From 5d104fb35cdc1dca2becf19c73ec6b6e1b47b4fa Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 19 Oct 2021 15:51:50 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=20E6=20technique=20d=C3=A9veloppement=20e?= =?UTF-8?q?t=20r=C3=A9duction?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../6E_bilan_dev_red.pdf | Bin 0 -> 51667 bytes .../6E_bilan_dev_red.tex | 144 ++++++++++++++++++ .../tpl_6E_bilan_dev_red.tex | 130 ++++++++++++++++ 3 files changed, 274 insertions(+) create mode 100644 2nd/01_Fraction_Developpement_Litteral/6E_bilan_dev_red.pdf create mode 100644 2nd/01_Fraction_Developpement_Litteral/6E_bilan_dev_red.tex create mode 100644 2nd/01_Fraction_Developpement_Litteral/tpl_6E_bilan_dev_red.tex diff --git a/2nd/01_Fraction_Developpement_Litteral/6E_bilan_dev_red.pdf b/2nd/01_Fraction_Developpement_Litteral/6E_bilan_dev_red.pdf new file mode 100644 index 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--git a/2nd/01_Fraction_Developpement_Litteral/6E_bilan_dev_red.tex b/2nd/01_Fraction_Developpement_Litteral/6E_bilan_dev_red.tex new file mode 100644 index 0000000..5dcb6ef --- /dev/null +++ b/2nd/01_Fraction_Developpement_Litteral/6E_bilan_dev_red.tex @@ -0,0 +1,144 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +\usepackage{amsmath} + +\author{Benjamin Bertrand} +\title{Information chiffrée 1 - Exercices} +\date{Octobre 2021} + +\pagestyle{empty} + +\xsimsetup{ + solution/print = false +} + +\begin{document} + +\begin{exercise}[subtitle={Réductions}] + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $- 3x - 10 + 4x + 7$ + \item $3x + 2 - 9x - 7$ + + \item $- 9x^{2} - 7 - 7x^{2} + 6 + 6x - 7$ + \item $- 7x - 1 - 7x + 8 + 4x + 3x$ + + \item $3x + 15 + 9x + 18x + 17$ + \item $- 4x - 5 + 4x + 1$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{2} + \begin{flalign*} + A =& - 3x - 10 + 4x + 7\\ =& - 3x - 10 + 4x + 7\\ =& - 3x + 4x - 10 + 7\\ =& (- 3 + 4) \times x - 3\\ =& x - 3 + \end{flalign*} + \begin{flalign*} + B =& 3x + 2 - 9x - 7\\ =& 3x + 2 - 9x - 7\\ =& 3x - 9x + 2 - 7\\ =& (3 - 9) \times x - 5\\ =& - 6x - 5 + \end{flalign*} + \begin{flalign*} + C =& - 9x^{2} - 7 - 7x^{2} + 6 + 6x - 7\\ =& - 9x^{2} - 7x^{2} - 7 - 1 + 6x\\ =& (- 9 - 7) \times x^{2} + 6x - 7 - 1\\ =& - 16x^{2} + 6x - 8 + \end{flalign*} + \begin{flalign*} + D =& - 7x - 1 - 7x + 8 + 4x + 3x\\ =& - 7x - 1 + 8 - 7x + (4 + 3) \times x\\ =& (- 7 - 7) \times x + 7 + 7x\\ =& - 14x + 7 + 7x\\ =& - 14x + 7x + 7\\ =& (- 14 + 7) \times x + 7\\ =& - 7x + 7 + \end{flalign*} + \begin{flalign*} + E =& 3x + 15 + 9x + 18x + 17\\ =& 3x + 15 + (9 + 18) \times x + 17\\ =& 3x + 15 + 17 + 27x\\ =& (3 + 27) \times x + 32\\ =& 30x + 32 + \end{flalign*} + \begin{flalign*} + F =& - 4x - 5 + 4x + 1\\ =& - 4x - 5 + 4x + 1\\ =& - 4x + 4x - 5 + 1\\ =& (- 4 + 4) \times x - 4\\ =& 0x - 4\\ =& - 4 + \end{flalign*} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Simple développement}] + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $10(x + 3)$ + \item $8(- 10x + 2)$ + \item $3(- 9x + 3)$ + + \item $- 10x(- 6x + 3)$ + \item $2x(10x - 2) - 4$ + \item $- 3x - 7x(- 10x + 9)$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{2} + \begin{flalign*} + A =& 10(x + 3)\\ =& 10x + 10 \times 3\\ =& 10x + 30 + \end{flalign*} + \begin{flalign*} + B =& 8(- 10x + 2)\\ =& 8 \times - 10x + 8 \times 2\\ =& 8(- 10) \times x + 16\\ =& - 80x + 16 + \end{flalign*} + \begin{flalign*} + C =& 3(- 9x + 3)\\ =& 3 \times - 9x + 3 \times 3\\ =& 3(- 9) \times x + 9\\ =& - 27x + 9 + \end{flalign*} + \begin{flalign*} + D =& - 10x(- 6x + 3)\\ =& - 10x \times - 6x - 10x \times 3\\ =& - 10(- 6) \times x^{1 + 1} + 3(- 10) \times x\\ =& 60x^{2} - 30x + \end{flalign*} + \begin{flalign*} + E =& 2x(10x - 2) - 4\\ =& 2x \times 10x + 2x(- 2) - 4\\ =& 2 \times 10 \times x^{1 + 1} - 2 \times 2 \times x - 4\\ =& 20x^{2} - 4x - 4 + \end{flalign*} + \begin{flalign*} + F =& - 3x - 7x(- 10x + 9)\\ =& - 3x - 7x \times - 10x - 7x \times 9\\ =& - 3x - 7(- 10) \times x^{1 + 1} + 9(- 7) \times x\\ =& - 3x - 63x + 70x^{2}\\ =& (- 3 - 63) \times x + 70x^{2}\\ =& 70x^{2} - 66x + \end{flalign*} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Double développement}] + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $(x + 10)(x + 6)$ + \item $(8x - 6)(- 5x - 10)$ + \item $(- 6x + 9)(7x - 3)$ + + \item $(5x + 2)(- 6x + 2)$ + \item $(- 8x + 8)^{2}$ + \item $(2x - 6)^{2}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{2} + \begin{flalign*} + A =& 10(x + 3)\\ =& 10x + 10 \times 3\\ =& 10x + 30 + \end{flalign*} + \begin{flalign*} + B =& 8(- 10x + 2)\\ =& 8 \times - 10x + 8 \times 2\\ =& 8(- 10) \times x + 16\\ =& - 80x + 16 + \end{flalign*} + \begin{flalign*} + C =& 3(- 9x + 3)\\ =& 3 \times - 9x + 3 \times 3\\ =& 3(- 9) \times x + 9\\ =& - 27x + 9 + \end{flalign*} + \begin{flalign*} + D =& - 10x(- 6x + 3)\\ =& - 10x \times - 6x - 10x \times 3\\ =& - 10(- 6) \times x^{1 + 1} + 3(- 10) \times x\\ =& 60x^{2} - 30x + \end{flalign*} + \begin{flalign*} + E =& 2x(10x - 2) - 4\\ =& 2x \times 10x + 2x(- 2) - 4\\ =& 2 \times 10 \times x^{1 + 1} - 2 \times 2 \times x - 4\\ =& 20x^{2} - 4x - 4 + \end{flalign*} + \begin{flalign*} + F =& - 3x - 7x(- 10x + 9)\\ =& - 3x - 7x \times - 10x - 7x \times 9\\ =& - 3x - 7(- 10) \times x^{1 + 1} + 9(- 7) \times x\\ =& - 3x - 63x + 70x^{2}\\ =& (- 3 - 63) \times x + 70x^{2}\\ =& 70x^{2} - 66x + \end{flalign*} + \end{multicols} +\end{solution} + +\vfill + +\printexercise{exercise}{1} +\printexercise{exercise}{2} +\printexercise{exercise}{3} +\vfill + +\printexercise{exercise}{1} +\printexercise{exercise}{2} +\printexercise{exercise}{3} + +\newpage + +\printsolutionstype{exercise} + +\end{document} diff --git a/2nd/01_Fraction_Developpement_Litteral/tpl_6E_bilan_dev_red.tex b/2nd/01_Fraction_Developpement_Litteral/tpl_6E_bilan_dev_red.tex new file mode 100644 index 0000000..74b2c00 --- /dev/null +++ b/2nd/01_Fraction_Developpement_Litteral/tpl_6E_bilan_dev_red.tex @@ -0,0 +1,130 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +\usepackage{amsmath} + +\author{Benjamin Bertrand} +\title{Information chiffrée 1 - Exercices} +\date{Octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} + +\begin{exercise}[subtitle={Réductions}] + Développer puis réduire les expressions suivantes + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + %- set a = Expression.random("{a}x + {b} + {c}x + {d}") + \item $\Var{a}$ + %- set b = Expression.random("{a}x + {b} + {c}x + {d}") + \item $\Var{b}$ + + %- set c = Expression.random("{a}x^2 + {b} + {c}x^2 + {d} + {d}x + {e}") + \item $\Var{c}$ + %- set d = Expression.random("{a}x + {b} + {c}x + {d} + {e}x + {f}x") + \item $\Var{d}$ + + %- set e = Expression.random("{a}*x + {b} + {c}x + {d}x + {e}", min_max=(2, 20)) + \item $\Var{e}$ + %- set f = Expression.random("{a}x + {b} + {c}x + {d}", conditions=["a+c==0"]) + \item $\Var{f}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{2} + \begin{flalign*} + A =& \Var{a.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + B =& \Var{b.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + C =& \Var{c.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + D =& \Var{d.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + E =& \Var{e.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + F =& \Var{f.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Simple développement}] + Développer puis réduire les expressions suivantes + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + %- set a = Expression.random("{a}*(x + {b})", rejected=[-1,0,1]) + \item $\Var{a}$ + %- set b = Expression.random("{a}*({c}x + {d})", rejected=[-1,0,1]) + \item $\Var{b}$ + %- set c = Expression.random("{a}*({c}x + {d})", rejected=[-1,0,1]) + \item $\Var{c}$ + + %- set d = Expression.random("{c}*x*({a}x + {b})", rejected=[-1,0,1]) + \item $\Var{d}$ + %- set e = Expression.random("{a}*x*({b}x + {c}) + {d}", rejected=[-1,0,1]) + \item $\Var{e}$ + %- set f = Expression.random("{c}*x + {d}*x*({a}x + {b})", rejected=[-1,0,1]) + \item $\Var{f}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{2} + \begin{flalign*} + A =& \Var{a.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + B =& \Var{b.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + C =& \Var{c.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + D =& \Var{d.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + E =& \Var{e.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \begin{flalign*} + F =& \Var{f.simplify().explain() | join('\\\ =& ')} + \end{flalign*} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Double développement}] + Développer puis réduire les expressions suivantes + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + %- set a = Expression.random("(x + {a})*(x + {b})", rejected=[-1,0,1]) + \item $\Var{a}$ + %- set b = Expression.random("({a}x + {b})*({c}x + {d})", rejected=[-1,0,1]) + \item $\Var{b}$ + %- set c = Expression.random("({a}x + {b})*({c}x + {d})", rejected=[-1,0,1]) + \item $\Var{c}$ + + %- set d = Expression.random("({c}*x + {d})*({a}x + {b})", rejected=[-1,0,1]) + \item $\Var{d}$ + %- set e = Expression.random("({b}x + {c})^2", rejected=[-1,0,1]) + \item $\Var{e}$ + %- set f = Expression.random("({a}x + {b})^2", rejected=[-1,0,1]) + \item $\Var{f}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\newpage + +\printsolutionstype{exercise} + +\end{document}