115 lines
4.2 KiB
TeX
115 lines
4.2 KiB
TeX
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\begin{parts}
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\vfill
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\part Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible).
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\begin{multicols}{4}
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\begin{subparts}
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\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1"])}
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\subpart $B = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "B")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {d}", ["{b} > 1", "{d} > 1", "gcd({b},{d})==1"])}
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\subpart $D = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "D")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} * {c}", ["{b} > 1", "{a} > 0", "{c} > 1", "{c} != {b}"])}
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\subpart $E = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "E")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} * {c} / {d}", ["{b} > 1", "{a} > 0", "{c} > 0", "{d} > 1"])}
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\subpart $F = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "F")}
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\end{eqnarray*}
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\end{solution}
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\end{subparts}
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\end{multicols}
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\part Développer puis réduire les expressions suivantes
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\begin{multicols}{2}
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\begin{subparts}
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\Block{set e = Expression.random("_*(_*x + _)")}
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\subpart $A = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "A")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("_*x(_*x + _)")}
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\subpart $B = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "B")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("_*(_*x + _) + _")}
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\subpart $A = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "C")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("_*x+_*x(_*x + _)+_")}
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\subpart $B = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "D")}
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\end{eqnarray*}
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\end{solution}
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\end{subparts}
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\end{multicols}
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\part Résoudre les équations suivantes.
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\begin{multicols}{4}
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\begin{subparts}
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\Block{set e = Equation.random("x + _ = _", val_min = 1, val_max = 100)}
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\subpart $\Var{e}$
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\begin{solution}
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\begin{align*}
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\Block{for i in e.solve()} \Var{i[0]} &= \Var{i[1]} \\ \Block{endfor}
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\end{align*}
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\end{solution}
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\Block{set e = Equation.random("y - _ = _", val_min = 1, val_max = 100)}
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\subpart $\Var{e}$
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\begin{solution}
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\begin{align*}
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\Block{for i in e.solve()} \Var{i[0]} &= \Var{i[1]} \\ \Block{endfor}
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\end{align*}
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\end{solution}
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\Block{set e = Equation.random("_x = _")}
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\subpart $\Var{e}$
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\begin{solution}
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\begin{align*}
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\Block{for i in e.solve()} \Var{i[0]} &= \Var{i[1]} \\ \Block{endfor}
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\end{align*}
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\end{solution}
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\Block{set e = Equation.random("_x = _/_", val_min = 2, val_max = 20)}
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\subpart $\Var{e}$
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\begin{solution}
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\begin{align*}
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\Block{for i in e.solve()} \Var{i[0]} &= \Var{i[1]} \\ \Block{endfor}
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\end{align*}
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\end{solution}
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\end{subparts}
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\end{multicols}
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\end{parts}
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