Algorithmique du cycle 4 - 4e

Niveau 2 : variables

Exercice 1 : Afficher une table de multiplication (boucle et variables)

Écrire un algorithme qui permet d'afficher les tables de multiplications.
Le programme doit commencer par demander le nombre de la table à afficher puis les 10 valeurs de la tables (la multiplication de ce nombre par les nombres de 1 à 10 compris).
Par exemple si l'utilisateur rentre \(8\), le programme doit afficher :

\(8\)
\(16\)
\(24\)
\(32\)
\(40\)
\(48\)
\(56\)
\(64\)
\(72\)
\(80\)

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Exercice 2 : Calcul d'un côté dans une figure de Thales

Compléter le programme suivant permettant de trouver la longueur \( AE \) connaissant \( AB \), \( AC \) et \( AD \) dans la figure de Thales suivante :

Par exemple si l'utilisateur rentre \( AB=10 \), \( AC=10 \) et \( AD=5 \), votre programme doit afficher en sortie la valeur de \( AE \), soit \( 5 \)

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Exercice 3 : Utiliser Pythagore pour calculer l'hypoténuse (niv 1)

Soit ABC un triangle rectangle en A. Écrire un algorithme capable de calculer la longueur du segment bleu :

Votre algorithme doit afficher les mêmes résultats pour les exemples suivants :

pour segment n°1 = 32, segment n°2 = 24 on affiche 40.
pour segment n°1 = 15, segment n°2 = 20 on affiche 25.

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Exercice 4 : Additionner deux fractions (dénominateurs différents, sans simplication, niv 2)

Écrire un algorithme capable de calculer la somme de deux fractions. Il donnera le résultat sous la forme d'une fraction en affichant le numérateur puis «--» puis le dénominateur.
\[ \frac{\mbox{num 1}}{\mbox{denom 1}} + \frac{\mbox{num 2}}{\mbox{denom 2}} \]
Votre algorithme doit afficher les mêmes résultats pour les exemples suivants :

pour :
- num 1 = 2
- num 2 = 6
- denom 1 = 5
- denom 2 = 8
on affiche « 46 » puis «--» puis « 40 ».
pour :
- num 1 = 3
- num 2 = 7
- denom 1 = 6
- denom 2 = 2
on affiche « 48 » puis «--» puis « 12 ».

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Exercice 5 : Utiliser Pythagore pour calculer un côté (niv 2)

Soit ABC un triangle rectangle en A. Écrire un algorithme capable de calculer la longueur du segment bleu :

Votre algorithme doit afficher les mêmes résultats pour les exemples suivants :

pour segment n°1 = 21, segment n°2 = 29 on affiche 20.
pour segment n°1 = 25, segment n°2 = 20 on affiche 15.

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