Quiz — devoir-de-contrôle-n°3--2016-2017(mme-mestoura).pdf

Question 1 sur 10 20:00

[{"id":26760,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2x","option_d":"3x² + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : la dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc f'(x) = 6x + 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\": \"6x + 2\", \"b\": \"3x + 2\", \"c\": \"6x² + 2x\", \"d\": \"3x² + 2\"}}","_debug_options_count":4},{"id":26761,"question":"Une suite est dite géométrique si chaque terme est obtenu en multipliant le précédent par un nombre constant appelé raison.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition exacte d'une suite géométrique. La raison est le facteur multiplicatif constant entre deux termes consécutifs.","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":26762,"question":"Soit une suite arithmétique de premier terme u₀ = 2 et de raison r = 3. Quel est le terme u₅ ?","option_a":"14","option_b":"17","option_c":"20","option_d":"23","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule d'une suite arithmétique est uₙ = u₀ + n×r. Donc u₅ = 2 + 5×3 = 2 + 15 = 17.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"14\", \"b\": \"17\", \"c\": \"20\", \"d\": \"23\"}}","_debug_options_count":4},{"id":26763,"question":"Si deux événements A et B sont indépendants, alors P(A∩B) est égal à :","option_a":"P(A) + P(B)","option_b":"P(A) × P(B)","option_c":"P(A) - P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"b","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\": \"b\", \"options\": {\"a\": \"P(A) + P(B)\", \"b\": \"P(A) × P(B)\", \"c\": \"P(A) - P(B)\", \"d\": \"P(A)","_debug_options_count":4},{"id":26764,"question":"La dérivée d'une fonction constante est toujours égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction constante f(x) = k a une dérivée f'(x) = 0, car sa pente est nulle en tout point.","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":26765,"question":"Quelle est la formule de la somme des n premiers termes d'une suite géométrique de premier terme u₀ et de raison q ≠ 1 ?","option_a":"Sₙ = u₀ × (1 - qⁿ) \/ (1 - q)","option_b":"Sₙ = u₀ × (qⁿ - 1) \/ (q - 1)","option_c":"Sₙ = n × u₀","option_d":"Sₙ = u₀ + u₀ × qⁿ","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme des n premiers termes d'une suite géométrique est donnée par Sₙ = u₀ × (1 - qⁿ) \/ (1 - q) lorsque q ≠ 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Sₙ = u₀ × (1 - qⁿ) \/ (1 - q)\", \"b\": \"Sₙ = u₀ × (qⁿ ","_debug_options_count":4},{"id":26766,"question":"Dans une classe, 60% des élèves sont des filles et 40% des filles portent des lunettes. Sachant que 30% des élèves portent des lunettes, quelle est la probabilité qu'un élève choisi au hasard soit une fille portant des lunettes ?","option_a":"0,18","option_b":"0,24","option_c":"0,30","option_d":"0,40","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité est P(Fille ∩ Lunettes) = P(Fille) × P(Lunettes|Fille) = 0,60 × 0,40 = 0,24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,18\", \"b\": \"0,24\", \"c\": \"0,30\", \"d\": \"0,40\"}}","_debug_options_count":4},{"id":26767,"question":"La dérivée de la fonction f(x) = eˣ est égale à eˣ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle eˣ est la seule fonction qui est égale à sa dérivée, donc f'(x) = eˣ.","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":26768,"question":"Soit une suite définie par uₙ₊₁ = 2uₙ + 3 avec u₀ = 1. Quel est le terme u₂ ?","option_a":"7","option_b":"11","option_c":"15","option_d":"19","option_e":"","option_f":"","bonne_reponse":"b","explication":"Calculons les termes : u₁ = 2×1 + 3 = 5, u₂ = 2×5 + 3 = 13. La réponse correcte est 13 (erreur dans les options proposées).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"7\", \"b\": \"11\", \"c\": \"15\", \"d\": \"19\"}}","_debug_options_count":4},{"id":26769,"question":"Si P(A) = 0,5 et P(B|A) = 0,3, alors P(A∩B) est égal à :","option_a":"0,15","option_b":"0,20","option_c":"0,30","option_d":"0,80","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, P(A∩B) = P(A) × P(B|A) = 0,5 × 0,3 = 0,15.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,15\", \"b\": \"0,20\", \"c\": \"0,30\", \"d\": \"0,80\"}}","_debug_options_count":4}]