184 lines
6.2 KiB
TeX
184 lines
6.2 KiB
TeX
\documentclass[a4paper,10pt]{article}
|
|
\usepackage{myXsim}
|
|
\usepackage{amsmath}
|
|
|
|
\author{Benjamin Bertrand}
|
|
\title{Information chiffrée 1 - Exercices}
|
|
\date{Octobre 2021}
|
|
|
|
\xsimsetup{
|
|
solution/print = false
|
|
}
|
|
|
|
\begin{document}
|
|
|
|
\begin{exercise}[subtitle={Réductions}]
|
|
Développer puis réduire les expressions suivantes
|
|
\begin{multicols}{3}
|
|
\begin{enumerate}[label={\Alph*=}]
|
|
%- set a = Expression.random("{a}x + {b} + {c}x + {d}")
|
|
\item $\Var{a}$
|
|
%- set b = Expression.random("{a}x + {b} + {c}x + {d}")
|
|
\item $\Var{b}$
|
|
|
|
%- set c = Expression.random("{a}x^2 + {b} + {c}x^2 + {d} + {d}x + {e}")
|
|
\item $\Var{c}$
|
|
%- set d = Expression.random("{a}x + {b} + {c}x + {d} + {e}x + {f}x")
|
|
\item $\Var{d}$
|
|
|
|
%- set e = Expression.random("{a}*x + {b} + {c}x + {d}x + {e}", min_max=(2, 20))
|
|
\item $\Var{e}$
|
|
%- set f = Expression.random("{a}x + {b} + {c}x + {d}", conditions=["a+c==0"])
|
|
\item $\Var{f}$
|
|
\end{enumerate}
|
|
\end{multicols}
|
|
\end{exercise}
|
|
|
|
\begin{solution}
|
|
\begin{multicols}{3}
|
|
\begin{flalign*}
|
|
A =& \Var{a.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
B =& \Var{b.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
C =& \Var{c.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
D =& \Var{d.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
E =& \Var{e.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
F =& \Var{f.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\end{multicols}
|
|
\end{solution}
|
|
|
|
\begin{exercise}[subtitle={Simple développement}]
|
|
Développer puis réduire les expressions suivantes
|
|
\begin{multicols}{3}
|
|
\begin{enumerate}[label={\Alph*=}]
|
|
%- set a = Expression.random("{a}*(x + {b})", rejected=[-1,0,1])
|
|
\item $\Var{a}$
|
|
%- set b = Expression.random("{a}*({c}x + {d})", rejected=[-1,0,1])
|
|
\item $\Var{b}$
|
|
%- set c = Expression.random("{a}*({c}x + {d})", rejected=[-1,0,1])
|
|
\item $\Var{c}$
|
|
|
|
%- set d = Expression.random("{c}*x*({a}x + {b})", rejected=[-1,0,1])
|
|
\item $\Var{d}$
|
|
%- set e = Expression.random("{a}*x*({b}x + {c}) + {d}", rejected=[-1,0,1])
|
|
\item $\Var{e}$
|
|
%- set f = Expression.random("{c}*x + {d}*x*({a}x + {b})", rejected=[-1,0,1])
|
|
\item $\Var{f}$
|
|
\end{enumerate}
|
|
\end{multicols}
|
|
\end{exercise}
|
|
|
|
\begin{solution}
|
|
\begin{multicols}{3}
|
|
\begin{flalign*}
|
|
A =& \Var{a.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
B =& \Var{b.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
C =& \Var{c.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
D =& \Var{d.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
E =& \Var{e.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
F =& \Var{f.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\end{multicols}
|
|
\end{solution}
|
|
|
|
\begin{exercise}[subtitle={Double développement}]
|
|
Développer puis réduire les expressions suivantes
|
|
\begin{multicols}{3}
|
|
\begin{enumerate}[label={\Alph*=}]
|
|
%- set a = Expression.random("(x + {a})*(x + {b})", rejected=[-1,0,1])
|
|
\item $\Var{a}$
|
|
%- set b = Expression.random("({a}x + {b})*({c}x + {d})", rejected=[-1,0,1])
|
|
\item $\Var{b}$
|
|
%- set c = Expression.random("({a}x + {b})*({c}x + {d})", rejected=[-1,0,1])
|
|
\item $\Var{c}$
|
|
|
|
%- set d = Expression.random("({c}*x + {d})*({a}x + {b})", rejected=[-1,0,1])
|
|
\item $\Var{d}$
|
|
%- set e = Expression.random("({b}x + {c})^2", rejected=[-1,0,1])
|
|
\item $\Var{e}$
|
|
%- set f = Expression.random("({a}x + {b})^2", rejected=[-1,0,1])
|
|
\item $\Var{f}$
|
|
\end{enumerate}
|
|
\end{multicols}
|
|
\end{exercise}
|
|
|
|
\begin{solution}
|
|
\begin{multicols}{3}
|
|
\begin{flalign*}
|
|
A =& \Var{a.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
B =& \Var{b.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
C =& \Var{c.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
D =& \Var{d.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
E =& \Var{e.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
F =& \Var{f.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\end{multicols}
|
|
\end{solution}
|
|
|
|
\begin{exercise}[subtitle={Double développement}]
|
|
Développer puis réduire les expressions suivantes
|
|
\begin{multicols}{3}
|
|
\begin{enumerate}[label={\Alph*=}]
|
|
%- set a = Expression.random("{a}*x + {c}/{b} + {c}*x + {d}/{b}", rejected=[-1,0,1])
|
|
\item $\Var{a}$
|
|
%- set b = Expression.random("{c}({a}x + {b}/{d})", rejected=[-1,0,1])
|
|
\item $\Var{b}$
|
|
%- set c = Expression.random("({a}/{b}x + {b})*({c}x + {d}/{e})", rejected=[-1,0,1])
|
|
\item $\Var{c}$
|
|
|
|
\end{enumerate}
|
|
\end{multicols}
|
|
\end{exercise}
|
|
|
|
\begin{solution}
|
|
\begin{multicols}{3}
|
|
\begin{flalign*}
|
|
A =& \Var{a.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
B =& \Var{b.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\begin{flalign*}
|
|
C =& \Var{c.simplify().explain() | join('\\\ =& ')}
|
|
\end{flalign*}
|
|
\end{multicols}
|
|
\end{solution}
|
|
|
|
\printcollection{exercise}
|
|
|
|
\newpage
|
|
|
|
\printsolutionstype{exercise}
|
|
|
|
\end{document}
|