omrking punktet $x = 2\pi$.
Vær nøye med din begrunnelse.
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT-1001-2019-H-O-Problem-4-c,
university = {UiT},
topic = {continuous,differentiable}
]
En funksjon $g\colon[0,1] \to [0,1]$ er definert ved $g(1) = 1$, og
\begin{equation*}
g(x) = \frac{k - 1}{k} \cdot x \quad \text{og} \quad
\frac{k - 1}{k} \leq x < \frac{k}{k+1} \quad \text{når} \quad
k = 1, 2, 3, \ldots
\end{equation*}
Er $g$ kontinuerlig? Er $g$ integrerbar? Begrunn dine svar.
\end{question}
\begin{exercise}[
year=2019,semester=H,type={prob},exam=O,
topic={integral, IBP, substitution,FTC,
linear-approximation,continuous,differentiable},
ID=MAT-1001-2019-H-O-Problem-4,
university = {UiT},
title={Oppgave~4 (H19, UiT)}]
\begin{enumerate}
\includeQuestion{MAT-1001-2019-H-O-Problem-4-a}
\includeQuestion{MAT-1001-2019-H-O-Problem-4-b}
\includeQuestion{MAT-1001-2019-H-O-Problem-4-c}
\end{enumerate}
\end{exercise}
\begin{question}[
year=2018,semester=V,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-1-a,
university = {UiS},
topic = {complex}
]
Gitt $z = 1 + 2i$ og $w = 3 - i$. Regn ut $z^2$, $|z|$ og $z/w$.
\end{question}
\begin{question}[
year=2018,semester=H,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-1-b,
university = {UiS},
topic = {complex, polar, normalform}
]
Skriv $a = 1 \sqrt{-3}i$ og $b=-2i$ på eksponentiell form og
finn $a^3 b^4$. Skriv svaret på kartesisk form.
\end{question}
\begin{question}[
year=2018,semester=H,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-1-c,
university = {UiS},
topic = {complex, root}
]
For hvilke positive heltall $n$ er $i^n = -1$?
\end{question}
\begin{exercise}[
year=2018,semester=H,type={prob},exam=O,
topic={complex, root, polar, normalform},
ID=MAT100-2018-V-O-Problem-1,
university = {UiS},
title={Oppgave~1 (H18, UiS)}]
\begin{enumerate}
\includeQuestion{MAT100-2018-V-O-Problem-1-a}
\includeQuestion{MAT100-2018-V-O-Problem-1-b}
\includeQuestion{MAT100-2018-V-O-Problem-1-c}
\end{enumerate}
\end{exercise}
\begin{question}[
year=2018,semester=V,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-2-a,
university = {UiS},
topic = {integral,trigonometric}
]
$\displaystyle \int \bigl(2x^{5/3} + \cos x) \dl x$
\end{question}
\begin{question}[
year=2018,semester=H,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-2-b,
university = {UiS},
topic = {integral,logarithm,IBP}
]
$\displaystyle \int x^2 \log x \dl x$
\end{question}
\begin{question}[
year=2018,semester=H,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-2-c,
university = {UiS},
topic = {integral,substitution}
]
$\displaystyle \int \frac{x^2}{\sqrt{2x^3 + 1}} \dl x$
\end{question}
\begin{question}[
year=2018,semester=H,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-2-d,
university = {UiS},
topic = {integral,PFD}
]
$\displaystyle \int \frac{x^2+1}{(x+1)^2(x+2)} \dl x$
\end{question}
\begin{question}[
year=2018,semester=H,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-2-e,
university = {UiS},
topic = {integral, substitution}
]
$\displaystyle \int \frac{\tan^{-1}x}{1+x^2} \dl x$
\end{question}
\begin{exercise}[
year=2018,semester=H,type={prob},exam=O,
topic={integral},
ID=MAT100-2018-V-O-Problem-2,
university = {UiS},
title={Oppgave~2 (H18, UiS)}]
Finn følgende integraler. Utregning må vises!
\begin{multicols}{2}
\begin{enumerate}
\includeQuestion{MAT100-2018-V-O-Problem-2-a}
\includeQuestion{MAT100-2018-V-O-Problem-2-b}
\includeQuestion{MAT100-2018-V-O-Problem-2-c}
\includeQuestion{MAT100-2018-V-O-Problem-2-d}
\includeQuestion{MAT100-2018-V-O-Problem-2-e}
\item[\vspace{\fill}]
\end{enumerate}
\end{multicols}
\end{exercise}
\begin{question}[
year=2018,semester=H,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-3-a,
university = {UiS},
topic = {ODE, IVP}
]
Løs initialverdiproblemet:
\begin{equation*}
\begin{cases}
4 y'' + y' + y = 0, \\
y(0) = 0, \quad y'(0) = 1.
\end{cases}
\end{equation*}
\end{question}
\begin{question}[
year=2018,semester=H,exam=O,type={subprob},
ID=MAT100-2018-V-O-Problem-3-b,
university = {UiS},
topic = {ODE, 1-order, separable}
]
Løs differensialligningen
\begin{equation*}
\diff yx = x^2 + y^2 x^2.
\end{equation*}
\end{question}
\begin{exercise}[
year=2018,semester=H,type={prob},exam=O,
topic={ODE, IVP, 1-order, separable},
ID=MAT100-2018-V-O-Problem-3,
university = {UiS},
title={Oppgave~3 (H18, UiS)}]
Finn følgende integraler. Utregning må vises!
\begin{enumerate}
\includeQuestion{MAT100-2018-V-O-Problem-3-a}
\includeQuestion{MAT100-2018-V-O-Problem-3-b}
\end{enumerate}
\end{exercise}
\begin{exercise}[
year=2018,semester=H,type={prob},exam=O,
topic={derivative, max-min, integral, surface-of-revolution},
ID=MAT100-2018-V-O-Problem-5,
university = {UiS},
title={Oppgave~5 (H18, UiS)}]
Funksjonen $f$ er gitt som
\begin{equation*}
f(x) = x \sqrt{1 - x^2}, \qquad x \in [-1, 1].
\end{equation*}
\begin{enumerate}
\item Finn alle ekstremalpunktene for $f$. Avgjør om de er logale eller globale
maksimum og minimum.
\item La $D$ være området avgrenset av grafen til $f$, $x$-aksen, $x=0$,
og $x=1$. Finn volumet av omdreiningslegemet som fremkommer ved å dreie $D$
om $y$-aksen.
\end{enumerate}
\end{exercise}
\begin{exercise}[
year=2018,semester=H,type={prob},exam=O,
topic={curve, implicitt-derivative},
ID=MAT100-2018-V-O-Problem-5,
university = {UiS},
title={Oppgave~5 (H18, UiS)}]
En kurve er definert implisitt ved $x^2 y^3 - x^3 y^2 = 12$
\begin{enumerate}
\item Finn $\diff x/y$.
\item Finn likningene for tangenten og normalen til kurven gjennom punktet
$(-1, 2)$.
\end{enumerate}
\end{exercise}
\begin{exercise}[
year=2018,semester=H,type={prob},exam=O,
topic={IVT, ODE, word-problem},
ID=MAT100-2018-V-O-Problem-6,
university = {UiS},
title={Oppgave~6 (H18, UiS)}]
Ali Gruffalo har akkuratt brygget seg en kopp kaffe. Kaffen er kjempevarm
og holder temperaturen $96^\circ$C. Dette er alt for varmt for å drikkes og
Ali venter derfor litt for at kaffen skal kjøle seg ned. Vi antar nedkjølinga
følger Newtons kjølelov
\begin{equation*}
\diff Tt = -k(T - A)
\end{equation*}
hvor $T$ er temperaturen (i $^\circ$C, $t$ er tiden (i minutter), $A$
er temperaturen til omgivelsene, og $k$ er konstant. Temperaturen i rommet
er $21^\circ$C, så vi lar $A = 21$.
\begin{enumerate}
\item Løs differensiallikningen med initialbetingelsen $T(0) = 96$.
\item Etter $5$ minutter måler Ali temperaturen i kaffen til å være
$66^\circ$C. Når er temperaturen i kaffen $45^\circ$C?
\end{enumerate}
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={partialderivative,derivative},exam=O,
ID=MAT1100-2019-H-O-Problem-1,
university = {UiO},
title={Oppgave~1 (H19, UiO)}]
Finn de partiellderiverte
$\diffp{f}{x}$, $\diffp{f}{x}$, $\diffp{f}{x}$ til
\begin{equation*}
f(x, y, z) = y^2 \tan(x z^3).
\end{equation*}
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={gradient,derivative,steepest-descent},exam=O,
ID=MAT1100-2019-H-O-Problem-2,
university = {UiO},
title={Oppgave~2 (H19, UiO)}]
Finn stigningstallet til funksjonen $f(x, y) = x^3y + x^2$ i punktet
$(1, -1)$ i den retningen der funksjonen vokser raskest.
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={gradient,derivative,steepest-descent},exam=O,
ID=MAT1100-2019-H-O-Problem-3,
university = {UiO},
title={Oppgave~3 (H19, UiO)}]
Finn stigningstallet til funksjonen $f(x, y) = x^3y + x^2$ i punktet
$(1, -1)$ i den retningen der funksjonen vokser raskest.
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={matrix,inverse},exam=O,
ID=MAT1100-2019-H-O-Problem-4,
university = {UiO},
title={Oppgave~4 (H19, UiO)}]
\begin{flalign*}
&\text{La} &
\begin{pmatrix}
1 & a \\
0 & 1
\end{pmatrix}, \quad \text{der $a$ er ett reelt tall}.&&
\end{flalign*}
\begin{enumerate}
\item Regn ut matriseproduktene $M(2)M(3)$ og $M(1)M(2)$
og matrisepotensen $\bigl(M(a)\Bigr)^3$.
\item Regn ut $M(a)M(b)$ og finn den inverse matrisen til $M(a)$.
\end{enumerate}
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={integral, convergence},exam=O,
ID=MAT1100-2019-H-O-Problem-5,
university = {UiO},
title={Oppgave~5 (H19, UiO)}]
Avgjør om det uegentlige integralet
\begin{equation*}
\int_0^1 \frac{\arctan x}{x^2} \dl x
\end{equation*}
konvergerer eller divergerer.
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={FTC,derivative,second-derivative},exam=O,
ID=MAT1100-2019-H-O-Problem-6,
university = {UiO},
title={Oppgave~6 (H19, UiO)}]
Finn den andrederiverte til funksjonen
\begin{equation*}
f(x) = \int_1^{2x^2} \e^{3t} \dl t, x \in [1, \infty)
\end{equation*}
\end{exercise}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT1100-2019-H-O-Problem-7-a,
university = {UiO},
topic = {complex,root,polar}
]
Skriv de komplekse røttene til polynomet
\begin{equation*}
x^2 + x + 1
\end{equation*}
både på $a + ib$ form og på polarform.
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT1100-2019-H-O-Problem-7-b,
university = {UiO},
topic = {complex,root,factorization}
]
Faktoriser
\begin{equation*}
x^4 + x^2 + 1
\end{equation*}
i reelle andregradspolynomer.
\end{question}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={complex,root,polar,factorization},exam=O,
ID=MAT1100-2019-H-O-Problem-7,
university = {UiO},
title={Oppgave~7 (H19, UiO)}]
\begin{enumerate}
\includeQuestion{MAT1100-2019-H-O-Problem-7-a}
\includeQuestion{MAT1100-2019-H-O-Problem-7-b}
\end{enumerate}
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={continuous,differentiable,integrable},exam=O,
ID=MAT1100-2019-H-O-Problem-8,
university = {UiO},
title={Oppgave~8 (H19, UiO)}]
La $a$, $b$ og $c$ være reelle tall. La
\begin{equation*}
f(x) = \begin{cases}
c & \text{hvis} \ x = 0\\
\frac{ax \cos x}{\sin x} + 2 & \text{hvis} 0 < x < \frac{\pi}{2}\\
bx + 1 & \text{hvis} \ \frac{\pi}{2} \leq x \leq 2
\end{cases}
\end{equation*}
\begin{enumerate}
\item For hvilke reelle tall $a$ og $c$ er $f$ kontinuerlig i $x = 0$.
\item Finn $a$, $b$ og $c$ slik at $f$ er kontinuerlig på $[0, 2]$ og
deriverbart på $(0, 2)$.
\item Forklar hvorfor $f$ er integrerbar på hele intervallet $[0, 2]$
for alle reelle tall $a$, $b$ og $c$. (Du skal ikke finne integralet.)
\end{enumerate}
\end{exercise}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-1-a,
university = {UiB},
topic = {complex,root,normalform}
]
Skriv de komplekse tallene nedenfor på normalform (på formen $a + ib$):
\begin{tasks}(2)
\task $\displaystyle \frac{2 + 3i}{1 + 4i}$
\task $\displaystyle \Bigr(\frac{1}{2} - \frac{\sqrt{3}}{2}i\Bigl)^9$
\end{tasks}
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-1-b,
university = {UiB},
topic = {complex,root,normal}
]
Finn alle løsningene til ligningen $z^3 = -1 $ og skriv dem på normalform.
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-1-c,
university = {UiB},
topic = {complex,root,factorization}
]
Faktoriser $z^3 + 1$ i lineære faktorier over $\mathbb{C}$ og i lineære
kvadratiske faktorer over $\mathbb{R}$.
\end{question}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={complex},exam=O,
ID=MAT111-2019-H-O-Problem-1,
university = {UiB},
title={Oppgave~1 (H19, UiB)}]
\begin{enumerate}
\includeQuestion{MAT111-2019-H-O-Problem-1-a}
\includeQuestion{MAT111-2019-H-O-Problem-1-b}
\includeQuestion{MAT111-2019-H-O-Problem-1-c}
\end{enumerate}
\end{exercise}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={IVT,ODE,1-order,seperable},exam=O,
ID=MAT111-2019-H-O-Problem-2,
university = {UiB},
title={Oppgave~2 (H19, UiB)}
]
En kiselalge (\textit{Tacphoria arlyc Ketil, 2019})
blomstrer i takt med tilgangen på næring, slik
at den totale massen $y(t)$ (i megatonn) kiselalger
i Beringhavet ved tid t (i måneder etter
nyttår) tilfredsstiller differensialligningen
\begin{equation*}
y'(t) = k \sin \Bigl( \frac{2\pi t}{12} \Bigr) \cdot y(t),
\end{equation*}
der $k$ er en konstant. Gitt at $y(0) = 100$ og $y(6) = 400$, finn $y(t)$.
\end{exercise}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-3-a,
university = {UiB},
topic = {limit,epsilon-delta}
]
Bruk den \emph{formelle definisjonen av grenseverdi} (\enquote{$\varepsilon-\delta$ definisjonen}) til å vise at:
\begin{equation*}
\lim_{x \to 1} \Bigl( x^2 + x + 1 \Bigr) = 3,
\end{equation*}
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-3-b,
university = {UiB},
topic = {lhopital,limit,derivative}
]
La $f$ og $g$ være deriverbare funksjoner og $a$ et reelt tall slik at
\begin{equation*}
f(a) = g(a) = 0, \quad g'(a) = 0
\end{equation*}
Begrunn at
\begin{equation*}
\frac{f'(a)}{g'(a)} = \lim_{x \to a} \frac{f(x)}{g(x)}.
\end{equation*}
Du får \emph{bare} bruke definisjonen av den deriverte og grensesetningene, ikke f.eks.
l'Hôpital's regel.
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-3-c,
university = {UiB},
topic = {lhopital,limit,derivative}
]
Bruk l'Hôpitals regel til å regne ut
\begin{equation*}
\lim_{x \to 0} \frac{x}{\e^x - 1}
\end{equation*}.
\end{question}
\begin{exercise}[year=2019,semester=H,type={prob},
topic={limit,epsilon-delta,derivative,lhopital},exam=O,
ID=MAT111-2019-H-O-Problem-3,
university = {UiB},
title={Oppgave~3 (H19, UiB)}]
\begin{enumerate}
\includeQuestion{MAT111-2019-H-O-Problem-3-a}
\includeQuestion{MAT111-2019-H-O-Problem-3-b}
\includeQuestion{MAT111-2019-H-O-Problem-3-c}
\end{enumerate}
\end{exercise}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-4-a,
university = {UiB},
topic = {integral,partial-fractions}
]
\begin{equation*}
\int \frac{\dl x}{x^2 + 2x - 15}
\end{equation*}
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-4-b,
university = {UiB},
topic = {integral,IBP}
]
\begin{equation*}
\int_0^1 \tan^{-1}x \dl x
\end{equation*}
\end{question}
\begin{question}[
year=2019,semester=H,exam=O,type={subprob},
ID=MAT111-2019-H-O-Problem-4-c,
university = {UiB},
topic = {integral,substitution}
]
(Hint: bruk delvis integrasjon)
\begin{equation*}
\int_0^1 \frac{x^2}{\sqrt{1 - x^2}}\dl x
\end{equation*}
\end{question}
\begin{exercise}[
year=2019,semester=H,type={prob},exam=O,
topic={limit,epsilon-delta,derivative,lhopital},
ID=MAT111-2019-H-O-Problem-4,
university = {UiB},
title={Oppgave~4 (H19, UiB)}
]
Regn ut integralene ved grunnleggende integrasjonsteknikker (ikke ved å slå opp i permen
i læreboken)
\begin{enumerate}
\includeQuestion{MAT111-2019-H-O-Problem-4-a}
\includeQuestion{MAT111-2019-H-O-Problem-4-b}
\includeQuestion{MAT111-2019-H-O-Problem-4-c}
\end{enumerate}
\end{exercise}
答案1
辅助文件背后的原因在第 5 节中解释演习环境如何运作手册：因为这是允许练习和解决方案中的逐字材料的最简单方法。
因为从一开始就很明显，那些可能很多很多的文件弄乱了项目文件夹可能会分散注意力，甚至会让人烦恼，所以xsim总是有一个名为的选项path：
path = {<path>}使用此选项可以指定主项目文件夹内的子文件夹或路径。练习将被写入并包含在该路径中。该路径必须存在于您的系统中，您才能使用它！
在 v0.13（2019/10/06）中引入了选项 `no-files'。
no-files此选项可防止 xsim 将练习和解决方案写入外部文件。这将使您的工作文件夹保持“干净”，但也会阻止在练习和解决方案中使用逐字材料，并可能进一步减慢处理速度。
的开发xsim正在进行中。您这个并不简单的示例在我的计算机上第一次编译大约需要 30 秒，后续编译则需要 80 到 85 秒。使用我的下一版本草稿，同一文件第一次编译大约需要 2 秒，后续编译则需要 7 到 8 秒：仅需十分之一的时间。使用其他示例进行的其他测试也显示出了相同的性能提升。敬请期待 :)
答案2
dbshow提供了一种方法来实现这些功能。下面的示例展示了如何使用不同的条件（或组合）来过滤问题。过滤并显示了四组问题。
- 难题
- 多次答错的难题
- 计划于 2022-01-07 审核的问题
- 2022-01-02 之后记录的问题
\documentclass{article}
\usepackage{amsmath, physics}
\usepackage{geometry}
\usepackage{dbshow}
\usepackage{tikz}
\usepackage{tcolorbox}
\tcbuselibrary{skins}
\usetikzlibrary{shadings}
\usepackage[hidelinks]{hyperref}
\geometry{
margin=2cm
}
% #1 link node #2 target node #3 text to show
\NewDocumentCommand \linktarget { m m m } {%
\hyperlink{#1}{#3}%
\raisebox{1em}{\hypertarget{#2}{}}%
}
% question box
\tcbset{
base/.style={
empty,
frame engine=path,
colframe=yellow!10,
coltitle=red!70,
fonttitle=\bfseries\sffamily,
sharp corners,
left=4pt,
right=4pt,
drop fuzzy shadow,
drop fuzzy shadow,
borderline west={3pt}{-3pt}{red!80},
}
}
\newtcolorbox{mybox}[1]{%
base, title = {#1}
}
\dbNewReviewPoints{review}{1, 3, 7, 15, 30, 60}
\dbNewDatabase{ques-book}{
ques = tl,
answer = tl,
count = int|1,
labels = clist,
date = date,
}
\begin{dbFilters}{ques-book}
\dbNewConditional{hard}{labels}{hard}
\dbNewConditional{bad}{count}{\dbval > 1}
\dbNewConditional{review}{date}{review|2022-01-07}
\dbNewConditional*{after}{date}{\dbval > 2022-01-02}
\end{dbFilters}
% show all questions with hyperlink to answers
\dbNewStyle{ques}{ques-book}{
before-code = {\section{Questions}},
item-code = {
\begin{mybox}{%
\linktarget{answer_\dbIndex}{ques_\dbIndex}{%
Question \dbarabic%
\hspace{2em}\dbuse{date}%
\hspace{2em}\dbuse{labels}%
\hfill\dbuse{count}%
}%
}
\dbuse{ques}%
\end{mybox}
},
labels/sep = /,
}
% show all questions and answers with hyperlink to questions
\dbNewStyle{answer}{ques-book}{
before-code = {\section{Questions and Answers}},
item-code = {
\begin{mybox}{%
\linktarget{ques_\dbIndex}{answer_\dbIndex}{%
Question \dbarabic%
\hspace{2em}\dbuse{date}%
\hspace{2em}\dbuse{labels}%
\hfill\dbuse{count}%
}%
}
\dbuse{ques}\tcbsubtitle{Answer}\dbuse{answer}%
\end{mybox}
},
labels/sep = /,
}
% show all hard questions with hyperlink to answers
\dbNewStyle{hard}{ques-book}{
before-code = {\section{Hard Questions}},
item-code = {
\begin{mybox}{%
\hyperlink{answer_\dbIndex}{%
Question \dbarabic%
\hspace{2em}\dbuse{date}%
\hspace{2em}\dbuse{labels}%
\hfill\dbuse{count}%
}%
}
\dbuse{ques}%
\end{mybox}
},
raw-filter = hard,
labels/sep = /,
}
% show all hard questions that have answered incorrectly for more than one
% time with hyperlink to answers
\dbNewStyle[hard]{bad}{ques-book}{
before-code = {\section{Bad Questions}},
raw-filter = {bad && hard},
}
% show all questions that plan to be reviewed on 2022-01-07 with hyperlink to
% answers
\dbNewStyle[hard]{review}{ques-book}{
before-code = {\section{Questions to be Reviewed}},
raw-filter = {review},
}
% show all questions that is record after 2022-01-02 with hyperlink to answers
\dbNewStyle[hard]{after}{ques-book}{
before-code = {\section{Questions after 2022-01-02}},
raw-filter = {after},
}
\AtEndDocument{
\dbshow{review}{ques-book}
\dbshow{hard}{ques-book}
\dbshow{bad}{ques-book}
\dbshow{after}{ques-book}
\dbshow{ques}{ques-book}
\dbshow{answer}{ques-book}
}
\begin{document}
\begin{dbitem}{ques-book}[
date=2022-01-01,
labels={math, equation, easy},
count=2
]
\dbsave{ques}{%
Solve the linear equation: $x + 16 = 31$.
}
\dbsave{answer}{%
$x = 31 - 16 = 15$
}
\end{dbitem}
\begin{dbitem}{ques-book}[
date=2022-01-01,
labels={math, equation, hard},
count=3
]
\dbsave{ques}{%
Solve the linear equation: $2y = 16$.
}
\dbsave{answer}{%
$y = 16 / 2 = 8$
}
\end{dbitem}
\begin{dbitem}{ques-book}[
date=2022-01-04,
labels={math, integral, hard},
count=1
]
\dbsave{ques}{%
Find the indefinite integral: $\int 2x \dd x$.
}
\dbsave{answer}{%
$\int 2x \dd x = x^2$
}
\end{dbitem}
\end{document}