Quiz — synth 14M2011-2012.pdf

Question 1 sur 10 20:00

[{"id":4041,"question":"Quelle est la solution de l'équation du second degré x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les solutions sont obtenues en factorisant l'équation : (x - 2)(x - 3) = 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\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":4042,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x).","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":4043,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"1","option_b":"0","option_c":"-1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\", \"b\": \"0\", \"c\": \"-1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":4044,"question":"La dérivée de la fonction f(x) = sin(x) est :","option_a":"cos(x)","option_b":"-cos(x)","option_c":"tan(x)","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de sin(x) est cos(x), selon les règles de dérivation des fonctions trigonométriques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"cos(x)\", \"b\": \"-cos(x)\", \"c\": \"tan(x)\", \"d\": \"1\"}}","_debug_options_count":4},{"id":4045,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général :","option_a":"uₙ = 3 + 2n","option_b":"uₙ = 3 * 2ⁿ","option_c":"uₙ = 3 * n²","option_d":"uₙ = 2 * 3ⁿ","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le terme général d'une suite géométrique est uₙ = u₀ * qⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"uₙ = 3 + 2n\", \"b\": \"uₙ = 3 * 2ⁿ\", \"c\": \"uₙ = 3 * n²\", \"d","_debug_options_count":4},{"id":4046,"question":"L'intégrale ∫₀¹ x² dx est égale à :","option_a":"1\/3","option_b":"1","option_c":"0","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de x² est x³\/3. Évaluée entre 0 et 1, cela donne 1\/3 - 0 = 1\/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\": \"1\/3\", \"b\": \"1\", \"c\": \"0\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":4047,"question":"Deux droites parallèles dans l'espace ont toujours le même vecteur directeur.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Des droites parallèles partagent un vecteur directeur proportionnel.","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":4048,"question":"La limite de la fonction f(x) = (2x² + 3x - 1)\/(x² + 1) quand x tend vers l'infini est :","option_a":"0","option_b":"2","option_c":"∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient 2 + 3\/x - 1\/x², qui tend vers 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"∞\", \"d\": \"1\"}}","_debug_options_count":4},{"id":4049,"question":"Quel est le déterminant d'une matrice triangulaire supérieure ?","option_a":"La somme des éléments diagonaux","option_b":"Le produit des éléments diagonaux","option_c":"0","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le déterminant d'une matrice triangulaire est le produit des éléments de sa diagonale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"La somme des éléments diagonaux\", \"b\": \"Le produit des élémen","_debug_options_count":4},{"id":4050,"question":"La fonction f(x) = eˣ est-elle convexe sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée seconde de eˣ est eˣ \u003E 0, donc la fonction est convexe.","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}]