1502 lines
60 KiB
TeX
1502 lines
60 KiB
TeX
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% Calcul et priorité
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%-----------------------
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\question
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\begin{center}
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\textbf{Durée : 10min \hspace{3cm} Thème : Calcul}
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\end{center}
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Calculer les quantités suivantes
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("{a}*{b}*{c}*{d}")}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a}-{b}-{c}", conditions = ["{a} > 0", "{a} < {b}", "{b} > 0", "{c}<0"])}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("{a}*{b}*{e}-{c}*{d}")}
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\part $C = \Var{C}$
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\begin{savedSolution}
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$ C = \Var{C.simplify()}$
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\end{savedSolution}
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\Block{set D = Expression.random("{a}-{b}*{c}-{d}")}
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\part $D = \Var{D}$
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\begin{savedSolution}
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$ D = \Var{D.simplify()}$
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\end{savedSolution}
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\Block{set E = Expression.random("{a}-{b}+{c}-{d}")}
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\part $E = \Var{E}$
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\begin{savedSolution}
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$ E = \Var{E.simplify()}$
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\end{savedSolution}
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\Block{set F = Expression.random("{a}*{b}*{c}*{d}")}
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\part $F = \Var{F}$
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\begin{savedSolution}
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$ F = \Var{F.simplify()}$
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\end{savedSolution}
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\end{multicols}
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\end{parts}
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\question
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\begin{center}
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\textbf{Durée : 10min \hspace{3cm} Thème : Calcul}
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\end{center}
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Calculer les quantités suivantes
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("{a}*{b}*{c}*{d}")}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a}-{b}-{c}", conditions = ["{a} > 0", "{a} < {b}", "{b} > 0", "{c}<0"])}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("{a}*{b}*{e}-{c}*{d}")}
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\part $C = \Var{C}$
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\begin{savedSolution}
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$ C = \Var{C.simplify()}$
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\end{savedSolution}
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\Block{set D = Expression.random("{a}-{b}*{c}-{d}")}
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\part $D = \Var{D}$
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\begin{savedSolution}
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$ D = \Var{D.simplify()}$
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\end{savedSolution}
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\Block{set E = Expression.random("{a}-{b}+{c}-{d}")}
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\part $E = \Var{E}$
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\begin{savedSolution}
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$ E = \Var{E.simplify()}$
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\end{savedSolution}
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\Block{set F = Expression.random("{a}*{b}*{c}*{d}")}
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\part $F = \Var{F}$
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\begin{savedSolution}
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$ F = \Var{F.simplify()}$
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\end{savedSolution}
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\end{multicols}
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\end{parts}
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\question
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\begin{center}
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\textbf{Durée: 10min \hspace{3cm} Thème: Calcul}
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\end{center}
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Calculer les quantités suivantes
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("({a}+{b}*{c})-{d}")}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a}-({b}-{c})")}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("{a}*{b}*({e}-{c}) + {d}")}
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\part $C = \Var{C}$
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\begin{savedSolution}
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$ C = \Var{C.simplify()}$
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\end{savedSolution}
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\Block{set D = Expression.random("({a}+{b})*{c}-{d}")}
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\part $D = \Var{D}$
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\begin{savedSolution}
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$ D = \Var{D.simplify()}$
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\end{savedSolution}
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\Block{set E = Expression.random("{a}-({b}+({c}-{d}))")}
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\part $E = \Var{E}$
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\begin{savedSolution}
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$ E = \Var{E.simplify()}$
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\end{savedSolution}
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\Block{set F = Expression.random("({a}*{b})+({c}*{d})")}
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\part $F = \Var{F}$
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\begin{savedSolution}
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$ F = \Var{F.simplify()}$
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\end{savedSolution}
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\end{multicols}
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\end{parts}
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\question
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\begin{center}
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\textbf{Durée: 10min \hspace{3cm} Thème: Calcul}
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\end{center}
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Calculer les quantités suivantes
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("({a}+{b})*({c}-{d})")}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a}-({b}+{c})")}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("({a}+{b})*({e}-{c}) + {d}")}
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\part $C = \Var{C}$
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\begin{savedSolution}
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$ C = \Var{C.simplify()}$
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\end{savedSolution}
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\Block{set D = Expression.random("-({a}+{b})*{c}-{d}")}
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\part $D = \Var{D}$
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\begin{savedSolution}
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$ D = \Var{D.simplify()}$
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\end{savedSolution}
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\Block{set E = Expression.random("{a}-({b}({c}-{d}) + {e})")}
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\part $E = \Var{E}$
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\begin{savedSolution}
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$ E = \Var{E.simplify()}$
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\end{savedSolution}
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\Block{set F = Expression.random("({a}-{b})*({c}*{d})")}
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\part $F = \Var{F}$
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\begin{savedSolution}
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$ F = \Var{F.simplify()}$
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\end{savedSolution}
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\end{multicols}
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\end{parts}
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\question
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\begin{center}
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\textbf{Durée: 10min \hspace{3cm} Thème: Calcul}
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\end{center}
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Calculer les quantités suivantes
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("{a}^2+{b}")}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a}^2*{a}")}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("{a}^2*{a}^3*{a}")}
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\part $C = \Var{C}$
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\begin{savedSolution}
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$ C = \Var{C.simplify()}$
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\end{savedSolution}
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\Block{set D = Expression.random("{a}*{-a}^2*{-a}^3")}
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\part $D = \Var{D}$
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\begin{savedSolution}
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$ D = \Var{D.simplify()}$
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\end{savedSolution}
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\end{multicols}
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\end{parts}
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\question
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\begin{center}
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\textbf{Durée: 10min \hspace{3cm} Thème: Calcul}
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\end{center}
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Calculer les quantités suivantes
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("({a}+{b})^2-{d}")}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a}-({b}+{c})^2")}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("{a}^2- {e}^2")}
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\part $C = \Var{C}$
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\begin{savedSolution}
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$ C = \Var{C.simplify()}$
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\end{savedSolution}
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\Block{set D = Expression.random("{a}^2*{a}^2*{-a}^3")}
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\part $D = \Var{D}$
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\begin{savedSolution}
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$ D = \Var{D.simplify()}$
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\end{savedSolution}
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\end{multicols}
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\end{parts}
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% Fractions
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% ----------------------
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\question
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\begin{center}
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\textbf{Durée: 10 min\hspace{3cm} Thème: Fractions}
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\end{center}
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Simplifier les fractions suivantes
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("{a}/{k*a}",conditions = ["{a}!=1", "{k} != 1"])}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a} / {k*a}", conditions = ["{a%k} != 0", "{a}!=1"])}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("{k*a} / {l*a}",conditions = ["{a}!=1", "{k} != 1", "{k}!={l}"])}
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\part $C = \Var{C}$
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\begin{savedSolution}
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$ C = \Var{C.simplify()}$
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\end{savedSolution}
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\Block{set D = Expression.random("{k*a} / {l*a}",conditions = ["{a}!=1", "{k} != 1", "{k}!={l}"])}
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\part $D = \Var{D}$
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\begin{savedSolution}
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$ D = \Var{D.simplify()}$
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\end{savedSolution}
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\Block{set E = Expression.random("{k*a} / {a}",conditions = ["{a}!=1", "{k} != 1"])}
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\part $E = \Var{E}$
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\begin{savedSolution}
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$ E = \Var{E.simplify()}$
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\end{savedSolution}
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\Block{set F = Expression.random("{l*a} / {k*a}",conditions = ["{a}!=1", "{k} != 1"])}
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\part $F = \Var{F}$
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\begin{savedSolution}
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$ F = \Var{F.simplify()}$
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\end{savedSolution}
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\end{multicols}
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\end{parts}
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\question
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\begin{center}
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\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
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\end{center}
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Calculer les quantités suivantes et simplifier le résultat
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("{a} / {b} + {c} / {b}",conditions = ["not {b} in [-1,1]"])}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a} / {b} + {c} / {k*b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("{a} / {k*b} + {c} / {b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
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\part $C = \Var{C}$
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\begin{savedSolution}
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$ C = \Var{C.simplify()}$
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\end{savedSolution}
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\Block{set D = Expression.random("{a}/{b} + {c}",conditions = ["not {b} in [-1,1]"])}
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\part $D = \Var{D}$
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\begin{savedSolution}
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$ D = \Var{D.simplify()}$
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\end{savedSolution}
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\Block{set E = Expression.random("{a} / {b} + {c} / {b}",conditions = ["not {b} in [-1,1]"])}
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\part $E = \Var{E}$
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\begin{savedSolution}
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$ E = \Var{E.simplify()}$
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\end{savedSolution}
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\Block{set F = Expression.random("{a} / {b} + {c} / {e}",conditions = ["not {b} in [-1,1]", "not {e} in [-1,1]", "gcd({b},{e})==1"])}
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\part $F = \Var{F}$
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\begin{savedSolution}
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$ F = \Var{F.simplify()}$
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\end{savedSolution}
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\end{multicols}
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\end{parts}
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\question
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\begin{center}
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\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
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\end{center}
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Calculer les quantités suivantes et simplifier le résultat
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\begin{parts}
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\begin{multicols}{2}
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\Block{set A = Expression.random("{a} / {b} * {c} / {b}",conditions = ["not {b} in [-1,1]"])}
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\part $A = \Var{A}$
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\begin{savedSolution}
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$ A = \Var{A.simplify()}$
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\end{savedSolution}
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\Block{set B = Expression.random("{a} / {b} * {c} / {k*b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
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\part $B = \Var{B}$
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\begin{savedSolution}
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$ B = \Var{B.simplify()}$
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\end{savedSolution}
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\Block{set C = Expression.random("{a} / {k*b} * {c} / {b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
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|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("{a}/{b} * {c}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set E = Expression.random("{a} * {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set F = Expression.random("{a} * {b} / {c} * {e}",conditions = ["not {c} in [-1,1]", "not {e} in [-1,1]", "gcd({b},{e})==1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ F = \Var{F.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 10 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Simplifier les fractions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a}/{k*a}",conditions = ["{a}!=1", "{k} != 1"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a} / {k*a}", conditions = ["{a%k} != 0", "{a}!=1"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("{k*a} / {l*a}",conditions = ["{a}!=1", "{k} != 1", "{k}!={l}"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("{k*a} / {l*a}",conditions = ["{a}!=1", "{k} != 1", "{k}!={l}"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set E = Expression.random("{k*a} / {a}",conditions = ["{a}!=1", "{k} != 1"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ E = \Var{E.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set F = Expression.random("{l*a} / {k*a}",conditions = ["{a}!=1", "{k} != 1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ F = \Var{F.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Calculer les quantités suivantes et simplifier le résultat
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a} / {b} + {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a} / {b} + {c} / {e}",conditions = ["not {b} in [-1,1]", "not {e} in [-1,1]", "gcd({b},{e})==1"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("{a}/{b} + {c}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("{a} / {k*b} + {c} / {b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set E = Expression.random("{a} / {b} + {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ E = \Var{E.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set F = Expression.random("{a} / {b} + {c} / {k*b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ F = \Var{F.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Calculer les quantités suivantes et simplifier le résultat
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a} / {k*b} + {c} / {q*b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a} / {b} + {c} / {k*b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("{a} / {k*b} + {c} / {b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random(" {c} + {a}/{b} ",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set E = Expression.random("{a} / {k*b} + {a} / {q*b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ E = \Var{E.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set F = Expression.random("{a} / {b} + {c} / {e}",conditions = ["not {b} in [-1,1]", "not {e} in [-1,1]", "gcd({b},{e})==1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ F = \Var{F.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Calculer les quantités suivantes et simplifier le résultat
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a} / {b} * {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a} / {b} * {c} / {k*b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("{a} / {k*b} * {c} / {b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("{a}/{b} * {c}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set E = Expression.random("{a} * {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ E = \Var{E.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set F = Expression.random("{a} * {b} / {c} * {e}",conditions = ["not {c} in [-1,1]", "not {e} in [-1,1]", "gcd({b},{e})==1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ F = \Var{F.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Calculer les quantités suivantes et simplifier le résultat
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("({a} / {b} + {e}) * {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("({a} / {b} + {c}) * 1 / {k*b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("{a} / {k*b} + {c} / {b} + {e}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("{d}({a}/{b} + {c})",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set E = Expression.random("({a} + {d}) * {c} / {b} + {e} / {a*b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ E = \Var{E.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set F = Expression.random("{a} + {b} / {c} * {e}",conditions = ["not {c} in [-1,1]", "not {e} in [-1,1]", "gcd({b},{e})==1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ F = \Var{F.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Calculer les quantités suivantes et simplifier le résultat
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("({a} / {b} + {e}) * {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("({a} + {c}) / {k*b}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("{a} / {k*b} + {c} / {b} + {e}", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("{d} / {b} * ({a}/{b} + {c})",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set E = Expression.random("({a} + {b}) / {b}" ,conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ E = \Var{E.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set F = Expression.random("({a} + {b}) / ({b} + {e})",conditions = ["not {c} in [-1,1]", "not {e} in [-1,1]", "gcd({b},{e})==1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ F = \Var{F.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 10 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Calculer les quantités suivantes et simplifier le résultat
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("({a} / {b})^2",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a}^2 / {b}", conditions = ["not {b} in [-1,1]", "{a}!={b}"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("({a} / {b} + {c})^2", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("({a} - {b}^2) / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set E = Expression.random("({a} + {b}) / {b}" ,conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ E = \Var{E.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set F = Expression.random("({a} + {b}) / ({b} + {e})",conditions = ["not {c} in [-1,1]", "not {e} in [-1,1]", "gcd({b},{e})==1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ F = \Var{F.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Mettre les calculs suivants sous forme d'une seule fraction.
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a} / {2*b} + {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\Block{set B = Expression.random("{a} / (2*n) + {c} / n")}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\Block{set C = Expression.random("{a}/ n + {c} / (3*n)")}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\Block{set D = Expression.random("{a} / n * {c} / (3*n)")}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\Block{set E = Expression.random("{a} / (x+1) + {c} / x",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\Block{set F = Expression.random("{a} / (x+1) * {c} / x", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20 min \hspace{3cm} Thème: Fractions}
|
||
|
|
\end{center}
|
||
|
|
Mettre les calculs suivants sous forme d'une seule fraction.
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a} / {2*b} + {c} / {b}",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\Block{set B = Expression.random("{a} / (2*n) + {c} / n")}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\Block{set C = Expression.random("{a}/ n + {c} / (3*n)")}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\Block{set D = Expression.random("{a} / n * {c} / (3*n)")}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\Block{set E = Expression.random("{a} / (x+1) + {c} / x",conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $E = \Var{E}$
|
||
|
|
\Block{set F = Expression.random("{a} / (x+1) * {c} / x", conditions = ["not {b} in [-1,1]", "{k}!=1"])}
|
||
|
|
\part $F = \Var{F}$
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
% Fonctions (calculs)
|
||
|
|
% ----------------------
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 10min \hspace{3cm} Thème: Fonctions}
|
||
|
|
\end{center}
|
||
|
|
Calculer l'image de $x_0$ par $f$ dans les cas suivants
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set x = Expression.random("{a}")}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \Var{P}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$f(x_0) = \Var{P(x)}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set x = Expression.random("{a}")}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \Var{P}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$f(x_0) = \Var{P(x)}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set x = Expression.random("{a}")}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \Var{P}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$f(x_0) = \Var{P(x)}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set x = Expression.random("{a}/{b}", conditions = ["not {b} in [-1,1]"])}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \Var{P}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$f(x_0) = \Var{P(x)}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Fonctions}
|
||
|
|
\end{center}
|
||
|
|
Calculer l'image de $x_0$ par $f$ dans les cas suivants
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set x = Expression.random("{a}")}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \Var{P}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$f(x_0) = \Var{P(x)}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 3)}
|
||
|
|
\Block{set x = Expression.random("{a}")}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \Var{P}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$f(x_0) = \Var{P(x)}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set x = Expression.random("{a}/{b}", conditions = ["not {b} in [-1,1]", "{a} != {b}"])}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \Var{P}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$f(x_0) = \Var{P(x)}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set x = Expression.random("{a}/{b}", conditions = ["not {b} in [-1,1]", "{a} != {b}"])}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \Var{P}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$f(x_0) = \Var{P(x)}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Fonctions}
|
||
|
|
\end{center}
|
||
|
|
Calculer l'image de $x_0$ par $f$ dans les cas suivants
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set P = Polynom.random(degree = 1)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 1)}
|
||
|
|
\Block{set x = Expression.random("{a}")}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \dfrac{\Var{P}}{\Var{Q}}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set ans = Expression([P(x), Q(x), '/']).simplify()}%
|
||
|
|
$f(x_0) = \Var{ans}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 1)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 1)}
|
||
|
|
\Block{set x = Expression.random("{a}")}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \dfrac{\Var{P}}{\Var{Q}}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set ans = Expression([P(x), Q(x), '/']).simplify()}%
|
||
|
|
$f(x_0) = \Var{ans}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 1)}
|
||
|
|
\Block{set x = Expression.random("{a}")}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \dfrac{\Var{P}}{\Var{Q}}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set ans = Expression([P(x), Q(x), '/']).simplify()}%
|
||
|
|
$f(x_0) = \Var{ans}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 1)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 1)}
|
||
|
|
\Block{set x = Expression.random("{a}/{b}", conditions = ["not {b} in [-1,1]", "{a} != {b}"])}
|
||
|
|
\part $x_0 = \Var{x}$ et $f(x) = \dfrac{\Var{P}}{\Var{Q}}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set ans = Expression([P(x), Q(x), '/']).simplify()}%
|
||
|
|
$f(x_0) = \Var{ans}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
|
||
|
|
% Expressions literales
|
||
|
|
% ---------------------
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 10min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Réduire les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 2)}
|
||
|
|
\part $A = \Var{Expression([P,Q,"+"])}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$A = \Var{Expression([P,Q,"+"]).simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 2)}
|
||
|
|
\part $B = \Var{Expression([P,Q,"+"])}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$B = \Var{Expression([P,Q,"+"]).simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 2)}
|
||
|
|
\part $C = \Var{Expression([P,Q,"-"])}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$C = \Var{Expression([P,Q,"-"]).simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 2)}
|
||
|
|
\Block{set R = Polynom.random(degree = 1)}
|
||
|
|
\part $D = \Var{Expression([P,R,"+",Q,"+"])}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$D = \Var{Expression([P,Q,"+"]).simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 10min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Réduire les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 2)}
|
||
|
|
\part $A = \Var{Expression([P,Q,"+"])}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$A = \Var{Expression([P,Q,"+"]).simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 2)}
|
||
|
|
\part $B = \Var{Expression([P,Q,"+"])}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$B = \Var{Expression([P,Q,"+"]).simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 2)}
|
||
|
|
\part $C = \Var{Expression([P,Q,"-"])}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$C = \Var{Expression([P,Q,"-"]).simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 2)}
|
||
|
|
\Block{set R = Polynom.random(degree = 1)}
|
||
|
|
\part $D = \Var{Expression([P,R,"-",Q,"+"])}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$D = \Var{Expression([P,R,'-',Q,"+"]).simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Développer puis réduire les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a} ( {b} x + {c})", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a}x ( {b} x + {c})", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("( {b} x + {c}) *{a}x", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("( {b} x + {c}) *{a}x^2")}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Développer puis réduire les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a} ( {b} x + {c}) + {d}x", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a}x^2 ( {b} x + {c}) + {d}x", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("( {b} x + {c}) *{a}x", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("( {b} x + {c}) *{a}x^2 + {e}x^3")}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Développer puis réduire les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set P = Polynom.random(degree = 1)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 1)}
|
||
|
|
\Block{set A = Expression([P,Q,'*'])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 1)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 1)}
|
||
|
|
\Block{set B = Expression([P,Q,'*'])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 1)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 1)}
|
||
|
|
\Block{set C = Expression([2,P,"*",Q,'*'])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 1)}
|
||
|
|
\Block{set Q = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D = Expression([P,Q,'*'])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Développer puis réduire les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("( {b} x + {c})^2", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("( {b} x + {c})^2", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("( {b} x + {c})^2 + {a}", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("( {b} x + {c})^2 + {a}x", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Développer puis réduire les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("( {b} x + {c})^2", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $A = \Var{A}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a}x + ( {b} x + {c})^2", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $B = \Var{B}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("( {b} x + {c})^2 + {a}", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $C = \Var{C}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("( {b} x + {c})^2 + {a}x", conditions = ["not {a} in [-1,1]"])}
|
||
|
|
\part $D = \Var{D}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D.simplify()}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Développer puis réduire les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\part $A = \Var{str(P).replace('x', '(h+1)')}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{P('h+1')}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\part $B = \Var{str(P).replace('x', '(h-1)')}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{P('h-1')}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\part $A = \Var{str(P).replace('x', '(h+2)')}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{P('h+2')}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set P = Polynom.random(degree = 2)}
|
||
|
|
\part $B = \Var{str(P).replace('x', '(h-2)')}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{P('h-2')}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 10min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Factoriser les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a}x({b}x +{c})") }
|
||
|
|
\part $A = \Var{A.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a}x({b}x -{c})") }
|
||
|
|
\part $B = \Var{B.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("{a}x({b}x^2 +{c})") }
|
||
|
|
\part $C = \Var{C.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("{a}x^2({b}x +{c})") }
|
||
|
|
\part $D = \Var{D.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 10min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Factoriser les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("{a}x({b}x +{c})") }
|
||
|
|
\part $A = \Var{A.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("{a}x({b}x^2 -{c})") }
|
||
|
|
\part $B = \Var{B.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("{a}x^2({b}x +{c})") }
|
||
|
|
\part $C = \Var{C.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("{a}x^3({b}x -{c})") }
|
||
|
|
\part $D = \Var{D.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée: 20min \hspace{3cm} Thème: Calcul littéral}
|
||
|
|
\end{center}
|
||
|
|
Factoriser les expressions suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Expression.random("({b}x +{c})^2") }
|
||
|
|
\part $A = \Var{A.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ A = \Var{A}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B = Expression.random("({b}x +{c})^2") }
|
||
|
|
\part $B = \Var{B.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ B = \Var{B}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set C = Expression.random("({b}x +{c})^2") }
|
||
|
|
\part $C = \Var{C.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ C = \Var{C}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D = Expression.random("({b}x +{c})({b}x - {c})") }
|
||
|
|
\part $D = \Var{D.simplify()}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
$ D = \Var{D}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
% Equation / Inéquation
|
||
|
|
% ----------------------
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 10min \hspace{3cm} Thème : Équations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Résoudre les équations suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Polynom.random(degree = 1)}
|
||
|
|
\part $\Var{A} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1)}
|
||
|
|
\part $\Var{A} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1)}
|
||
|
|
\part $\Var{A} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1)}
|
||
|
|
\part $\Var{A} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 10min \hspace{3cm} Thème : Équations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Résoudre les équations suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Polynom.random(degree = 1)}
|
||
|
|
\part $\Var{A} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set B2 = Polynom.random(degree = 1, conditions = ["{a} !="+str(B1._coef[1])])}
|
||
|
|
\part $\Var{B1} = \Var{B2}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-(B1._coef[0] - B2._coef[0]), (B1._coef[1] - B2._coef[1]), "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set B2 = Polynom.random(degree = 1, conditions = ["{a} !="+str(B1._coef[1])])}
|
||
|
|
\part $\Var{B1} = \Var{B2}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-(B1._coef[0] - B2._coef[0]), (B1._coef[1] - B2._coef[1]), "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set B2 = Polynom.random(degree = 1, conditions = ["{a} !="+str(B1._coef[1])])}
|
||
|
|
\part $\Var{B1} = \Var{B2}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-(B1._coef[0] - B2._coef[0]), (B1._coef[1] - B2._coef[1]), "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 20min \hspace{3cm} Thème : Équations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Résoudre les équations suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Polynom.random(degree = 1)}
|
||
|
|
\part $\Var{A} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set B1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set B2 = Polynom.random(degree = 1, conditions = ["{a} !="+str(B1._coef[1])])}
|
||
|
|
\part $\Var{B1} = \Var{B2}$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-(B1._coef[0] - B2._coef[0]), (B1._coef[1] - B2._coef[1]), "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\Block{set C1 = Polynom.random(degree = 2)}
|
||
|
|
\part $\Var{C1} = \Var{C1.a}x^2$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-C1._coef[0], C1._coef[1], "/"]).simplify()}%
|
||
|
|
La solution est $x = \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D2 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D = Expression([D1, D2, "*"])}
|
||
|
|
\part $\Var{D} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
\Block{set sol2 = Expression([-D2._coef[0], D2._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de cette équation sont $x = \Var{sol1}$ ou $x = \Var{sol2}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 20min \hspace{3cm} Thème : Équations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Résoudre les équations suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D2 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D = Expression([D1, D2, "*"])}
|
||
|
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\part $\Var{D} = 0$
|
||
|
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\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
\Block{set sol2 = Expression([-D2._coef[0], D2._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de cette équation sont $x = \Var{sol1}$ ou $x = \Var{sol2}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D2 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D = Expression([D1, D2, "*"])}
|
||
|
|
\part $\Var{D} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
\Block{set sol2 = Expression([-D2._coef[0], D2._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de cette équation sont $x = \Var{sol1}$ ou $x = \Var{sol2}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D = D1**2}
|
||
|
|
\part $\Var{D} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
La solution de cette équation est $x = \Var{sol1}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D2 = Polynom([-D1._coef[0], D1._coef[1]])}
|
||
|
|
\Block{set D = D1*D2}
|
||
|
|
\part $\Var{D} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
\Block{set sol2 = Expression([-D2._coef[0], D2._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de cette équation sont $x = \Var{sol1}$ ou $x = \Var{sol2}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 20min \hspace{3cm} Thème : Équations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Résoudre les équations suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D = D1**2}
|
||
|
|
\part $\Var{D} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
La solution de cette équation est $x = \Var{sol1}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D2 = Polynom([-D1._coef[0], D1._coef[1]])}
|
||
|
|
\Block{set D = D1*D2}
|
||
|
|
\part $\Var{D} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
\Block{set sol2 = Expression([-D2._coef[0], D2._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de cette équation sont $x = \Var{sol1}$ ou $x = \Var{sol2}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D = D1**2}
|
||
|
|
\part $\Var{D} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
La solution de cette équation est $x = \Var{sol1}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set D1 = Polynom.random(degree = 1)}
|
||
|
|
\Block{set D2 = Polynom([-D1._coef[0], D1._coef[1]])}
|
||
|
|
\Block{set D = D1*D2}
|
||
|
|
\part $\Var{D} = 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol1 = Expression([-D1._coef[0], D1._coef[1], "/"]).simplify()}%
|
||
|
|
\Block{set sol2 = Expression([-D2._coef[0], D2._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de cette équation sont $x = \Var{sol1}$ ou $x = \Var{sol2}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 10min \hspace{3cm} Thème : Inéquations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Compléter le tableau suivant
|
||
|
|
|
||
|
|
\begin{tabular}{|*{3}{c|}p{5cm}|}
|
||
|
|
\hline
|
||
|
|
\rowcolor{highlightbg} Inégalité & Intervalle & Représentation graphique & En français \\
|
||
|
|
\hline
|
||
|
|
$-2 \leq x \leq 4$&& \monaxe & \\
|
||
|
|
\hline
|
||
|
|
& $x \in \intOO{0}{+\infty}$ & \monaxe & \\
|
||
|
|
\hline
|
||
|
|
&& \axeCustom{[}{-4}{-2}{[} & \\
|
||
|
|
\hline
|
||
|
|
&& \monaxe & $x$ est strictement plus petit que 1\\
|
||
|
|
\hline
|
||
|
|
\end{tabular}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 10min \hspace{3cm} Thème : Inéquations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Compléter le tableau suivant
|
||
|
|
|
||
|
|
\begin{tabular}{|*{3}{c|}p{5cm}|}
|
||
|
|
\hline
|
||
|
|
\rowcolor{highlightbg} Inégalité & Intervalle & Représentation graphique & En français \\
|
||
|
|
\hline
|
||
|
|
$ x \leq 4$&& \monaxe & \\
|
||
|
|
\hline
|
||
|
|
& $x \in \R^{+}$ & \monaxe & \\
|
||
|
|
\hline
|
||
|
|
&& \infAxe{[}{2} & \\
|
||
|
|
\hline
|
||
|
|
&& \monaxe & $x$ est supérieur ou égale à -1\\
|
||
|
|
\hline
|
||
|
|
\end{tabular}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 10min \hspace{3cm} Thème : Inéquations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Résoudre les équations suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} > 0"])}
|
||
|
|
\part $\Var{A} > 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x > \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} > 0"])}
|
||
|
|
\part $\Var{A} > 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x > \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} < 0"])}
|
||
|
|
\part $\Var{A} > 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x < \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} < 0"])}
|
||
|
|
\part $\Var{A} < 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x > \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 10min \hspace{3cm} Thème : Inéquations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Résoudre les équations suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} > 0"])}
|
||
|
|
\part $\Var{A} \leq 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x \leq \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} > 0"])}
|
||
|
|
\part $\Var{A} > 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x > \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} < 0"])}
|
||
|
|
\part $\Var{A} > 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x < \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} < 0"])}
|
||
|
|
\part $\Var{A} < 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x > \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
\question
|
||
|
|
\begin{center}
|
||
|
|
\textbf{Durée prévu: 10min \hspace{3cm} Thème : Inéquations}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
Résoudre les équations suivantes
|
||
|
|
\begin{parts}
|
||
|
|
\begin{multicols}{2}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} > 0"])}
|
||
|
|
\part $\Var{A} \leq 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x \leq \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} > 0"])}
|
||
|
|
\part $\Var{A} > 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x > \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} < 0"])}
|
||
|
|
\part $\Var{A} > 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x < \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\Block{set A = Polynom.random(degree = 1, conditions = ["{a} < 0"])}
|
||
|
|
\part $\Var{A} < 0$
|
||
|
|
\begin{savedSolution}
|
||
|
|
\Block{set sol = Expression([-A._coef[0], A._coef[1], "/"]).simplify()}%
|
||
|
|
Les solutions de l'inéquations sont les $x$ tels que $x > \Var{sol}$
|
||
|
|
\end{savedSolution}
|
||
|
|
\end{multicols}
|
||
|
|
\end{parts}
|
||
|
|
|
||
|
|
|