Quiz — Lycée Pilote Ariana - DS 3 2012.pdf

Question 1 sur 10 20:00

[{"id":7125,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) + ln(x) ?","option_a":"A: 2e^(2x) + 1\/x","option_b":"B: e^(2x) + 1\/x","option_c":"C: 2e^(2x) - 1\/x","option_d":"D: e^(2x) - 1\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(2x) est 2e^(2x) (dérivée de e^u = u'e^u) et celle de ln(x) est 1\/x. La somme des dérivées donne 2e^(2x) + 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A: 2e^(2x) + 1\/x\", \"b\": \"B: e^(2x) + 1\/x\", \"c\": \"C: 2e^(2x) - 1\/x","_debug_options_count":4},{"id":7126,"question":"La suite définie par u_n = (n^2 + 1)\/n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite u_n = n + 1\/n tend vers +∞ quand n tend vers +∞, donc elle est divergente.","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":7127,"question":"Quel est le résultat de l'intégrale ∫(3x^2 + 2x) dx entre 0 et 1 ?","option_a":"A: 1","option_b":"B: 2","option_c":"C: 3","option_d":"D: 4","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 3x^2 est x^3 et celle de 2x est x^2. Évaluée entre 0 et 1, cela donne (1 + 1) - (0 + 0) = 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\": \"A: 1\", \"b\": \"B: 2\", \"c\": \"C: 3\", \"d\": \"D: 4\"}}","_debug_options_count":4},{"id":7128,"question":"Dans une loi normale centrée réduite, quelle est la probabilité P(-1 ≤ Z ≤ 1) ?","option_a":"A: 0.3413","option_b":"B: 0.6826","option_c":"C: 0.9544","option_d":"D: 0.9974","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une loi normale centrée réduite, P(-1 ≤ Z ≤ 1) ≈ 0.6826, soit environ 68.26%.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A: 0.3413\", \"b\": \"B: 0.6826\", \"c\": \"C: 0.9544\", \"d\": \"D: 0.9974\"}","_debug_options_count":4},{"id":7129,"question":"Le déterminant d'une matrice triangulaire est égal au produit des éléments diagonaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette propriété est vraie pour toute matrice triangulaire (supérieure ou inférieure).","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":7130,"question":"Quelle est la limite de (sin(x)\/x) quand x tend vers 0 ?","option_a":"A: 0","option_b":"B: 1","option_c":"C: +∞","option_d":"D: -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une limite fondamentale : lim(x→0) sin(x)\/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\": \"A: 0\", \"b\": \"B: 1\", \"c\": \"C: +∞\", \"d\": \"D: -1\"}}","_debug_options_count":4},{"id":7131,"question":"Un événement A a une probabilité de 0.4 et un événement B une probabilité de 0.5. Si A et B sont indépendants, quelle est P(A ∩ B) ?","option_a":"A: 0.2","option_b":"B: 0.4","option_c":"C: 0.5","option_d":"D: 0.9","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A: 0.2\", \"b\": \"B: 0.4\", \"c\": \"C: 0.5\", \"d\": \"D: 0.9\"}}","_debug_options_count":4},{"id":7132,"question":"La fonction f(x) = x^3 - 3x + 2 admet-elle un point d'inflexion en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée seconde f''(x) = 6x s'annule en x = 0, pas en x = 1. Donc pas de point d'inflexion en x = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7133,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"A: y = Ce^(-2x)","option_b":"B: y = Ce^(2x)","option_c":"C: y = Cx^2","option_d":"D: y = C\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation y' + 2y = 0 est une équation différentielle linéaire du premier ordre. Sa solution générale est y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A: y = Ce^(-2x)\", \"b\": \"B: y = Ce^(2x)\", \"c\": \"C: y = Cx^2\", \"d\":","_debug_options_count":4},{"id":7134,"question":"Dans un repère orthonormé, quelle est la distance entre les points A(1, 2, 3) et B(4, 5, 6) ?","option_a":"A: 3√3","option_b":"B: √27","option_c":"C: 3","option_d":"D: 9","option_e":"","option_f":"","bonne_reponse":"b","explication":"La distance est √[(4-1)² + (5-2)² + (6-3)²] = √(9 + 9 + 9) = √27 = 3√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\": \"A: 3√3\", \"b\": \"B: √27\", \"c\": \"C: 3\", \"d\": \"D: 9\"}}","_debug_options_count":4}]