Quiz — Corrigé rattrapage 2009-2010 .pdf

Question 1 sur 10 20:00

[{"id":19399,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"f'(x) = 6x - 5","option_b":"f'(x) = 3x - 5","option_c":"f'(x) = 6x² - 5x","option_d":"f'(x) = 6x - 5x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x - 5.","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) = 6x - 5\", \"b\": \"f'(x) = 3x - 5\", \"c\": \"f'(x) = 6x² - 5x\",","_debug_options_count":4},{"id":19400,"question":"Soit une suite géométrique de premier terme u₀ = 4 et de raison q = 2. Quelle est la valeur de u₃ ?","option_a":"8","option_b":"16","option_c":"32","option_d":"64","option_e":"","option_f":"","bonne_reponse":"c","explication":"La formule d'une suite géométrique est uₙ = u₀ * qⁿ. Donc u₃ = 4 * 2³ = 4 * 8 = 32.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"8\", \"b\": \"16\", \"c\": \"32\", \"d\": \"64\"}}","_debug_options_count":4},{"id":19401,"question":"Vrai ou Faux ? La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle, notée exp(x) ou eˣ, prend toujours des valeurs strictement positives pour tout x réel.","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":19402,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x → +∞, on divise chaque terme par x² : f(x) ≈ (2x²\/x²) = 2. La limite est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":19403,"question":"Vrai ou Faux ? Si deux événements A et B sont indépendants, alors P(A ∩ B) = P(A) * P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux événements sont indépendants si et seulement si P(A ∩ B) = P(A) * P(B).","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":19404,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x³ - 2x + 1 au point d'abscisse x = 1 ?","option_a":"y = x - 1","option_b":"y = 3x - 3","option_c":"y = x + 1","option_d":"y = 3x + 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La tangente a pour équation y = f'(a)(x - a) + f(a). Ici, f'(x) = 3x² - 2, f'(1) = 1, f(1) = 0. Donc y = 1*(x - 1) + 0 = x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"y = x - 1\", \"b\": \"y = 3x - 3\", \"c\": \"y = x + 1\", \"d\": \"y = 3x + 1","_debug_options_count":4},{"id":19405,"question":"Soit une variable aléatoire X suivant une loi normale N(μ, σ²). Que vaut P(X ≤ μ) ?","option_a":"0,5","option_b":"0","option_c":"1","option_d":"σ","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale centrée sur μ, la probabilité que X soit inférieure ou égale à μ est de 0,5 (symétrie de la courbe).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,5\", \"b\": \"0\", \"c\": \"1\", \"d\": \"σ\"}}","_debug_options_count":4},{"id":19406,"question":"Vrai ou Faux ? Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0 (par définition de l'orthogonalité).","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":19407,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 5 ?","option_a":"x \u003E 12","option_b":"x \u003C 12","option_c":"x \u003E 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant, on obtient x \u003E 12. Il faut donc soustraire 2x des deux côtés et ajouter 7.","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 \u003E 12\", \"b\": \"x \u003C 12\", \"c\": \"x \u003E 2\", \"d\": \"x \u003C 2\"}}","_debug_options_count":4},{"id":19408,"question":"Vrai ou Faux ? La fonction logarithme népérien est définie pour tout nombre réel strictement positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0 (domaine de définition).","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}]