diff --git a/2nd/01_Fraction_Developpement_Litteral/tpl_2E_tech_frac.tex b/2nd/01_Fraction_Developpement_Litteral/tpl_2E_tech_frac.tex new file mode 100644 index 0000000..be476f2 --- /dev/null +++ b/2nd/01_Fraction_Developpement_Litteral/tpl_2E_tech_frac.tex @@ -0,0 +1,283 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Information chiffrée 1 - Exercices} +\date{Septembre 2021} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Égalité de fractions}] + Déterminer les valeurs manquantes + \begin{multicols}{4} + \begin{enumerate}[label=\alph*)] + %- set A = random_list(["a", "b", "a*c", "b*c"], conditions = ["a != b"], min_max=(2, 9), rejected=[0, 1]) + \item $\dfrac{\Var{A[0]}}{\Var{A[1]}} = \dfrac{\ldots}{\Var{A[3]}}$ + %- set B = random_list(["a", "b", "a*c", "b*c"], conditions = ["a != b"], min_max=(2, 9), rejected=[0, 1]) + \item $\dfrac{\Var{B[0]}}{\Var{B[1]}} = \dfrac{\ldots}{\Var{B[3]}}$ + %- set C = random_list(["a", "b", "a*c", "b*c"], conditions = ["a != b", "a*b>0"], min_max=(-9, 9), rejected=[0, 1]) + \item $\dfrac{\Var{C[0]}}{\Var{C[1]}} = \dfrac{\ldots}{\Var{C[3]}}$ + %- set D = random_list(["a", "b", "a*c", "b*c"], conditions = ["a != b", "a*b<0"], min_max=(-9, 9), rejected=[0, 1]) + \item $\dfrac{\Var{D[0]}}{\Var{D[1]}} = \dfrac{\ldots}{\Var{D[3]}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{4} + \begin{enumerate}[label=\alph*)] + \item $\dfrac{\Var{A[0]}}{\Var{A[1]}} = \dfrac{\Var{A[2]}}{\Var{A[3]}}$ + \item $\dfrac{\Var{B[0]}}{\Var{B[1]}} = \dfrac{\Var{B[2]}}{\Var{B[3]}}$ + \item $\dfrac{\Var{C[0]}}{\Var{C[1]}} = \dfrac{\Var{C[2]}}{\Var{C[3]}}$ + \item $\dfrac{\Var{D[0]}}{\Var{D[1]}} = \dfrac{\Var{D[2]}}{\Var{D[3]}}$ + \end{enumerate} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Comparaison}] + Comparer les fractions suivantes + \begin{multicols}{4} + \begin{enumerate}[label=\alph*)] + %- set A1 = Fraction.random() + %- set A2 = Fraction.random() + \item $\Var{A1}$ et $\Var{A2}$ + %- set B1 = Fraction.random() + %- set B2 = Fraction.random() + \item $\Var{B1}$ et $\Var{B2}$ + %- set C1 = Fraction.random() + %- set C2 = Fraction.random() + \item $\Var{C1}$ et $\Var{C2}$ + %- set D1 = Fraction.random() + %- set D2 = Fraction.random() + \item $\Var{D1}$ et $\Var{D2}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{4} + \begin{enumerate}[label=\alph*)] + \item + %- if A1 > A2 + $\Var{A1}$ > $\Var{A2}$ + %- elif A1 < A2 + $\Var{A1}$ < $\Var{A2}$ + %- else + $\Var{A1}$ = $\Var{A2}$ + %- endif + \item + %- if B1 > B2 + $\Var{B1}$ > $\Var{B2}$ + %- elif B1 < B2 + $\Var{B1}$ < $\Var{B2}$ + %- else + $\Var{B1}$ = $\Var{B2}$ + %- endif + \item + %- if C1 > C2 + $\Var{C1}$ > $\Var{C2}$ + %- elif C1 < C2 + $\Var{C1}$ < $\Var{C2}$ + %- else + $\Var{C1}$ = $\Var{C2}$ + %- endif + \item + %- if D1 > D2 + $\Var{D1}$ > $\Var{D2}$ + %- elif D1 < D2 + $\Var{D1}$ < $\Var{D2}$ + %- else + $\Var{D1}$ = $\Var{D2}$ + %- endif + \end{enumerate} + \end{multicols} +\end{solution} + + +\begin{exercise}[subtitle={Additions}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + %- set A = Expression.random("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{A}$ + %- set B = Expression.random("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(-10, 10)) + \item $\Var{B}$ + %- set C = Expression.random("{a} / {b} + {c}", ["a!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{C}$ + %- set D = Expression.random("{a} / {b} + {c}", ["a!=b", "b > 1"], min_max=(-10, 10)) + \item $\Var{D}$ + + %- set E = Expression.random("{a} / {b} + {c} / {k*b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{E}$ + %- set F = Expression.random("{a} / {b} + {c} / {k*b}", ["a!=b", "c!=b", "b > 1", "k > 1"], min_max=(-10, 10)) + \item $\Var{F}$ + %- set G = Expression.random("{a} / {b} + {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(0, 10)) + \item $\Var{G}$ + %- set H = Expression.random("{a} / {b} + {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(-10, 10)) + \item $\Var{H}$ + + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\Var{A.simplify().explain() | join('=')}$ + \item $\Var{B.simplify().explain() | join('=')}$ + \item $\Var{C.simplify().explain() | join('=')}$ + \item $\Var{D.simplify().explain() | join('=')}$ + + \item $\Var{E.simplify().explain() | join('=')}$ + \item $\Var{F.simplify().explain() | join('=')}$ + \item $\Var{G.simplify().explain() | join('=')}$ + \item $\Var{H.simplify().explain() | join('=')}$ + \end{enumerate} +\end{solution} + + +\begin{exercise}[subtitle={Multiplications}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + %- set A = Expression.random("{a} / {b} * {c}", ["a!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{A}$ + %- set B = Expression.random("{a} / {b} * {c}", ["a!=b", "b > 1"], min_max=(-10, 10)) + \item $\Var{B}$ + %- set C = Expression.random("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{C}$ + %- set D = Expression.random("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(-10, 10)) + \item $\Var{D}$ + + %- set E = Expression.random("{a} / {b} * {c} / {k*b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{E}$ + %- set F = Expression.random("{a} / {b} * {c} / {k*b}", ["a!=b", "c!=b", "b > 1", "k > 1"], min_max=(-10, 10)) + \item $\Var{F}$ + %- set G = Expression.random("{a} / {b} * {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(0, 10)) + \item $\Var{G}$ + %- set H = Expression.random("{a} / {b} * {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(-10, 10)) + \item $\Var{H}$ + + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{multicols}{2} + \begin{enumerate}[label={\Alph*=}] + \item $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplify()}$ + \item $\Var{B.simplify().explain() | join('=')} = \Var{B.simplify().simplify()}$ + \item $\Var{C.simplify().explain() | join('=')} = \Var{C.simplify().simplify()}$ + \item $\Var{D.simplify().explain() | join('=')} = \Var{D.simplify().simplify()}$ + + \item $\Var{E.simplify().explain() | join('=')} = \Var{E.simplify().simplify()}$ + \item $\Var{F.simplify().explain() | join('=')} = \Var{F.simplify().simplify()}$ + \item $\Var{G.simplify().explain() | join('=')} = \Var{G.simplify().simplify()}$ + \item $\Var{H.simplify().explain() | join('=')} = \Var{H.simplify().simplify()}$ + \end{enumerate} + + \end{multicols} +\end{solution} + +\pagebreak + +\printsolutions +% +% \section{Ajouts de fractions} +% +% \begin{itemize} +% \item Fraction avec le même dénominateur +% \Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["b > 1"], min_max=(1, 10))} +% \begin{align*} +% A = \Var{e} +% \end{align*} +% Solution +% \begin{align*} +% \Var{e.simplify().explain() | join('=')} +% \end{align*} +% +% \item Fraction avec un denominateur multiple de l'autre +% \Block{set e = Expression.random("{a} / {b} + {c} / {b*d}", ["b > 1","d > 1"], min_max=(1, 10))} +% \begin{align*} +% A = \Var{e} +% \end{align*} +% Solution +% \begin{align*} +% \Var{e.simplify().explain() | join('=')} +% \end{align*} +% +% \item Une fraction et un entier +% \Block{set e = Expression.random("{a} / {b} + {c}", ["b > 1"], min_max=(1, 10))} +% \begin{align*} +% A = \Var{e} +% \end{align*} +% Solution +% \begin{align*} +% \Var{e.simplify().explain() | join('=')} +% \end{align*} +% +% \end{itemize} +% +% +% \section{Multiplications de fractions} +% \begin{itemize} +% \item Une fraction et un entier +% \Block{set e = Expression.random("{c} * {a} / {b}", min_max=(2, 10))} +% \begin{align*} +% A = \Var{e} +% \end{align*} +% Solution +% \begin{align*} +% \Var{e.simplify().explain() | join('=')} +% \end{align*} +% +% \item Fraction avec des dénominateurs quelconques +% \Block{set e = Expression.random("{a} / {b} * {c} / {d}", ["b > 1","d > 1"], min_max=(1, 10))} +% \begin{align*} +% A = \Var{e} +% \end{align*} +% Solution +% \begin{align*} +% \Var{e.simplify().explain() | join('=')} +% \end{align*} +% \end{itemize} +% +% +% \section{Division de fractions} +% \begin{itemize} +% \item Une fraction et un entier +% \Block{set e = Expression.random("{c} / {a} / {b}", min_max=(2, 10))} +% \begin{align*} +% A = \Var{e} +% \end{align*} +% Solution +% \begin{align*} +% \Var{e.simplify().explain() | join('=')} +% \end{align*} +% +% \item Fraction avec des dénominateurs quelconques +% \Block{set e = Expression.random("({a} / {b}) / ({c} / {d})", ["a != b", "c!= d", "b > 1","d > 1"], min_max=(1, 10))} +% \begin{align*} +% A = \Var{e} +% \end{align*} +% Solution +% \begin{align*} +% \Var{e.simplify().explain() | join('=')} +% \end{align*} +% \end{itemize} +% +% \section{Tout mélangé} +% \begin{itemize} +% \item +% \Block{set e = Expression.random("{d}/{e}*({c} / {a} + {b})", min_max=(2, 10))} +% \begin{align*} +% A = \Var{e} +% \end{align*} +% Solution +% \begin{align*} +% \Var{e.simplify().explain() | join('=')} +% \end{align*} +% \end{itemize} + +\end{document} diff --git a/2nd/01_Fraction_Developpement_Litteral/tpl_4E_tech_red_dev.tex b/2nd/01_Fraction_Developpement_Litteral/tpl_4E_tech_red_dev.tex new file mode 100644 index 0000000..907e74b --- /dev/null +++ b/2nd/01_Fraction_Developpement_Litteral/tpl_4E_tech_red_dev.tex @@ -0,0 +1,71 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Information chiffrée 1 - Exercices} +\date{Octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Réductions}] + Développer puis réduire les expressions suivantes + \begin{multicols}{2} + \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 + {b})^2") + \item $\Var{c}$ + %- set d = Expression.random("{c} + x*({a}x + {b})") + \item $\Var{d}$ + + %- set e = Expression.random("{c}*x^2 + x*({a}x + {b})") + \item $\Var{e}$ + %- set f = Expression.random("{a}(x+{b})(x+{c})") + \item $\Var{f}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{enumerate} + \item + \[ + \Var{a.simplify().explain() | join('=')} + \] + \item + \[ + \Var{b.simplify().explain() | join('=')} + \] + \item + \[ + \Var{c.simplify().explain() | join('=')} + \] + \item + \[ + \Var{d.simplify().explain() | join('=')} + \] + \item + \[ + \Var{e.simplify().explain() | join('=')} + \] + \item + \[ + \Var{f.simplify().explain() | join('=')} + \] + \end{enumerate} +\end{solution} + + +\pagebreak + +\printsolutionstype{exercise} + +\end{document}