From 19a4e4c45860965c288ab2e52e5b7bd68b1289a1 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 13 Sep 2022 17:36:00 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=20ajout=20le=20plan=20de=20travail=20sur?= =?UTF-8?q?=20le=20calcul=20litt=C3=A9ral?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/03_Calcul_litteral/1_exercises.tex | 162 +++++++++++++++++++++ 2nd/03_Calcul_litteral/bopytex_config.py | 12 ++ 2nd/03_Calcul_litteral/exercises.tex | 101 +++++++++++++ 2nd/03_Calcul_litteral/index.rst | 24 +++ 2nd/03_Calcul_litteral/plan_de_travail.pdf | Bin 0 -> 42999 bytes 2nd/03_Calcul_litteral/plan_de_travail.tex | 39 +++++ 2nd/03_Calcul_litteral/solutions.pdf | Bin 0 -> 29752 bytes 2nd/03_Calcul_litteral/solutions.tex | 29 ++++ 2nd/03_Calcul_litteral/tpl_exercises.tex | 106 ++++++++++++++ 9 files changed, 473 insertions(+) create mode 100644 2nd/03_Calcul_litteral/1_exercises.tex create mode 100644 2nd/03_Calcul_litteral/bopytex_config.py create mode 100644 2nd/03_Calcul_litteral/exercises.tex create mode 100644 2nd/03_Calcul_litteral/index.rst create mode 100644 2nd/03_Calcul_litteral/plan_de_travail.pdf create mode 100644 2nd/03_Calcul_litteral/plan_de_travail.tex create mode 100644 2nd/03_Calcul_litteral/solutions.pdf create mode 100644 2nd/03_Calcul_litteral/solutions.tex create mode 100644 2nd/03_Calcul_litteral/tpl_exercises.tex diff --git a/2nd/03_Calcul_litteral/1_exercises.tex b/2nd/03_Calcul_litteral/1_exercises.tex new file mode 100644 index 0000000..1769ca6 --- /dev/null +++ b/2nd/03_Calcul_litteral/1_exercises.tex @@ -0,0 +1,162 @@ +\begin{exercise}[subtitle={Réduire - technique}, step={1}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] + Réduire les expressions suivantes + + \begin{multicols}{2} + \begin{enumerate} + \item $A = 3x - 7 + 10x - 6$ + \item $B = - 7t - 3 - 10t - 4t$ + \item $C = 8t - 4 - 3t - 8t$ + \item $D = - 9x + 2 + 9x - 4$ + \item $E = 6t - 4 + 4t + 4 + 6t$ + \item $F = \dfrac{- 3}{3} + 4a - 7a - 2$ + \item $G = 8x^{2} + 10 + 9x^{2} - 3 - 6x^{2}$ + \item $H = - 8x + 10 - 4x^{2} - 5 + 4x^{2}$ + \item $I = 5x - 3 + 3x^{2} - 5x - 7x^{2}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{3} + \begin{enumerate} + \item + \begin{align*} + A & = 3x - 7 + 10x - 6 \\ & = 3x - 7 + 10x - 6 \\ & = 3x + 10x - 7 - 6 \\ & = (3 + 10) \times x - 13 \\ & = 13x - 13 + \end{align*} + \item + \begin{align*} + B & = - 7t - 3 - 10t - 4t \\ & = - 7t - 3 + (- 10 - 4) \times t \\ & = - 7t - 3 - 14t \\ & = - 7t - 14t - 3 \\ & = (- 7 - 14) \times t - 3 \\ & = - 21t - 3 + \end{align*} + \item + \begin{align*} + C & = 8t - 4 - 3t - 8t \\ & = 8t - 4 + (- 3 - 8) \times t \\ & = 8t - 4 - 11t \\ & = 8t - 11t - 4 \\ & = (8 - 11) \times t - 4 \\ & = - 3t - 4 + \end{align*} + \item + \begin{align*} + D & = - 9x + 2 + 9x - 4 \\ & = - 9x + 2 + 9x - 4 \\ & = - 9x + 9x + 2 - 4 \\ & = (- 9 + 9) \times x - 2 \\ & = 0x - 2 \\ & = - 2 + \end{align*} + \item + \begin{align*} + E & = 6t - 4 + 4t + 4 + 6t \\ & = 6t - 4 + (4 + 6) \times t + 4 \\ & = 6t - 4 + 4 + 10t \\ & = (6 + 10) \times t + 0 \\ & = 16t + \end{align*} + \item + \begin{align*} + F & = \dfrac{- 3}{3} + 4a - 7a - 2 \\ & = 4a + \dfrac{- 3}{3} - 7a - 2 \\ & = 4a - 7a + \dfrac{- 3}{3} - 2 \\ & = (4 - 7) \times a + \dfrac{- 3}{3} + \dfrac{- 2}{1} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 2 \times 3}{1 \times 3} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 6}{3} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 6}{3} \\ & = - 3a + \dfrac{- 3 - 6}{3} \\ & = - 3a + \dfrac{- 9}{3} + \end{align*} + \item + \begin{align*} + G & = 8x^{2} + 10 + 9x^{2} - 3 - 6x^{2} \\ & = 8x^{2} + 10 + (9 - 6) \times x^{2} - 3 \\ & = 8x^{2} + 10 - 3 + 3x^{2} \\ & = (8 + 3) \times x^{2} + 7 \\ & = 11x^{2} + 7 + \end{align*} + \item + \begin{align*} + H & = - 8x + 10 - 4x^{2} - 5 + 4x^{2} \\ & = - 4x^{2} - 8x + 10 - 5 + 4x^{2} \\ & = - 4x^{2} + 4x^{2} - 8x + 10 - 5 \\ & = (- 4 + 4) \times x^{2} - 8x + 5 \\ & = - 8x + 5 + \end{align*} + \item + \begin{align*} + I & = 5x - 3 + 3x^{2} - 5x - 7x^{2} \\ & = 3x^{2} + 5x - 3 - 5x - 7x^{2} \\ & = 3x^{2} - 7x^{2} + 5x - 5x - 3 \\ & = (3 - 7) \times x^{2} + (5 - 5) \times x - 3 \\ & = - 4x^{2} - 3 + \end{align*} + \end{enumerate} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Développer 1 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] + Réduire les expressions suivantes + + \begin{multicols}{2} + \begin{enumerate} + \item $A = 10(- 8x + 8)$ + \item $B = 7(- 4 + 8t)$ + \item $C = t(3 + 7t)$ + \item $D = - 9x(7x - 3)$ + \item $E = 5x(10x - 5)$ + \item $F = \dfrac{9}{4} \times x(2x + 8)$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{3} + \begin{enumerate} + \item + \begin{align*} + A & = 10(- 8x + 8) \\ & = 10 \times - 8x + 10 \times 8 \\ & = 10(- 8) \times x + 80 \\ & = - 80x + 80 + \end{align*} + \item + \begin{align*} + B & = 7(- 4 + 8t) \\ & = 7 \times 8t + 7(- 4) \\ & = 7 \times 8 \times t - 28 \\ & = 56t - 28 + \end{align*} + \item + \begin{align*} + C & = t(3 + 7t) \\ & = t \times 7t + t \times 3 \\ & = 7t^{2} + 3t + \end{align*} + \item + \begin{align*} + D & = - 9x(7x - 3) \\ & = - 9x \times 7x - 9x(- 3) \\ & = - 9 \times 7 \times x^{1 + 1} - 3(- 9) \times x \\ & = - 63x^{2} + 27x + \end{align*} + \item + \begin{align*} + E & = 5x(10x - 5) \\ & = 5x \times 10x + 5x(- 5) \\ & = 5 \times 10 \times x^{1 + 1} - 5 \times 5 \times x \\ & = 50x^{2} - 25x + \end{align*} + \item + \begin{align*} + F & = \dfrac{9}{4} \times x(2x + 8) \\ & = \dfrac{9}{4} \times x \times 2x + \dfrac{9}{4} \times x \times 8 \\ & = \dfrac{9}{4} \times 2 \times x^{1 + 1} + 8 \times \dfrac{9}{4} \times x \\ & = \dfrac{9 \times 2}{4} \times x^{2} + \dfrac{8 \times 9}{4} \times x \\ & = \dfrac{18}{4} \times x^{2} + \dfrac{72}{4} \times x + \end{align*} + \end{enumerate} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Développer 2 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] + Réduire les expressions suivantes + + \begin{multicols}{2} + \begin{enumerate} + \item $A = (- 8x - 3)(- 7x - 10)$ + \item $B = (- 2t + 10)(2t + 6)$ + \item $C = (- 9x - 5)(3x + 4)$ + \item $D = (6x - 2)(9x + 10)$ + \item $E = (- 8x - 4)^{2}$ + \item $F = (- 8x - 10)^{2}$ + \item $G = (- 10x + 6)^{2}$ + \item $H = (\dfrac{- 6}{4} \times x - 7)^{2}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{2} + \begin{enumerate} + \item + \begin{align*} + A & = (- 8x - 3)(- 7x - 10) \\ & = - 8x \times - 7x - 8x(- 10) - 3 \times - 7x - 3(- 10) \\ & = - 8(- 7) \times x^{1 + 1} - 10(- 8) \times x - 3(- 7) \times x + 30 \\ & = 80x + 21x + 56x^{2} + 30 \\ & = (80 + 21) \times x + 56x^{2} + 30 \\ & = 56x^{2} + 101x + 30 + \end{align*} + \item + \begin{align*} + B & = (- 2t + 10)(2t + 6) \\ & = - 2t \times 2t - 2t \times 6 + 10 \times 2t + 10 \times 6 \\ & = - 2 \times 2 \times t^{1 + 1} + 6(- 2) \times t + 10 \times 2 \times t + 60 \\ & = - 12t + 20t - 4t^{2} + 60 \\ & = (- 12 + 20) \times t - 4t^{2} + 60 \\ & = - 4t^{2} + 8t + 60 + \end{align*} + \item + \begin{align*} + C & = (- 9x - 5)(3x + 4) \\ & = - 9x \times 3x - 9x \times 4 - 5 \times 3x - 5 \times 4 \\ & = - 9 \times 3 \times x^{1 + 1} + 4(- 9) \times x - 5 \times 3 \times x - 20 \\ & = - 36x - 15x - 27x^{2} - 20 \\ & = (- 36 - 15) \times x - 27x^{2} - 20 \\ & = - 27x^{2} - 51x - 20 + \end{align*} + \item + \begin{align*} + D & = (6x - 2)(9x + 10) \\ & = 6x \times 9x + 6x \times 10 - 2 \times 9x - 2 \times 10 \\ & = 6 \times 9 \times x^{1 + 1} + 10 \times 6 \times x - 2 \times 9 \times x - 20 \\ & = 60x - 18x + 54x^{2} - 20 \\ & = (60 - 18) \times x + 54x^{2} - 20 \\ & = 54x^{2} + 42x - 20 + \end{align*} + \item + \begin{align*} + E & = (- 8x - 4)^{2} \\ & = (- 8x - 4)(- 8x - 4) \\ & = - 8x \times - 8x - 8x(- 4) - 4 \times - 8x - 4(- 4) \\ & = - 8(- 8) \times x^{1 + 1} - 4(- 8) \times x - 4(- 8) \times x + 16 \\ & = 32x + 32x + 64x^{2} + 16 \\ & = (32 + 32) \times x + 64x^{2} + 16 \\ & = 64x^{2} + 64x + 16 + \end{align*} + \item + \begin{align*} + F & = (- 8x - 10)^{2} \\ & = (- 8x - 10)(- 8x - 10) \\ & = - 8x \times - 8x - 8x(- 10) - 10 \times - 8x - 10(- 10) \\ & = - 8(- 8) \times x^{1 + 1} - 10(- 8) \times x - 10(- 8) \times x + 100 \\ & = 80x + 80x + 64x^{2} + 100 \\ & = (80 + 80) \times x + 64x^{2} + 100 \\ & = 64x^{2} + 160x + 100 + \end{align*} + \item + \begin{align*} + G & = (- 10x + 6)^{2} \\ & = (- 10x + 6)(- 10x + 6) \\ & = - 10x \times - 10x - 10x \times 6 + 6 \times - 10x + 6 \times 6 \\ & = - 10(- 10) \times x^{1 + 1} + 6(- 10) \times x + 6(- 10) \times x + 36 \\ & = - 60x - 60x + 100x^{2} + 36 \\ & = (- 60 - 60) \times x + 100x^{2} + 36 \\ & = 100x^{2} - 120x + 36 + \end{align*} + \item + \begin{align*} + H & = (\dfrac{- 6}{4} \times x - 7)^{2} \\ & = (\dfrac{- 6}{4} \times x - 7)(\dfrac{- 6}{4} \times x - 7) \\ & = \dfrac{- 6}{4} \times x \times \dfrac{- 6}{4} \times x + \dfrac{- 6}{4} \times x(- 7) - 7 \times \dfrac{- 6}{4} \times x - 7(- 7) \\ & = \dfrac{- 6}{4} \times \dfrac{- 6}{4} \times x^{1 + 1} - 7 \times \dfrac{- 6}{4} \times x - 7 \times \dfrac{- 6}{4} \times x + 49 \\ & = \dfrac{- 7(- 6)}{4} \times x + \dfrac{- 7(- 6)}{4} \times x + \dfrac{- 6(- 6)}{4 \times 4} \times x^{2} + 49 \\ & = \dfrac{42}{4} \times x + \dfrac{36}{16} \times x^{2} + \dfrac{42}{4} \times x + 49 \\ & = 49 + \dfrac{36}{16} \times x^{2} + \dfrac{42}{4} \times x + \dfrac{42}{4} \times x \\ & = 49 + \dfrac{36}{16} \times x^{2} + (\dfrac{42}{4} + \dfrac{42}{4}) \times x \\ & = 49 + \dfrac{36}{16} \times x^{2} + \dfrac{42 + 42}{4} \times x \\ & = \dfrac{36}{16} \times x^{2} + \dfrac{84}{4} \times x + 49 + \end{align*} + \end{enumerate} + \end{multicols} +\end{solution} diff --git a/2nd/03_Calcul_litteral/bopytex_config.py b/2nd/03_Calcul_litteral/bopytex_config.py new file mode 100644 index 0000000..599b6b5 --- /dev/null +++ b/2nd/03_Calcul_litteral/bopytex_config.py @@ -0,0 +1,12 @@ +# bopytex_config.py +from mapytex.calculus.random import expression as random_expression +from mapytex import render +import random + +random.seed(0) # Controlling the seed allows to make subject reproductible + +render.set_render("tex") + +direct_access = { + "random_expression": random_expression, +} diff --git a/2nd/03_Calcul_litteral/exercises.tex b/2nd/03_Calcul_litteral/exercises.tex new file mode 100644 index 0000000..d32b385 --- /dev/null +++ b/2nd/03_Calcul_litteral/exercises.tex @@ -0,0 +1,101 @@ +\begin{exercise}[subtitle={Programmes de calculs}, step={1}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\searchMode}] + Voici 2 programmes de calculs. + + \medskip + \setlength\fboxsep{10pt} + \Ovalbox{% + \begin{minipage}{0.3\linewidth} + \textbf{Programme A:} \\ + Choisir un nombre \\ + Multiplier par 4 \\ + Soustraire 1 \\ + Ajouter le nombre de départ \\ + Soustraire 2 + \end{minipage} + } + \hfill + \Ovalbox{% + \begin{minipage}{0.3\linewidth} + \textbf{Programme B:} \\ + Choisir un nombre \\ + Multiplier par 5 \\ + Enlever 3 + \end{minipage} + } + + \medskip + + Bob pense "\textit{Ces 2 programmes donnent toujours le même résultat.}". + + Qu'en pensez vous? +\end{exercise} + +\begin{exercise}[subtitle={Vrai ou faux}, step={1}, origin={MEpC}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\searchMode}] + Pour chacune des affirmations, expliquer si elles sont vraies ou fausses. + \begin{enumerate} + \item Pour tous les nombres $x$, on a $4+3x = 7x$. + \item Pour tous les nombres $y$, on a $y^2 = y$. + \item Pour tous les nombres $z$, on a $2z + z - 8 = 3z - 7 - 1$. + \item Pour tous les nombres $t$, on a $\dfrac{4t-8}{8} = 4t - 1$. + \item Pour lous les nombres $t$, on a $3t + 3 + 5 = t + 2t + 4$. + \end{enumerate} +\end{exercise} + + +\begin{exercise}[subtitle={Aire de rectangles}, step={2}, origin={Classique}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\searchMode}] + Trouver deux façons différentes de calculer l'aire de ces rectangles + \begin{multicols}{2} + \begin{enumerate} + \item + \begin{tikzpicture} + \draw (0, 0) -- node [midway, below] {1} + (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} + \draw (0, 0) -- node [midway, below] {$4$} + (3, 0) -- node [midway, right] {$2$} + (3, 1.5) coordinate (A) -- node [midway, right] {$x$} + (3, 2) -- + (0, 2) -- + (0, 1.5) coordinate (B)-- + cycle; + \draw (A) -- (B); + \end{tikzpicture} + \item + \begin{tikzpicture} + \draw (0, 0) -- node [midway, below] {$x$} + (1, 0) coordinate (A) -- node [midway, below] {$1$} + (3, 0) -- node [midway, right] {$3$} + (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} + \item + \begin{tikzpicture} + \draw (0, 0) -- node [midway, below] {$6x$} + (1, 0) coordinate (A) -- node [midway, below] {$3$} + (3, 0) -- node [midway, right] {$2$} + (3, 1.5) coordinate (C) -- node [midway, right] {$2x$} + (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} +\end{exercise} diff --git a/2nd/03_Calcul_litteral/index.rst b/2nd/03_Calcul_litteral/index.rst new file mode 100644 index 0000000..7b7f0f2 --- /dev/null +++ b/2nd/03_Calcul_litteral/index.rst @@ -0,0 +1,24 @@ +Calcul littéral +############### + +:date: 2022-09-13 +:modified: 2022-09-13 +:authors: Benjamin Bertrand +:tags: Calcul littéral +:category: 2nd +:summary: Retour sur les bases du calcul littéral + +Plan de travail +=============== + +Le plan de travail + +.. image:: ./plan_de_travail.pdf + :height: 200px + :alt: Plan de travail + +La solution des exercices techniques + +.. image:: ./solutions.pdf + :height: 200px + :alt: Les solutions diff --git a/2nd/03_Calcul_litteral/plan_de_travail.pdf b/2nd/03_Calcul_litteral/plan_de_travail.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b2857028b560ec3b7358952f5d9cbf874bb0066d GIT binary patch literal 42999 zcmce-1F$X4vZy<4+t!-4?YX9H+cwvFZ2~%JeJ2O=zxo;e zbL2nTKm7{Ej<(JYhQ^KrEPuKb{!C?Vvt3{K&DJOAAn&XRs-x4 znkrinS%EpcGoZ1enr+Omxp>RfP3?E2z*=MTA5*a(mh2yC8#`Z4eLNTax2wP@{IqWR zfIP+|gwNX7Hrua{`mXP-?{+!)LQg+R2(E6=W$LH)NYWft>L2T~=yQc#a(m8k#(RM!dJb zFDziu*Of|wh#z5*nr2#Vb}x>???gZp(!3hpatw?3&?8<+XH&u^Dl62f7Ssss5OjMV 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z>JPkwA`^L$%r0GQ2N?ps^&A1WpC5U5BrN{()pCQGLt$RXKN1d*mroFg!^9-3E{F5K E07ToKwg3PC literal 0 HcmV?d00001 diff --git a/2nd/03_Calcul_litteral/plan_de_travail.tex b/2nd/03_Calcul_litteral/plan_de_travail.tex new file mode 100644 index 0000000..81420fa --- /dev/null +++ b/2nd/03_Calcul_litteral/plan_de_travail.tex @@ -0,0 +1,39 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Calcul littéral - Plan de travail} +\tribe{2nd} +\date{septembre 2022} + +\pagestyle{empty} + +\DeclareExerciseCollection{banque} +\xsimsetup{ +} + +\begin{document} +\maketitle + +% Résumé + +\bigskip + + +\section{Réduction} + +\listsectionexercises + +\section{Développement} + +\listsectionexercises + + +\pagebreak + +\input{exercises.tex} +\input{1_exercises.tex} +\printcollection{banque} + + +\end{document} diff --git a/2nd/03_Calcul_litteral/solutions.pdf b/2nd/03_Calcul_litteral/solutions.pdf new file mode 100644 index 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+\input{exercises.tex} +\input{1_exercises.tex} +%\printcollection{banque} +%\printsolutions{exercises} + +\end{document} diff --git a/2nd/03_Calcul_litteral/tpl_exercises.tex b/2nd/03_Calcul_litteral/tpl_exercises.tex new file mode 100644 index 0000000..cd439da --- /dev/null +++ b/2nd/03_Calcul_litteral/tpl_exercises.tex @@ -0,0 +1,106 @@ +\begin{exercise}[subtitle={Réduire - technique}, step={1}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] + Réduire les expressions suivantes + \Block{ + set reduction = { + "A": random_expression("{a}x + {b} + {c}x + {d}", [], global_config={"rejected":[1, 0, -1]}), + "B": random_expression("{a}t + {b} + {c}t + {d}t", [], global_config={"rejected":[1, 0, -1]}), + "C": random_expression("{a}t + {b} + {c}t + {d}t", [], global_config={"rejected":[1, 0, -1]}), + "D": random_expression("{a}x + {b} + {c}x + {d}", ["a+c==0"], global_config={"rejected":[1, 0, -1]}), + "E": random_expression("{a}t + {b} + {c}t + {d} + {e}t", ["b+d==0"], global_config={"rejected":[1, 0, -1]}), + "F": random_expression("{a}/{k} + {b}a + {c}a + {d}", [], global_config={"rejected":[1, 0, -1]}), + "G": random_expression("{a}x^2 + {b} + {c}x^2 + {d} + {e}x^2", [], global_config={"rejected":[1, 0, -1]}), + "H": random_expression("{a}x + {b} + {c}x^2 + {d} + {e}x^2", [], global_config={"rejected":[1, 0, -1]}), + "I": random_expression("{a}x + {b} + {c}x^2 + {d}x + {e}x^2", ["a+d==0"], global_config={"rejected":[1, 0, -1]}), + } + } + \begin{multicols}{2} + \begin{enumerate} + %- for (l, e) in reduction.items() + \item $\Var{l} = \Var{e}$ + %- endfor + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{3} + \begin{enumerate} + %- for (l, e) in reduction.items() + \item + \begin{align*} + \Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')} + \end{align*} + %- endfor + \end{enumerate} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Développer 1 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] + Réduire les expressions suivantes + \Block{ + set reduction = { + "A": random_expression("{a}({c}x + {d})", global_config={"rejected":[1, 0, -1]}), + "B": random_expression("{a}({b} + {c}t)", global_config={"rejected":[1, 0, -1]}), + "C": random_expression("t({b} + {c}t)", global_config={"rejected":[1, 0, -1]}), + "D": random_expression("{a}x({b}x + {c})", global_config={"rejected":[1, 0, -1]}), + "E": random_expression("{a}x({b}x + {c})", global_config={"rejected":[1, 0, -1]}), + "F": random_expression("{a}/{d}x({b}x + {c})", global_config={"min_max":(1, 10)}), + } + } + \begin{multicols}{2} + \begin{enumerate} + %- for (l, e) in reduction.items() + \item $\Var{l} = \Var{e}$ + %- endfor + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{3} + \begin{enumerate} + %- for (l, e) in reduction.items() + \item + \begin{align*} + \Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')} + \end{align*} + %- endfor + \end{enumerate} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Développer 2 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] + Réduire les expressions suivantes + \Block{ + set reduction = { + "A": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}), + "B": random_expression("({a}t + {b})({c}t + {d})", global_config={"rejected":[1, 0, -1]}), + "C": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}), + "D": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}), + "E": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}), + "F": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}), + "G": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}), + "H": random_expression("({a}/{c}x + {b})^2", global_config={"rejected":[1, 0, -1]}), + } + } + \begin{multicols}{2} + \begin{enumerate} + %- for (l, e) in reduction.items() + \item $\Var{l} = \Var{e}$ + %- endfor + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{2} + \begin{enumerate} + %- for (l, e) in reduction.items() + \item + \begin{align*} + \Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')} + \end{align*} + %- endfor + \end{enumerate} + \end{multicols} +\end{solution}