Interprétation

L'algorithmique - Mathématiques Complémentaire

Exercice 1 : Resultat de boucle Tant que (reste de division)

On considère l'algorithme ci-dessous :

Tant que \(a \gt b\) :

\(a\) ← \(a - b\)

Si \(a=27\) et \(b=12\), quelle est la valeur finale de \(a\) ?

Exercice 2 : Etapes avec boucle Pour

On considère l'algorithme ci-dessous :

\(S\) ← \(0\)
Pour \(i\) allant de \(0\) à \(N\) :
\(S\) ← \(3 + S + i\)

Faire fonctionner l'algorithme précédent pour \(N=4\) et résumer les résultats obtenus à chaque étape dans le tableau ci-dessous.

Exercice 3 : Etapes avec Si/Sinon

On considère l'algorithme ci-dessous :

\(b\) ← \(8 + a\)
\(c\) ← \(9 \times a\)
\(a\) ← \(-8 + a\)
Si \(b \gt c\) :
\(b\) ← \(a + c\)
Sinon 
\(b\) ← \(a \times b\)

Faire fonctionner l'algorithme précédent pour \(a=1\) et résumer les résultats obtenus à chaque étape dans le tableau ci-dessous.

Exercice 4 : Initiation - Test simple et géométrie

On considère l'algorithme ci-dessous :

Tracer une droite \((d)\)
Choisir une forme géométrique au hasard
Si la forme choisie est un triangle :
Tracer un triangle \(ABC\)
Sinon 
Tracer un rectangle \(ABCD\)
Tracer le symétrique de la forme par rapport à la droite \((d)\)

Trouver parmi les figures suivantes, celles qui ont pu être tracées avec cet algorithme.

1.

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2.

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3.

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4.

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Exercice 5 : Initiation - Trois variables, deux lectures, un calcul

On considère l'algorithme ci-dessous :

\(N\) ← \(8 \times a + 8 \times b\)

Si \(a=7\) et \(b=7\), quelle est la valeur finale de \(N\) ?

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