\documentclass[12pt,a4paper]{article}
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\begin{document}\everymath{\displaystyle}
	
\thispagestyle{empty}
\boxit{4pt}{Minitest 13}\rightarrowfill\quad\boxit{3pt}{$\begin{matrix}\tvi\hbox{Nom :}\hskip 4cm~\hfill\cr \tvi\hbox{Prénom :
}\hfill~\end{matrix}$}\bigskip

1) Les composantes du vecteur $\vect{AB}$ lorsque  $A(1,3)$ et $B(5,1)$\vskip 1.5cm

2) Calculer le produit scalaire $\vect{u}\cdot\vect{v}$ \vskip 0.5cm

\qquad a) lorsque $||\vect{u}|| = 3$ et $||\vect{v}|| = 5$ et $(\vect{u},\vect{v}) = \dfrac{\pi}{3}$\vskip 1.5cm

\qquad b) $\vect{u}=\begin{pmatrix}-3\cr2\end{pmatrix}$ et $\vect{v}=\begin{pmatrix}4\cr1\end{pmatrix}$\vskip 3.5cm

3) Soit $f(x) = x^2-6x+1$

\qquad a) Calculer $f'(x)$\vskip 1.5cm

\qquad b) Résoudre $f'(x) = 0$\vskip 1.5cm

\qquad c) En déduire les variations de $f$


Simplifier les expressions : 

\(\overrightarrow{AC} + \overrightarrow{CB} + \overrightarrow{BA} = \).\vskip 1.5cm

 \(\overrightarrow{AB} - \overrightarrow{CB} = \).\vskip 1.5cm

 \(\overrightarrow{AC} + \overrightarrow{CD} - \overrightarrow{AD} = \).

\newpage

\boxit{4pt}{Minitest 13}\rightarrowfill\quad\boxit{3pt}{$\begin{matrix}\tvi\hbox{Nom :}\hskip 4cm~\hfill\cr \tvi\hbox{Prénom :
		}\hfill~\end{matrix}$}\bigskip

1) Les composantes du vecteur $\vect{AB}$ lorsque $A(7,3)$ et $B(1,8)$\vskip 1.5cm

2) Calculer le produit scalaire $\vect{u}\cdot\vect{v}$ \vskip 0.5cm

\qquad a) lorsque $||\vect{u}|| = 2$ et $||\vect{v}|| = 8$ et $(\vect{u},\vect{v}) = 120$°\vskip 1.5cm

\qquad b) $\vect{u}=\begin{pmatrix}5\cr2\end{pmatrix}$ et $\vect{v}=\begin{pmatrix}-3\cr2\end{pmatrix}$\vskip 2.5cm

3) Soit $f(x) = x^2+4x+2$

\qquad a) Calculer $f'(x)$\vskip 1.5cm

\qquad b) Résoudre $f'(x) = 0$\vskip 1.5cm

\qquad c) En déduire les variations de $f$\vskip 2.5cm

Simplifier les expressions : 

\(\overrightarrow{AC} + \overrightarrow{CB} + \overrightarrow{BA} = \).\vskip 1.5cm

\(\overrightarrow{AB} - \overrightarrow{CB} = \).\vskip 1.5cm

\(\overrightarrow{AC} + \overrightarrow{CD} - \overrightarrow{AD} = \).

\end{document} 