Niveau 2 : variables

Algorithmique du cycle 4 - Mathématiques 3e

Exercice 1 : Comprendre la notion de variable

L'algorithme suivant représente un calcul :
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Vous pouvez tenter de le modifier pour le comprendre.

{"options": {"runner": {"environment": "input/output", "test_cases": [[0, -4.0], [1, -3.6666666666666665], [2, -3.3333333333333335], [3, -3.0], [4, -2.6666666666666665], [5, -2.3333333333333335], [6, -2.0], [7, -1.6666666666666667], [8, -1.3333333333333333], [9, -1.0], [10, -0.6666666666666666], [11, -0.3333333333333333], [12, 0.0], [13, 0.3333333333333333], [14, 0.6666666666666666], [15, 1.0], [16, 1.3333333333333333], [17, 1.6666666666666667], [18, 2.0], [19, 2.3333333333333335]]}, "blocks": {"base_varvalue": {"output": true, "colour": 330, "tooltip": "Fourni la valeur d'une variable", "inputs": [{"type": "dummy_input", "fields": [{"name": "var_name", "default": "x", "type": "variable"}], "align": "left"}]}, "simple_input_output_print": {"previous_statement": true, "next_statement": true, "colour": 160, "tooltip": "Afficher une valeur", "inputs": [{"type": "value_input", "fields": [{"text": "Afficher", "type": "text"}], "align": "left", "name": "value", "check": null}]}, "base_simplecalculus": {"output": "Number", "colour": 260, "tooltip": "Effectue un calcul simple", "inputs": [{"type": "value_input", "fields": [], "align": "left", "name": "value_1", "check": "Number"}, {"type": "dummy_input", "fields": [{"name": "op", "values": [["+", "PLUS"], ["-", "MINUS"], ["\u00d7", "TIMES"], ["\u00f7", "DIV"]], "type": "dropdown"}], "align": "left"}, {"type": "value_input", "fields": [], "align": "left", "name": "value_2", "check": "Number"}], "inline": true}, "simple_input_output_readnumber": {"output": true, "colour": 160, "tooltip": "Demander un nombre \u00e0 l'utilisateur", "inputs": [{"type": "dummy_input", "fields": [{"text": "demander un nombre", "type": "text"}], "align": "left"}]}, "base_numberinput": {"output": "Number", "colour": 260, "tooltip": "Fourni un nombre", "inputs": [{"type": "dummy_input", "fields": [{"name": "value", "default": 0.0, "type": "number_input"}], "align": "left"}]}, "base_start": {"next_statement": true, "colour": 65, "tooltip": "D\u00e9marrage de l'algorithme", "inputs": [{"type": "dummy_input", "fields": [{"text": "Au d\u00e9marrage", "type": "text"}], "align": "left"}], "creatable": false, "on_event": "start"}, "base_setvar": {"previous_statement": true, "next_statement": true, "colour": 330, "tooltip": "Affecter une valeur \u00e0 une variable", "inputs": [{"type": "value_input", "fields": [{"text": "mettre", "type": "text"}, {"name": "var_name", "default": "x", "type": "variable"}, {"text": "\u00e0", "type": "text"}], "align": "left", "name": "value", "check": null}]}}, "toolbox": [{"type": "base_numberinput"}, {"type": "base_setvar"}, {"type": "base_simplecalculus"}, {"type": "base_varvalue"}, {"type": "simple_input_output_print"}, {"type": "simple_input_output_readnumber"}]}, "ast": [[{"type": "base_start", "deletable": false, "editable": false}, {"type": "base_setvar", "value": {"type": "simple_input_output_readnumber"}, "var_name": "x"}, {"type": "base_setvar", "value": {"type": "base_simplecalculus", "value_1": {"type": "base_simplecalculus", "value_1": {"type": "base_varvalue", "var_name": "x"}, "value_2": {"type": "base_numberinput", "value": 3.0}, "op": "DIV"}, "value_2": {"type": "base_numberinput", "value": 4.0}, "op": "MINUS"}, "var_name": "total"}, {"type": "simple_input_output_print", "value": {"type": "base_varvalue", "var_name": "total"}}]]}

On choisit \(x\) comme nombre d'entrée.
Indiquer l'expression littérale simplifiée donnant \( total \).
(Exemple de réponse : \(0.01 \times x + 1\))

Exercice 2 : 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 \(6\), le programme doit afficher :

\(6\)
\(12\)
\(18\)
\(24\)
\(30\)
\(36\)
\(42\)
\(48\)
\(54\)
\(60\)

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Exercice 3 : Programmer le calcul d'une longueur (petit côté) avec Thalès (emboîté), données (directes), inconnue (directe)

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

Par exemple si l'utilisateur rentre \( AB=10 \), \( AC=9 \) et \( AD=3 \), votre programme doit afficher en sortie la valeur de \( AE \), soit \( 2\mbox{,}7 \)

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Exercice 4 : Déplacement véhicule - Décrémentation de variables (2/5)

Votre véhicule est équipé d'un réservoir contenant 20 litres d'essence, plein au démarrage, et il consomme de l'essence à chaque déplacement.

Nous allons modifier notre compteur pour qu'il diminue à chaque déplacement. Une variable peut être réutilisée pour faire un calcul avec sa valeur. Par exemple le bloc fournit la valeur actuellement mémorisée par la variable soustrait de 1. Combiné avec la balise , il est donc possible de modifier une variable en fonction de sa valeur précédente.

Modifier l'algorithme pour initialiser la variable et diminuer de 1 le niveau d'essence après chaque déplacement d'une case du véhicule.

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Exercice 5 : Initiation - Passer d'une instruction à une opération mathématiques

On considère l'algorithme ci-dessous :

Demander un nombre à l'utilisateur.
Ajouter 9
Multiplier par 8
Afficher le résultat

Si l'on note \(x\) le nombre fourni par l'utilisateur, donner l'expression du calcul réalisé par cet algorithme.

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