Quiz — 67f4188603ca5_Synthèse n°3.pdf

Question 1 sur 10 20:00

[{"id":39210,"question":"Quelle est la solution de l'équation 2x + 5 = 11 ?","option_a":"x = 3","option_b":"x = 4","option_c":"x = 5","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résoudre 2x + 5 = 11 : soustraire 5 des deux côtés donne 2x = 6, puis diviser par 2 donne x = 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\": \"x = 3\", \"b\": \"x = 4\", \"c\": \"x = 5\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":39211,"question":"La fonction f(x) = x² est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [0, +∞[, donc elle n'est pas strictement croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":39212,"question":"Quel est le développement de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² - x - 6","option_c":"x² + x + 6","option_d":"x² - x + 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant (x + 3)(x - 2), on obtient x² - 2x + 3x - 6 = x² + x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + x - 6\", \"b\": \"x² - x - 6\", \"c\": \"x² + x + 6\", \"d\": \"x² -","_debug_options_count":4},{"id":39213,"question":"La somme des angles d'un triangle est toujours égale à 180° ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans un triangle, la somme des trois angles est toujours égale à 180°, c'est une propriété fondamentale de la géométrie euclidienne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":39214,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/n quand n tend vers +∞ ?","option_a":"+∞","option_b":"0","option_c":"1","option_d":"n","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = 1 + 1\/n², donc la limite est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"+∞\", \"b\": \"0\", \"c\": \"1\", \"d\": \"n\"}}","_debug_options_count":4},{"id":39215,"question":"Le théorème de Thalès s'applique-t-il uniquement dans un triangle rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Thalès s'applique à tout triangle, pas seulement aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":39216,"question":"Résoudre l'inéquation 3x - 7 ≤ 2x + 5.","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ -12","option_d":"x ≥ -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Soustraire 2x des deux côtés donne x - 7 ≤ 5, puis ajouter 7 donne x ≤ 12.","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 ≥ 12\", \"c\": \"x ≤ -12\", \"d\": \"x ≥ -12\"}}","_debug_options_count":4},{"id":39217,"question":"La médiane d'un ensemble de données est toujours égale à la moyenne ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane et la moyenne sont deux indicateurs différents : la médiane est la valeur centrale, la moyenne est la somme divisée par le nombre de données.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":39218,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"indéfini","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs orthogonaux ont un produit scalaire égal à 0, car cos(90°) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"indéfini\"}}","_debug_options_count":4},{"id":39219,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0, car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]