From 8df39e5e7c578caabba07029f0cdd075f4234030 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Wed, 3 May 2023 16:16:35 +0200 Subject: [PATCH] Feat(2nd): ajoute DS7 --- 2nd/Evaluations/DS_2023-05-05/exercises.tex | 108 ++++++++++++++++++++ 2nd/Evaluations/DS_2023-05-05/sujet.pdf | Bin 0 -> 39897 bytes 2nd/Evaluations/DS_2023-05-05/sujet.tex | 27 +++++ 3 files changed, 135 insertions(+) create mode 100644 2nd/Evaluations/DS_2023-05-05/exercises.tex create mode 100644 2nd/Evaluations/DS_2023-05-05/sujet.pdf create mode 100644 2nd/Evaluations/DS_2023-05-05/sujet.tex diff --git a/2nd/Evaluations/DS_2023-05-05/exercises.tex b/2nd/Evaluations/DS_2023-05-05/exercises.tex new file mode 100644 index 0000000..be60cda --- /dev/null +++ b/2nd/Evaluations/DS_2023-05-05/exercises.tex @@ -0,0 +1,108 @@ +\begin{exercise}[subtitle={Tableau}, step={1}, origin={Création}, topics={Informations chiffrées}, tags={Taux d'évolution}, points={5}] + Compléter le tableau en détaillant les calculs dans les cases + \begin{center} + \begin{tabular}{|c|*{3}{c|}} + \hline + Valeur de départ & Valeur d'arrivée & Coefficient multiplicateur & Taux d'évolution \\ + \hline + 185 & & & Augmentation de 20\% \\[10ex] + \hline + & 22.95 & & Diminution de 15\% \\[10ex] + \hline + 1075 & & 1.002 & \\[10ex] + \hline + 240 & 180 & & \\[10ex] + \hline + & 38.01 & 0.21 & \\[10ex] + \hline + \end{tabular} + \end{center} +\end{exercise} + +\begin{exercise}[subtitle={Problèmes divers}, step={1}, origin={Le livre scolaire}, topics={Informations chiffrées}, tags={Taux d'évolution}, points={5}] + Les questions suivantes peuvent toutes être traitées individuellement. + \begin{enumerate} + \item La population d'une ville de 45 304 habitants augmente de 5\% puis diminue de 10\% l'année suivante. + + Calculer le nombre d'habitants après ces évolutions. + \item Le prix moyen d'une baguette de pain en euros par kg a augmenté de 0,87\% de 2011 à 2015 puis de 0,57\% de 2015 à 2017. + + Quel est le taux d'évolution du prix de la baguette entre 2011 et 2017? + \item Suite à son passage en machine à laver, un pull a rétréci de 7 \%. + + En utilisant des astuces pour récupérer sa taille d'origine, de quel pourcentage (à 0,1 \% près) doit-il alors s'agrandir ? + \item Après une augmentation de ses prix de 11,3 \% puis de 5,7 \%, un commerçant souhaite récompenser un client fidèle en lui accordant une remise telle qu'elle compense ses deux dernières augmentations. + + Déterminer le pourcentage de remise que doit effectuer le commerçant. + \item (*) En 2015, il y a eu 17 268 immatriculations de voitures électriques. Ce nombre a augmenté de 44,26\% en 2 ans dont 25,96\% la première année (source : Fiches-auto.fr). + + Déterminer le taux d'évolution du nombre d'immatriculations de voitures électriques de 2016 à 2017. Arrondir à 0,01\% près. + \end{enumerate} +\end{exercise} + + +\begin{exercise}[subtitle={Représentation}, step={1}, origin={Exercices}, topics={Intervalles}, tags={}, points={4}] + Compléter le tableau suivant + + \newcommand{\Raxe}{% + \begin{tikzpicture}[xscale=0.7] + \draw[gray](-5.5,0)grid(4.5,0); + \draw[-stealth]|-(4.5,0)node[above]{$x$}; + \foreach \x in {-5,...,4} \draw (\x,-.1) -- (\x,0); + \end{tikzpicture} + } + + \begin{tabular}{|p{5cm}|c|c|c|} + \hline + En français & Inégalité & sur la droite & Notation \\ + \hline + Réels inférieur ou égal à 2 & & \Raxe & \\[5ex] + \hline + & $2 \leq x \leq$ 5 & \Raxe & \\[5ex] + \hline + & $-5 < x \leq 0$ & \Raxe & \\[5ex] + \hline + & & \Raxe & $x\in \intFO{2}{+\infty}$\\[5ex] + \hline + \end{tabular} +\end{exercise} + + +\begin{exercise}[subtitle={Inéquations}, step={1}, origin={Exercices}, topics={Intervalles}, tags={}, points={4}] + Résoudre les inéquations suivantes. Vous donnerez la réponse sous forme d'intervalles. + \begin{multicols}{2} + \begin{enumerate} + \item $3x + 6 > 3$ + \item $-10x + 8 \geq -2$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Inéquations graphiques}, step={1}, origin={Exercices}, topics={Intervalles}, tags={}, points={4}] + Sur le graphique ci-contre, on a tracé les représentations de 2 fonctions $f$ et $g$. + + Résoudre les inéquations suivantes en utilisant le graphique, vous donnerez les solutions sous forme d'intervalles. + \begin{multicols}{3} + \begin{enumerate} + \item $f(x) > 2$ + \item $g(x) \leq 0$ + \item $g(x) > f(x)$ + \end{enumerate} + \end{multicols} + + + \begin{center} + \begin{tikzpicture}[xscale=1, yscale=1] + \tkzInit[xmin=-3,xmax=8,xstep=1, + ymin=-3,ymax=4,ystep=1] + \tkzGrid + \tkzAxeXY + \tkzFct[domain = -3:8,color=red,very thick]{0.25*(x-2)**2 - 2}; + \tkzText(-1.8, 3.2){$\mathcal{C}_f$}; + + \tkzFct[domain = -3:8,color=green,very thick]{-0.5*x+1}; + \tkzText(2.5, 3.2){$\mathcal{C}_g$}; + + \end{tikzpicture} + \end{center} +\end{exercise} diff --git a/2nd/Evaluations/DS_2023-05-05/sujet.pdf b/2nd/Evaluations/DS_2023-05-05/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f1106c5cb8cd5a2e730f406324132becba6ae645 GIT binary patch literal 39897 zcmce;1CVUZvNk-nZQHhO+qUi5W83!ZJ+^Jzw)WVb`S*M8|9$6;xF=5B_#)2fh_!lk zRaa(bXRciNWMvhpf`}L`BONOg>Eu%1;?U~s;4l;m0Rw@(krfmV4*|W3r-La0y@tGz zm8r1{0ll)Tk;{Lzh}k>Y643v3{;zK^63`0?*?SOZ{~5|az{v35hb{rVtf7mOU&iv~e+Y`txpM=wd2jYHV-vhp&vOowfz zAC-ggFAe^C6vFtI5&Y*g!pQXRljJ{ZTa5oc<6`vd6IJconyC@C?J+( zln4rQ1J*%iZ&6|`;$NQw8}8TkJABzWED$F-gJ+*{?3n`JWn({P0m;!j9ZpN1=@(|u zDOsf~1*DE@dOE*H*~HEJkZrA#>n=0gcJK->udnU>n?D=T!7dJYAc`Iy&eK|6xUuMG zvmisB7(O50A4WEMR;!h`1&GR0oDv$vu3fiXy~81^k|Dy!9Sf+D*&ys~QME8B_XP1f z{fY$jilJKWWT`~)wZ8+oeOY{u+3d!%UxMW15y(f7oUA=&}yercTLh z!<=!x*S|7ZSq9UDtojjd%zbO3yiFFwPS*PgM^B!RXI2FIjkHk}`h<=4E!BnWGG*N@ z(^~l#jLYOtMH?d(GS>Gzb}{5VGw!`p0DRtza`^&%VuB*jR<{V`mjEycFZr8r=ronJ 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