Control 03 Semester 02 , Géneralités sur les Fonctions (B)

📅 June 20, 2025   |   👁️ Views: 642   |   ❓ 11 questions



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%%%%%%%%%%%%%%%%%%%%%%%%%%%% Start of the exam %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\noindent
\exo{Exercice 1: (\textit{3 pts}) }\\
\hspace*{0.5cm} Déterminer le domaine de définition dans les cas suivants
\begin{questions}
  \question[3]
  ~$f(x)=\frac{2+\sqrt{x}}{x-3}$~
  \hspace*{0.5cm};\hspace*{0.5cm} ~$f(x)=\sqrt{x^2+2x-4}$~
  \hspace*{0.5cm};\hspace*{0.5cm} ~$f(x)=\frac{x^2+1}{x^2+x+1}$~
\end{questions}
\exo{Exercice 2: (\textit{17 pts}) }\\
\hspace*{0.5cm} Soit la fonction ~$f$~ définie par ~$f(x)=x^2-6x+5$~
\begin{questions}
  \question[1]
  Déterminer ~$D_f$~
  \question[2]
  Calculer ~$f(1)$~ et ~$f(-1)$~
  \question[2]
  Dresser le tableau des variations de ~$f$~ sur ~$D_f$~
  \question[2]
  Vérifier que ~$f(x)+4=(x-3)^2$~
  \question
  On pose ~$g(x)=x^2$~
  \begin{parts}
    \part[1]
    Construire ~$\mathscr{C}_g$~ dans un repère orthonormé
    \part[1]
    Donner une équation cartésienne de ~$\mathscr{C}_f$
    \part[2]
    Montrer que ~$t\left(\mathscr{C}_g\right)=\mathscr{C}_f$~ avec ~$t$~ est une
    translation d'un vecteur ~$\vec u$~ à déterminer
    \part[1]
    Déterminer la nature de ~$\mathscr{C}_f$~
    \part[2]
    Construire ~$\mathscr{C}_f$~ dans le meme repère.
  \end{parts}
  \question
  \begin{parts}
    \part[1]
    Résoudre graphiquement l'inéquation ~$f(x)<0$~
    \part[0.5]
    Donner le nombre de solutions de l'équation ~$f(x)=0$~
    \part[0.5]
    Donner le nombre de solutions de l'équation ~$f(x)=2$~
    \part[1]
    Quelles sont les valeurs du paramètre ~$m$~ pour que l'équation ~$f(x)=m$~ n'a pas de solutions
  \end{parts}
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Frequently Asked Questions

What chapters or courses does this exam cover?
This exam covers: عموميات حول الدوال العددية نسخة 2, Généralités sur les fonctions, دراسة وتمثيل الدوال الاعتيادية نسخة 2, دراسة وتمثيل الدوال الاعتيادية, الشلجم و الهذلول, عموميات حول الدوال العددية. It is designed to test understanding of these topics.

How many questions are in this exam?
The exam contains approximately 11 questions.

Is this exam aligned with the official curriculum?
Yes, it follows the tronc-commun-sciences maths guidelines.

What topics are covered in this course?
The course "Généralités sur les fonctions" covers key concepts of maths for tronc-commun-sciences. Designed to help students master the curriculum.

Is this course suitable for beginners?
Yes, the material is structured to be accessible while providing depth for advanced learners.

Are there exercises or practice problems?
Exercises are included to help you practice.

Does this course include solutions?
Solutions are available separately.


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