From 8b8c31255e229464c0b7f8c7b08595a134a9ea41 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 2 Oct 2025 14:38:44 +0200 Subject: [PATCH] feat(2nd): V1 pour DS2 --- 2nd/Evaluations/DS_2025-10-08/exercises.tex | 124 ++++++++++++++++++++ 2nd/Evaluations/DS_2025-10-08/sujet.pdf | Bin 0 -> 20389 bytes 2nd/Evaluations/DS_2025-10-08/sujet.tex | 27 +++++ 3 files changed, 151 insertions(+) create mode 100644 2nd/Evaluations/DS_2025-10-08/exercises.tex create mode 100644 2nd/Evaluations/DS_2025-10-08/sujet.pdf create mode 100644 2nd/Evaluations/DS_2025-10-08/sujet.tex diff --git a/2nd/Evaluations/DS_2025-10-08/exercises.tex b/2nd/Evaluations/DS_2025-10-08/exercises.tex new file mode 100644 index 0000000..f75c53f --- /dev/null +++ b/2nd/Evaluations/DS_2025-10-08/exercises.tex @@ -0,0 +1,124 @@ +\begin{exercise}[subtitle={Lecture de graphiques}, step={1}, origin={Le chapeau}, topics={Calculs}, tags={Fractions}, points=5] + On a représenté ci-contre la fonction $f$ pour $x$ allant -5 à 5. + + \noindent\begin{minipage}{0.5\linewidth} + \begin{enumerate} + \item + Décrire avec une phrase la/les quantité(s) cherchée(s) (représentée par des pointillés) puis la/les déterminer graphiquement (vous laisserez les traits de constructions) + \bigskip + \begin{multicols}{2} + \begin{enumerate} + \item $f(-3) = \dots$ + \item $f(\dots) = -2$ + \item $f(\dots) = 5$ + \item $f(\dots) \geq 3$ + \end{enumerate} + \end{multicols} + + \item Expliquer si la phrase suivante est vraie ou fausse. Vous illustrerez vos réponses avec un croquis. + \begin{center} + Une image peut avoir seulement 1 ou 2 antécédents. + \end{center} + \end{enumerate} + + \end{minipage} + \begin{minipage}{0.5\linewidth} + \begin{tikzpicture}[scale=0.8] + \tkzInit[xmin=-5,xmax=5,xstep=1, + ymin=-5,ymax=5,ystep=1] + \tkzGrid + \tkzAxeXY + \draw[very thick, color=red] plot [smooth,tension=0.5] coordinates{% + (-5, 1) + (-4, 3) + (-3, 4) + (-2, 3) + (-1, 0) + (0, -2) + (1, -4) + (2, -3) + (3, -4) + (4, -2) + (5, 0) + }; + \end{tikzpicture} + \end{minipage} +\end{exercise} + +\begin{solution} +\end{solution} + +\begin{exercise}[subtitle={Calculs avec les fractions}, step={1}, origin={Le chapeau}, topics={Calculs}, tags={Fractions}, points=4] + Calculer les quantités suivantes et donner le résultat sous forme de fraction irréductible (un calcul non justifié ne rapporte pas de points). + \begin{multicols}{2} + \begin{enumerate}[label={\Alph*}] + \item $= \dfrac{4}{6} - \dfrac{7}{4}$ + \item $= 3 - \dfrac{5}{8}$ + \item $= \dfrac{16}{21} \times \dfrac{6}{10}$ + \item $= \dfrac{1}{a} + \dfrac{4}{3a}$ + \end{enumerate} + \end{multicols} + +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\Alph*}] + \item $= \dfrac{4}{15} + \dfrac{21}{15} = \dfrac{25}{15} = \dfrac{5}{3}$ + \vfill + \item $= \dfrac{4}{6} - \dfrac{7}{4} = \dfrac{8}{12} -\dfrac{21}{12} = \dfrac{-13}{12}$ + \vfill + \item $= 3 - \dfrac{5}{8} = \dfrac{24}{8} - \dfrac{5}{8} = \dfrac{19}{8}$ + \vfill + \item $= \dfrac{1}{a} + \dfrac{4}{3a} = \dfrac{3}{3a} + \dfrac{4}{3a} = \dfrac{7}{3a}$ + \vfill + %\item $= \dfrac{9}{10} \times 5 = \dfrac{9 \times 5}{10} = \dfrac{9 \times 5}{2 \times 5} = \dfrac{9}{2}$ + % \vfill + \item $= \dfrac{16}{21} \times \dfrac{6}{10} = \dfrac{16 \times 6}{21 \times 10} = \dfrac{2 \times 8 \times 3\times 2}{3 \times 7 \times 2 \times 5} = \dfrac{16}{35}$ + \vfill + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Développer et réduire}, step={1}, origin={Le chapeau}, topics={Calculs}, tags={Fractions}, points=5] + \begin{enumerate} + \item On note $x$ un longueur. Proposer deux façons différentes pour calculer l'aire des rectangles ci-dessous. + \begin{multicols}{2} + \begin{enumerate} + \item + \begin{tikzpicture}[baseline=(current bounding box.north)] + \draw (0, 0) -- node [midway, below] {10} + (1, 0) coordinate (A) -- node [midway, below] {$x$} + (3, 0) -- node [midway, right] {3} + (3, 2) -- + (1, 2) coordinate (B)-- + (0, 2) -- + cycle; + \draw (A) -- (B); + \end{tikzpicture} + \item + \begin{tikzpicture}[baseline=(current bounding box.north)] + \draw (0, 0) -- node [midway, below] {$x$} + (1, 0) coordinate (A) -- node [midway, below] {$3$} + (3, 0) -- node [midway, right] {$5$} + (3, 1.5) coordinate (C) -- node [midway, right] {$x$} + (3, 2) -- + (1, 2) coordinate (B)-- + (0, 2) -- + (0, 1.5) coordinate (D)-- + cycle; + \draw (A) -- (B); + \draw (C) -- (D); + \end{tikzpicture} + \end{enumerate} + \end{multicols} + + \item Développer puis réduire les expressions suivantes + \begin{multicols}{3} + \begin{enumerate}[label={\Alph* = } ] + \item $5x(2x + 2)$ + \item $-3x\left(x + \dfrac{5}{3}\right)$ + \item $(4x - 3)(-6x + 1)$ + \end{enumerate} + \end{multicols} + \end{enumerate} +\end{exercise} + diff --git a/2nd/Evaluations/DS_2025-10-08/sujet.pdf b/2nd/Evaluations/DS_2025-10-08/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b220b5809642ebb2830e3d9975df80b0ad76bf46 GIT binary patch literal 20389 zcmce;1CS-nx-Q&3t!dk~ZF}0rv~AnAZQGc(rfu7{ZT~&{{O5jO#M!a$i5s!^TC1vZ zWoA|8Tlr?jt9*!Mg?>=e)38DikIi?_^)F5J4L~sA(cxL^nL%)I;n6C(+8E-|s>tY> z8R|RW(JDCVIs7B%hqaw09_^p=KWfn9(FzDyyWpvR-Aac?PxoJkCLXPnu7jQFpM3iN zD*4CxD_`Ew-rCVl-_Rb9`72BQ>rti_4u*DLR|{PSLm@+bYlE+LB@L~N9Zc}(neljd z@c#P)VeepPsA~z~vN8)hAxk!~^$h^*9qITUVE>QO zLH}n2|2+dj|Az_wb0b2}@b9DKKg(P6|32no_%q!9xiMk*!vg;v?qXp4&rz=feBauG!~5oSFc>x)*UPoRDYmPkPJ=ePlLrs*gA@fs(yd+PGDXSk`K{ya zdZ=YCgK|rwq?niYbHSmi5-`{jlQ@AqJNNOK@a$v%w)b%++dY)$OQ&ygg!OP^=F}FH4n{pL2Yd#(fjd}Q z*D}1BL{}m-Z}u+(fnB`W-uN6?a5$CO4j-Y34Q>cNo!tp$6iS6Mv%1ft<<|-aU38}J 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