107 lines
4.9 KiB
TeX
107 lines
4.9 KiB
TeX
\begin{exercise}[subtitle={Réduire - technique}, step={1}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
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Réduire les expressions suivantes
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\Block{
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set reduction = {
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"A": random_expression("{a}x + {b} + {c}x + {d}", [], global_config={"rejected":[1, 0, -1]}),
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"B": random_expression("{a}t + {b} + {c}t + {d}t", [], global_config={"rejected":[1, 0, -1]}),
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"C": random_expression("{a}t + {b} + {c}t + {d}t", [], global_config={"rejected":[1, 0, -1]}),
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"D": random_expression("{a}x + {b} + {c}x + {d}", ["a+c==0"], global_config={"rejected":[1, 0, -1]}),
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"E": random_expression("{a}t + {b} + {c}t + {d} + {e}t", ["b+d==0"], global_config={"rejected":[1, 0, -1]}),
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"F": random_expression("{a}/{k} + {b}a + {c}a + {d}", [], global_config={"rejected":[1, 0, -1]}),
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"G": random_expression("{a}x^2 + {b} + {c}x^2 + {d} + {e}x^2", [], global_config={"rejected":[1, 0, -1]}),
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"H": random_expression("{a}x + {b} + {c}x^2 + {d} + {e}x^2", [], global_config={"rejected":[1, 0, -1]}),
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"I": random_expression("{a}x + {b} + {c}x^2 + {d}x + {e}x^2", ["a+d==0"], global_config={"rejected":[1, 0, -1]}),
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}
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}
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\begin{multicols}{2}
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\begin{enumerate}
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%- for (l, e) in reduction.items()
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\item $\Var{l} = \Var{e}$
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%- endfor
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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\begin{solution}
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\begin{multicols}{3}
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\begin{enumerate}
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%- for (l, e) in reduction.items()
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\item
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\begin{align*}
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\Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')}
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\end{align*}
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%- endfor
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\end{enumerate}
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\end{multicols}
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\end{solution}
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\begin{exercise}[subtitle={Développer 1 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
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Développer puis réduire les expressions suivantes
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\Block{
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set reduction = {
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"A": random_expression("{a}({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
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"B": random_expression("{a}({b} + {c}t)", global_config={"rejected":[1, 0, -1]}),
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"C": random_expression("t({b} + {c}t)", global_config={"rejected":[1, 0, -1]}),
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"D": random_expression("{a}x({b}x + {c})", global_config={"rejected":[1, 0, -1]}),
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"E": random_expression("{a}x({b}x + {c})", global_config={"rejected":[1, 0, -1]}),
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"F": random_expression("{a}/{d}x({b}x + {c})", global_config={"min_max":(1, 10)}),
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}
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}
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\begin{multicols}{2}
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\begin{enumerate}
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%- for (l, e) in reduction.items()
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\item $\Var{l} = \Var{e}$
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%- endfor
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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\begin{solution}
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\begin{multicols}{3}
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\begin{enumerate}
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%- for (l, e) in reduction.items()
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\item
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\begin{align*}
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\Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')}
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\end{align*}
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%- endfor
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\end{enumerate}
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\end{multicols}
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\end{solution}
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\begin{exercise}[subtitle={Développer 2 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}]
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Développer puis réduire les expressions suivantes
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\Block{
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set reduction = {
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"A": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
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"B": random_expression("({a}t + {b})({c}t + {d})", global_config={"rejected":[1, 0, -1]}),
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"C": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
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"D": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}),
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"E": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}),
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"F": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}),
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"G": random_expression("({a}x + {b})^2", global_config={"rejected":[1, 0, -1]}),
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"H": random_expression("({a}/{c}x + {b})^2", global_config={"rejected":[1, 0, -1]}),
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}
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}
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\begin{multicols}{2}
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\begin{enumerate}
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%- for (l, e) in reduction.items()
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\item $\Var{l} = \Var{e}$
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%- endfor
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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\begin{solution}
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\begin{multicols}{2}
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\begin{enumerate}
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%- for (l, e) in reduction.items()
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\item
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\begin{align*}
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\Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')}
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\end{align*}
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%- endfor
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\end{enumerate}
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\end{multicols}
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\end{solution}
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