\documentclass[12pt,a4paper]{article}
\usepackage[cp1250]{inputenc} 
\pagestyle{empty}
\usepackage[left=19mm,right=19mm,top=20mm,bottom=22mm]  
{geometry}
\usepackage{makeidx, graphicx, amsmath, amssymb, amsthm, ae}
\usepackage[croatian, english]{babel}
\usepackage{esint, hvfloat}
%%\usepackage[T1]{fontenc}
\def\tr{{\mbox{$\triangle$}}}
\def\du{{\mbox{\rm d$u$}}}
\def\dx{{\mbox{\rm d$x$}}}
\def\df{{\mbox{\rm d$f$}}}
\def\dr{{\mbox{\rm d$r$}}}
\def\dt{{\mbox{\rm d$t$}}}
\def\dy{{\mbox{\rm d$y$}}}
\def\dz{{\mbox{\rm d$z$}}}
\def\dfi{{\mbox{\rm d$\varphi$}}}
\def\dro{{\mbox{\rm d$\rho$}}}
\def\ds{{\mbox{\rm d$s$}}}
\def\dS{{\mbox{\rm d$S$}}}
\def\tg{{\mbox{\rm tg\,}}}
\def\R{{\mbox{$\mathbb R$}}}
\def\arctg{{\mbox{\rm arc\,tg\,}}}
\def\arcsin{{\mbox{\rm arc\,sin\,}}}
\def\arccos{{\mbox{\rm arc\,cos\,}}}
\def\ctg{{\mbox{\rm ctg\,}}}
\newtheoremstyle{zaFiguru} %name
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  {\rm}   %Body font
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  {\thmname{#1} \thmnumber{\Large #2.}\thmnote{\,(#3)}}       %Thm head spec  
%%\swapnumbers
\theoremstyle{zaFiguru}
\newtheorem{zad}{}
\setlength{\textheight}{275mm}
\setlength{\textwidth}{175mm}



\begin{document}
\raggedright


\renewcommand{\thesection}{}
\section{Grupa A, 03.10.2013., ispit pisati hemijskom olovkom}
\setcounter{zad}{0}


\begin{zad}
Rješiti sistem linearnih jednačina

\vspace*{-6mm}
\begin{alignat*}{9}
x  & \,\,-\,\, & y &\,\,+\,\,&  z &= 3\\
x  & \,\,-\,\, & y &\,\,-\,\,&  z &= 4\\
x  & \,\,+\,\, & y &\,\,-\,\,&  z &= 5\\
x  & \,\,+\,\, & y &\,\,+\,\,&  z &= 6\,\,\,.
\end{alignat*}
\end{zad}


\begin{zad}
Za koje vrijednosti parametra $m$ vektori $\vec{a}=(2m,1+m,1)^\top$, $\vec{b}=(-m,1,m)^\top$, $\vec{c}=(m,1,m-2)^\top$ čine bazu trodimenzionalnog vektorskog prostora?
\end{zad}


\begin{zad}
Odrediti prvi izvod funkcije
$\displaystyle{
y=\ln\frac{x^2-1}{x+1}+\arctg x^2
}$.
\end{zad}


\begin{zad}
Odrediti integral 
$\displaystyle{
\int \frac{7x-17}{x^2-5x+6}\dx
}$.
\end{zad}


\begin{zad}
Primjenom određenog integrala odrediti površinu figure koju ograničava $x$-osa zajedno sa linijama $x+3y-3=0$, $x=-3$ i $x=6$.
\end{zad}

\begin{zad}
Rješiti diferencijalnu jednačinu $\displaystyle{xy'+y-e^x=0}$.
\end{zad}


















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\section{Grupa B, 03.10.2013., ispit pisati hemijskom olovkom}
\setcounter{zad}{0}


\begin{zad}
Rješiti sistem linearnih jednačina

\vspace*{-6mm}
\begin{alignat*}{9}
x  & \,\,-\,\, & y &\,\,+\,\,&  z &= 2\\
x  & \,\,-\,\, & y &\,\,-\,\,&  z &= 3\\
x  & \,\,+\,\, & y &\,\,-\,\,&  z &= 4\\
x  & \,\,+\,\, & y &\,\,+\,\,&  z &= 5\,\,\,.
\end{alignat*}
\end{zad}


\begin{zad}
Za koje vrijednosti parametra $m$ vektori $\vec{a}=(m,-m,1)^\top$, $\vec{b}=(-m,m,2m+2)^\top$, $\vec{c}=(m,m+1,1-m)^\top$ čine bazu trodimenzionalnog vektorskog prostora?
\end{zad}


\begin{zad}
Odrediti prvi izvod funkcije
$\displaystyle{
y=\ln\frac{x}{x-1}+\arcsin x^2
}$.
\end{zad}


\begin{zad}
Odrediti integral 
$\displaystyle{
\int \frac{9x-2}{x^2-x-6}\dx
}$.
\end{zad}


\begin{zad}
Primjenom određenog integrala odrediti površinu figure koju ograničava $x$-osa zajedno sa linijama $-x-2y+2=0$, $x=-4$ i $x=2$.
\end{zad}

\begin{zad}
Rješiti diferencijalnu jednačinu $\displaystyle{y'-y\,tg\,x=\frac{1}{cos\,x}}$.
\end{zad}







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\newpage
\section{Grupa C, 03.10.2013., ispit pisati hemijskom olovkom}
\setcounter{zad}{0}


\begin{zad}
Rješiti sistem linearnih jednačina

\vspace*{-6mm}
\begin{alignat*}{9}
x  & \,\,-\,\, & y &\,\,+\,\,&  z &= 1\\
x  & \,\,-\,\, & y &\,\,-\,\,&  z &= 2\\
x  & \,\,+\,\, & y &\,\,-\,\,&  z &= 3\\
x  & \,\,+\,\, & y &\,\,+\,\,&  z &= 4\,\,\,.
\end{alignat*}
\end{zad}


\begin{zad}
Za koje vrijednosti parametra $m$ vektori $\vec{a}=(2m,1-m,1)^\top$, $\vec{b}=(-2m,m,2m+2)^\top$, $\vec{c}=(m,1+m,1-m)^\top$ čine bazu trodimenzionalnog vektorskog prostora?
\end{zad}


\begin{zad}
Odrediti prvi izvod funkcije
$\displaystyle{
y=\ln\frac{x^2}{x+1}+\tg x^2
}$.
\end{zad}


\begin{zad}
Odrediti integral 
$\displaystyle{
\int \frac{11x+14}{x^2+3x-4}\dx
}$.
\end{zad}


\begin{zad}
Primjenom određenog integrala odrediti površinu figure koju ograničava $y$-osa zajedno sa linijama $x+y-1=0$, $y=3$ i $y=-2$.
\end{zad}



\begin{zad}
Rješiti diferencijalnu jednačinu $\displaystyle{xy'-3y=x^4e^x}$.
\end{zad}






\end{document}