Please wait
Exercises sheet for high school students in Skoura-Boulmane , Morocco
\documentclass[10pt,a4paper,notitlepage]{article}
%Mise en page
\usepackage[left=2cm, right=2cm, lines=45, top=0.8in, bottom=0.7in]{geometry}
\usepackage{fancyhdr}
\usepackage{fancybox}
\usepackage{pdfpages}
\renewcommand{\headrulewidth}{1.5pt}
\renewcommand{\footrulewidth}{1.5pt}
\pagestyle{fancy}
\newcommand\Loadedframemethod{TikZ}
\usepackage[framemethod=\Loadedframemethod]{mdframed}
\usepackage{tikz}
\usetikzlibrary{calc,through,backgrounds}
\usetikzlibrary{matrix,positioning}
%Desssins geometriques
\usetikzlibrary{arrows}
\usetikzlibrary{shapes.geometric}
\usetikzlibrary{datavisualization}
\usetikzlibrary{automata} % LATEX and plain TEX
\usetikzlibrary{shapes.multipart}
\usetikzlibrary{decorations.pathmorphing}
\usepackage{pgfplots}
\usepackage{physics}
\usepackage{titletoc}
\usepackage{mathpazo}
\usepackage{algpseudocode}
\usepackage{algorithmicx}
\usepackage{bohr}
\usepackage{xlop}
\usepackage{bbding}
%\usepackage{minibox}
%Ecriture arabe
\usepackage{mathdesign}
\usepackage{bbding}
\usepackage{romande}
\lhead{
\textbf{LYCEE COLLEGIAL CHARIF IDRISSI}
}
\rhead{\textbf{INFORMATIQUE}
}
\chead{\textbf{
TCS
}}
\lfoot{}
\cfoot{\textbf{$\mathsf{2015-2016}$}}
%\rfoot{\textit{Pr. $\mathcal{A}$.Kaal}}
%=====================Algo setup
\algblock{If}{EndIf}
\algcblock[If]{If}{ElsIf}{EndIf}
\algcblock{If}{Else}{EndIf}
\algrenewtext{If}{\textbf{si}}
\algrenewtext{Else}{\textbf{sinon}}
\algrenewtext{EndIf}{\textbf{finsi}}
\algrenewtext{Then}{\textbf{alors}}
\algrenewtext{While}{\textbf{tant que}}
\algrenewtext{EndWhile}{\textbf{fin tant que}}
\algrenewtext{Repeat}{\textbf{r\'ep\'eter}}
\algrenewtext{Until}{\textbf{jusqu'\`a}}
\algcblockdefx[Strange]{If}{Eeee}{Oooo}
[1]{\textbf{Eeee} "#1"}
{\textbf{Wuuuups\dots}}
\algrenewcommand\algorithmicwhile{\textbf{TantQue}}
\algrenewcommand\algorithmicdo{\textbf{Faire}}
\algrenewcommand\algorithmicend{\textbf{Fin}}
\algrenewcommand\algorithmicrequire{\textbf{Variables}}
\algrenewcommand\algorithmicensure{\textbf{Constante}}% replace ensure by constante
\algblock[block]{Begin}{End}
\newcommand\algo[1]{\textbf{algorithme} #1;}
\newcommand\vars{\textbf{variables } }
\newcommand\consts{\textbf{constantes}}
\algrenewtext{Begin}{\textbf{debut}}
\algrenewtext{End}{\textbf{fin}}
%================================
%================================
\setlength{\parskip}{1cm}
\setlength{\parindent}{1cm}
\tikzstyle{titregris} =
[draw=gray,fill=white, shading = exersicetitle, %
text=gray, rectangle, rounded corners, right,minimum height=.3cm]
\pgfdeclarehorizontalshading{exersicebackground}{100bp}
{color(0bp)=(green!40); color(100bp)=(black!5)}
\pgfdeclarehorizontalshading{exersicetitle}{100bp}
{color(0bp)=(red!40);color(100bp)=(black!5)}
\newcounter{exercise}
\renewcommand*\theexercise{exercice \textbf{Exercice}~n\arabic{exercise}}
\makeatletter
\def\mdf@@exercisepoints{}%new mdframed key:
\define@key{mdf}{exercisepoints}{%
\def\mdf@@exercisepoints{#1}
}
\mdfdefinestyle{exercisestyle}{%
outerlinewidth=1em,outerlinecolor=white,%
leftmargin=-1em,rightmargin=-1em,%
middlelinewidth=0.5pt,roundcorner=3pt,linecolor=black,
apptotikzsetting={\tikzset{mdfbackground/.append style ={%
shading = exersicebackground}}},
innertopmargin=0.1\baselineskip,
skipabove={\dimexpr0.1\baselineskip+0\topskip\relax},
skipbelow={-0.1em},
needspace=0.5\baselineskip,
frametitlefont=\sffamily\bfseries,
settings={\global\stepcounter{exercise}},
singleextra={%
\node[titregris,xshift=0.5cm] at (P-|O) %
{~\mdf@frametitlefont{\theexercise}~};
\ifdefempty{\mdf@@exercisepoints}%
{}%
{\node[titregris,left,xshift=-1cm] at (P)%
{~\mdf@frametitlefont{\mdf@@exercisepoints points}~};}%
},
firstextra={%
\node[titregris,xshift=1cm] at (P-|O) %
{~\mdf@frametitlefont{\theexercise}~};
\ifdefempty{\mdf@@exercisepoints}%
{}%
{\node[titregris,left,xshift=-1cm] at (P)%
{~\mdf@frametitlefont{\mdf@@exercisepoints points}~};}%
},
}
\makeatother
%%%%%%%%%
%%%%%%%%%%%%%%%
\mdfdefinestyle{theoremstyle}{%
outerlinewidth=0.01em,linecolor=black,middlelinewidth=0.5pt,%
frametitlerule=true,roundcorner=2pt,%
apptotikzsetting={\tikzset{mfframetitlebackground/.append style={%
shade,left color=white, right color=blue!20}}},
frametitlerulecolor=black,innertopmargin=1\baselineskip,%green!60,
innerbottommargin=0.5\baselineskip,
frametitlerulewidth=0.1pt,
innertopmargin=0.7\topskip,skipabove={\dimexpr0.2\baselineskip+0.1\topskip\relax},
frametitleaboveskip=1pt,
frametitlebelowskip=1pt
}
\setlength{\parskip}{0mm}
\setlength{\parindent}{10mm}
\mdtheorem[style=theoremstyle]{definition}{\textbf{Exercice}}
%================Liste definition--numList-and alphList=============
\newcounter{alphListCounter}
\newenvironment
{alphList}
{\begin{list}
{\alph{alphListCounter})}
{\usecounter{alphListCounter}
\setlength{\rightmargin}{0cm}
\setlength{\leftmargin}{0.5cm}
\setlength{\itemsep}{0.2cm}
\setlength{\partopsep}{0cm}
\setlength{\parsep}{0cm}}
}
{\end{list}}
\newcounter{numListCounter}
\newenvironment
{numList}
{\begin{list}
{\arabic{numListCounter})}
{\usecounter{numListCounter}
\setlength{\rightmargin}{0cm}
\setlength{\leftmargin}{0.5cm}
\setlength{\itemsep}{0cm}
\setlength{\partopsep}{0cm}
\setlength{\parsep}{0cm}}
}
{\end{list}}
%===========================================================
\begin{document}
\begin{center}
\large{\textbf{Serie N\textdegree 6: \textsc{Structures it\'eratives}}}
\end{center}
\begin{definition}[]
\hspace{2ex}Ecrire, en utilisant la boucle \textbf{Pour}, les algorithmes qui effecturent les calculs suivants
\begin{enumerate}
\item
\begin{tabular}{p{3cm}p{3cm}p{3cm}}
a) S = $\sum_{i=1}^{20} i$ & b) S = $\sum_{i=1}^{20} i^2$ & c) S = $ \sum_{i=1}^{20} i^i$
\end{tabular}
\item
\begin{tabular}{p{3cm}p{3cm}p{3cm}}
a) P = $\prod_{k=1}^{20} k$ & b) P = $ \prod_{k=1}^{20} k^2$ &c) P = $ \prod_{k=1}^{20} k^k $\\
\end{tabular}
\end{enumerate}
\end{definition}
\begin{definition}
\hspace{2ex} Ecrire les boucles appropri\'es pour cacluler chacune des expressions ci-desosus\\
\begin{enumerate}
\item
\begin{tabular}{p{7cm}p{7cm}}
a) $s= 1^2-2^2+\dots +19^2-20^2$ & b)$ s = 1^1 - 2^2 + \dots +19^{19} -20^{20}$ \\
\end{tabular}
\item
\begin{tabular}{p{7cm}p{7cm}}
a) $s= 1^2\times (-2)^2 \times \dots \times 19^2 \times (-20)^{2}$&b)$ p = 1^1 \times 2^2 + \dots +19^{19} \times 20^{20}$ \\
\end{tabular}
\item
\begin{tabular}{p{7cm}p{7cm}}
a) $s= \sqrt{1}+\sqrt{2}+\dots +\sqrt{19}+\sqrt{20}$ &b)$ s = \dfrac{1^1}{\sqrt{2}} + \dfrac{2^2}{\sqrt{3}} + \dots +\dfrac{19^{19}}{\sqrt{20}}$ \\
\end{tabular}
\end{enumerate}
\end{definition}
\begin{definition}[]
\begin{minipage}{0.7\textwidth}
\hspace{2ex}Ex\'ecuter l'algorithme ci-contre avec les entr\'ee de la ligne 1 du tableau ci-dessous et compl\'eter la ligne 2.\\[2ex]
\begin{tabular}{c|c|c|c|c|c|c}
Ex\'ecution \HandRight & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$N$ & 7 & 11 & 13 & 25 & 37 & 38 \\
\hline
$p$ & ... & ... & ... & ... & ... & ... \\
\hline
\end{tabular}
\vspace{3mm}\\
D'apr\`es les valeurs de $N$ et de $p$, que repr\'esente la valeur de $p$.
\end{minipage}
\begin{minipage}{0.3\textwidth}
\begin{scriptsize}
\begin{algorithmic}[1]
\State $p \leftarrow vrai$;
\State $i \leftarrow 2$;
\State Lire (N)
\Repeat
\State $r \leftarrow Reste(N, i)$;
\If{(r==0)} \textbf{alors}
\State $p \leftarrow faux$
\EndIf
\State $i\leftarrow i+1$
\Until{(($i>=N-1$) OU ($p==faux$))}
\end{algorithmic}
\end{scriptsize}
\end{minipage}
\end{definition}
\begin{definition}[]
\begin{minipage}{0.7\textwidth}
Ex\'ecuter l'algorithme ci-contre avec les entr\'ees $a$ et $b$ des lignes 1 et 2 du tableau ci-dessous et compl\'ter la ligne 3.\\[3ex]
\begin{tabular}{c|c|c|c|c|c|c}
Ex\'ecution \HandRight & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$a$ & 2 & 3 & 13 & 25 & 37 & 16 \\
\hline
$b$ & 4 & 5 & 6 & 12 & 12 & 38 \\
\hline
$q$ & ... & ... & ... & ... & ... & ... \\
\hline
\end{tabular}
\vspace{3mm}
D'apr\`es les valeurs de $a$, $b$ et de $q$, qu'indique de la valeur de $q$ ?
\begin{alphList}
\item le maximum de $a$ et $b$,
\item le PGCD de $a$ et $b$,
\item le PPCM de $a$ et $b$.
\end{alphList}
\end{minipage}
\begin{minipage}{0.3\textwidth}
\begin{scriptsize}
\begin{algorithmic}[1]
\State Lire(a,b);
\State $i \leftarrow 2$;
\If{(a<b)}\textbf{}alors
\State $temp\leftarrow a$;
\State $a\leftarrow b$;
\State $b\leftarrow temp$;
\EndIf
\State $r \leftarrow Reste(a,b)$;
\While{($r<>0$)} \textbf{faire}
\State $a \leftarrow b$;
\State $b \leftarrow r$;
\State $r \leftarrow Reste(a,b)$;
\EndWhile
\State $q \leftarrow b$;
\end{algorithmic}
\end{scriptsize}
\end{minipage}
\end{definition}
\begin{definition}[]
\begin{numList}
\item Ecrire, en utilisant une structure de contr\^ole de votre choix, un algorithme qui calcule le produit suivant
$$f = \prod_{k=1}^{k=n}k = k!= 1 \times 2 \times \dots \times (n-1) \times n $$
\item Ecrire, en utilisant une structure de contr\^ole de votre choix, un algorithme qui calcule la somme
$$s = \sum_{q=1}^{q=M}q! = 1! + 2! + \dots + M!$$
\end{numList}
\end{definition}
%% Macros for ``successive divisions''
%%
%\def\Division#1#2#3{ % Dividend, divisor, remainder
% \matrix (D) [matrix of nodes,
% below=0pt of D-1-2.south east,
% row sep=1pt, column sep=1pt,
% every node/.append style={minimum width=12mm}] {
% #1 \pgfmatrixnextcell #2 \\
% |[marcar] (R#1)| #3 \\
% };
% \draw[shorten >=2pt, shorten <=2pt]
% (D-1-2.north west) |- (D-1-2.south east);
%}
%\def\FinDivision#1{
%\node[marcar, below=2pt of D-1-2.south] (C)(C) {#1};
%}
%\tikzset{marcar/.style={circle,draw,inner sep=2pt,minimum width=0pt,
%fill=yellow!10}}
%
%
%\begin{tikzpicture}
% \coordinate (D-1-2) at (0,0) {}; % We must start with this command.
% \Division{25}{2}{1} % First dividend, divisor, remainder
% \Division{12}{2}{0} % Dividend (previous quotient), divisor, remainder
% \Division{6}{2}{0}
% \Division{3}{2}{1}
% \FinDivision{1} % Last remainder.
%
%% We can draw an arrow jumping from one remainder
%% to the next one. Every reminder is a node called
%% Rdividend. Last remainder is node C.
% \draw[shorten <=1mm, ->, dashed] (C) to[out=-150,in=-65] (R3);
% \draw[shorten <=1mm, ->, dashed] (R3) to[out=-150,in=-65] (R6);
% \draw[shorten <=1mm, ->, dashed] (R6) to[out=-150,in=-65] (R12);
% \draw[shorten <=1mm, ->, dashed] (R12) to[out=-150,in=-65] (R25);
%
%% Some more information:
% \node (MSB) at ([yshift=-1.3cm]R6.south) {Most significant bit (MSB)};
% \node (LSB) at ([yshift=-2mm]MSB.south) {Less significant bit (LSB)};
%\draw[ ->] (MSB.east) to[out=30,in=-55] (C);
%\draw[ ->] (LSB.west) to[out=150,in=-95] (R25);
%\end{tikzpicture}
%\begin{center}\SnowflakeChevronBold \SnowflakeChevronBold \SnowflakeChevronBold \end{center}
%%----------------------------------------------------------------------------------------------------------------------------------------
%
%%\includepdf[doublepages=true]{serie55}
\end{document}
Our gallery is the easiest way to put your LaTeX templates, examples and articles online. Just create a free project and use the publish menu. It only takes a couple of clicks!
The LaTeX templates, examples and articles in the Overleaf gallery all come from our amazing community.
New content is added all the time. Follow us on twitter for the highlights!