Quiz — 1614922586_91492_Exercice 1 _ exemples d'enregistrements_ok.pdf

Question 1 sur 10 20:00

[{"id":47438,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2","option_d":"D. 6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme. Pour 3x², la dérivée est 6x ; pour 2x, elle est 2 ; et la constante -5 a une dérivée nulle.","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. 6x + 2\", \"b\": \"B. 3x + 2\", \"c\": \"C. 6x² + 2\", \"d\": \"D. 6x + 2","_debug_options_count":4},{"id":47439,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est bien arithmétique.","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":47440,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x) \/ (2x² - 1) quand x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 3\/2","option_c":"C. 1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour les fonctions rationnelles, la limite à l'infini est le rapport des coefficients des termes de plus haut degré. Ici, 3x² \/ 2x² = 3\/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. 0\", \"b\": \"B. 3\/2\", \"c\": \"C. 1\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":47441,"question":"Si P(A) = 0.4 et P(B) = 0.5, et que A et B sont indépendants, quelle est P(A ∩ B) ?","option_a":"A. 0.2","option_b":"B. 0.9","option_c":"C. 0.1","option_d":"D. 0.4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour deux 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. 0.9\", \"c\": \"C. 0.1\", \"d\": \"D. 0.4\"}}","_debug_options_count":4},{"id":47442,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante entre -1 et 1, donc elle n'est pas 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":47443,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"A. x = 2","option_b":"B. x = 1","option_c":"C. x = 3","option_d":"D. x = 0","option_e":"","option_f":"","bonne_reponse":"b","explication":"8 peut s'écrire 2³. Donc 2^(x+1) = 2³ ⇒ x + 1 = 3 ⇒ x = 2. Cependant, l'équation donnée est 2^(x+1) = 8, donc x + 1 = 3 ⇒ x = 2. La bonne réponse est A.","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. x = 2\", \"b\": \"B. x = 1\", \"c\": \"C. x = 3\", \"d\": \"D. x = 0\"}}","_debug_options_count":4},{"id":47444,"question":"Un dé équilibré est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"A. 1\/6","option_b":"B. 1\/36","option_c":"C. 1\/12","option_d":"D. 1\/18","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'obtenir un 6 en un lancer est 1\/6. Pour deux lancers indépendants, c'est (1\/6) × (1\/6) = 1\/36.","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\/6\", \"b\": \"B. 1\/36\", \"c\": \"C. 1\/12\", \"d\": \"D. 1\/18\"}}","_debug_options_count":4},{"id":47445,"question":"La fonction f(x) = ln(x) est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le logarithme naturel ln(x) n'est défini que pour x \u003E 0. Donc f(0) n'existe pas.","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":47446,"question":"Quelle est la primitive de f(x) = 4x³ qui s'annule en x = 1 ?","option_a":"A. x⁴ + C","option_b":"B. x⁴ - 1","option_c":"C. 4x⁴ + C","option_d":"D. x⁴ - 3","option_e":"","option_f":"","bonne_reponse":"b","explication":"La primitive de 4x³ est x⁴ + C. Pour qu'elle s'annule en x = 1, on a 1⁴ + C = 0 ⇒ C = -1. Donc la primitive est x⁴ - 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. x⁴ + C\", \"b\": \"B. x⁴ - 1\", \"c\": \"C. 4x⁴ + C\", \"d\": \"D. x","_debug_options_count":4},{"id":47447,"question":"Si une fonction est continue sur [a, b] et dérivable sur ]a, b[, alors elle admet un extremum sur [a, b].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est le théorème des bornes atteintes, mais il ne garantit pas un extremum. Par exemple, f(x) = x³ sur [-1, 1] est continue et dérivable, mais n'a pas d'extremum.","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}]