Exercice type Brevet de Mathématiques
Programme A
Choisir un nombre.
Prendre le carré du nombre choisi.
Multiplier le résultat par 2.
Ajouter le quadruple du nombre de départ.
Soustraire 3 au résultat.
Programme B
{"options": {"blockly": {"readOnly": true}, "blocks": {"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"}, "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_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"}]}, "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}]}}}, "ast": [[{"type": "base_start", "deletable": false, "editable": false}, {"type": "base_setvar", "value": {"type": "simple_input_output_readnumber"}, "var_name": "nombre choisi"}, {"type": "base_setvar", "value": {"type": "base_simplecalculus", "value_1": {"type": "base_varvalue", "var_name": "nombre choisi"}, "value_2": {"type": "base_numberinput", "value": 3.0}, "op": "PLUS"}, "var_name": "r\u00e9sultat 1"}, {"type": "base_setvar", "value": {"type": "base_simplecalculus", "value_1": {"type": "base_varvalue", "var_name": "nombre choisi"}, "value_2": {"type": "base_numberinput", "value": 4.0}, "op": "MINUS"}, "var_name": "r\u00e9sultat 2"}, {"type": "simple_input_output_print", "value": {"type": "base_simplecalculus", "value_1": {"type": "base_varvalue", "var_name": "r\u00e9sultat 1"}, "value_2": {"type": "base_varvalue", "var_name": "r\u00e9sultat 2"}, "op": "TIMES"}}]]}
1. a. Calculer le résultat du programme A si on choisit \(5\) comme nombre de départ.
b. Calculer le résultat du programme B si on choisit \(-10\) comme nombre de départ.
2. On choisit un nombre quelconque \(x\) comme nombre de départ.
a. Parmi les trois propositions ci-dessous, sélectionner l'expression qui donne le résultat obtenu par
le programme B.
b. Exprimer en fonction de \(x\) le résultat obtenu avec le programme A.
