Quiz — correction Serie d'exercice N°4 d'algèbre.pdf

Question 1 sur 5 10:00

[{"id":764,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = -2","option_c":"x = 2","option_d":"x = -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 2x + 7, on soustrait 2x des deux côtés : x - 5 = 7, puis on ajoute 5 : x = 12. Vérifiez en remplaçant x par 12 dans l'équation initiale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 12\", \"b\": \"x = -2\", \"c\": \"x = 2\", \"d\": \"x = -12\"}}","_debug_options_count":4},{"id":765,"question":"Quelle est la forme canonique de la fonction f(x) = 2x² - 8x + 5 ?","option_a":"f(x) = 2(x - 2)² - 3","option_b":"f(x) = 2(x + 2)² - 3","option_c":"f(x) = 2(x - 2)² + 3","option_d":"f(x) = 2(x + 2)² + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique s'obtient par complétion du carré : f(x) = 2(x² - 4x) + 5 = 2[(x - 2)² - 4] + 5 = 2(x - 2)² - 8 + 5 = 2(x - 2)² - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f(x) = 2(x - 2)² - 3\", \"b\": \"f(x) = 2(x + 2)² - 3\", \"c\": \"f(x) ","_debug_options_count":4},{"id":766,"question":"Quelle est la solution de l'inéquation 5x - 3 ≤ 2x + 9 ?","option_a":"x ≤ 4","option_b":"x ≥ 4","option_c":"x \u003C 4","option_d":"x \u003E 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvez 5x - 3 ≤ 2x + 9 : soustrayez 2x (3x - 3 ≤ 9), puis ajoutez 3 (3x ≤ 12), et divisez par 3 (x ≤ 4). N'oubliez pas de représenter la solution sur une droite graduée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x ≤ 4\", \"b\": \"x ≥ 4\", \"c\": \"x \u003C 4\", \"d\": \"x \u003E 4\"}}","_debug_options_count":4},{"id":767,"question":"Quelle est l'image de -3 par la fonction f(x) = -x² + 4x - 1 ?","option_a":"f(-3) = -22","option_b":"f(-3) = 22","option_c":"f(-3) = 14","option_d":"f(-3) = -14","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculez f(-3) = -(-3)² + 4*(-3) - 1 = -9 - 12 - 1 = -22. Cette valeur représente l'ordonnée du point de la courbe d'abscisse -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f(-3) = -22\", \"b\": \"f(-3) = 22\", \"c\": \"f(-3) = 14\", \"d\": \"f(-3) =","_debug_options_count":4},{"id":768,"question":"Quelle propriété permet de résoudre l'équation (x + 1)(x - 3) = 0 ?","option_a":"Propriété des racines carrées","option_b":"Propriété du produit nul","option_c":"Propriété des fonctions affines","option_d":"Propriété des identités remarquables","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le produit (x + 1)(x - 3) est nul si et seulement si l'un des facteurs est nul : x + 1 = 0 ou x - 3 = 0, donc x = -1 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Propriété des racines carrées\", \"b\": \"Propriété du produit n","_debug_options_count":4}]