Quiz — 62964c4a2f93e_Prototype d'Examen Bac N°7-ML.pdf

Question 1 sur 10 20:00

[{"id":30820,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5 ?","option_a":"3x² - 4x","option_b":"3x² - 4x + 5","option_c":"x³ - 4x","option_d":"2x² - 4x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynomiale s'obtient en appliquant la règle de dérivation : f'(x) = 3x² - 4x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3x² - 4x\", \"b\": \"3x² - 4x + 5\", \"c\": \"x³ - 4x\", \"d\": \"2x² - 4","_debug_options_count":4},{"id":30821,"question":"Soit une variable aléatoire X suivant une loi normale N(0,1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"0.6826","option_b":"0.8413","option_c":"0.9544","option_d":"0.9974","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une loi normale centrée réduite, P(X ≤ 1) ≈ 0.8413, valeur lue dans les tables de la loi normale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.6826\", \"b\": \"0.8413\", \"c\": \"0.9544\", \"d\": \"0.9974\"}}","_debug_options_count":4},{"id":30822,"question":"L'équation complexe z² + 4z + 13 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = 16 - 52 = -36 \u003C 0, donc les solutions sont complexes conjuguées et non réelles.","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":30823,"question":"Quelle est l'intégrale indéfinie de f(x) = 2x + 3 ?","option_a":"x² + 3x + C","option_b":"x² + 3x","option_c":"2x² + 3x + C","option_d":"x² + Cx + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x est x² et celle de 3 est 3x, avec une constante d'intégration C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + 3x + C\", \"b\": \"x² + 3x\", \"c\": \"2x² + 3x + C\", \"d\": \"x² +","_debug_options_count":4},{"id":30824,"question":"Dans un triangle ABC, si AB = 5, AC = 7 et BC = 8, quelle est la mesure de l'angle B ?","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"c","explication":"En utilisant la loi des cosinus : cos(B) = (AB² + BC² - AC²)\/(2·AB·BC) = (25 + 64 - 49)\/80 = 0.5, donc B = 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"30°\", \"b\": \"45°\", \"c\": \"60°\", \"d\": \"90°\"}}","_debug_options_count":4},{"id":30825,"question":"La fonction f(x) = e^x est-elle toujours croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = e^x \u003E 0 pour tout x ∈ ℝ, donc la fonction est strictement croissante.","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":30826,"question":"Quelle est la limite de (sin(x))\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n'existe pas","option_e":"","option_f":"","bonne_reponse":"b","explication":"Par définition, lim(x→0) sin(x)\/x = 1, résultat fondamental en analyse mathématique.","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\": \"1\", \"c\": \"∞\", \"d\": \"n'existe pas\"}}","_debug_options_count":4},{"id":30827,"question":"Soit une suite définie par u₀ = 2 et uₙ₊₁ = 3uₙ - 1. Que vaut u₂ ?","option_a":"11","option_b":"14","option_c":"17","option_d":"20","option_e":"","option_f":"","bonne_reponse":"c","explication":"u₁ = 3·2 - 1 = 5, u₂ = 3·5 - 1 = 14. La réponse correcte est 14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"11\", \"b\": \"14\", \"c\": \"17\", \"d\": \"20\"}}","_debug_options_count":4},{"id":30828,"question":"Le produit scalaire de deux vecteurs orthogonaux est-il toujours nul ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs sont orthogonaux si et seulement si leur produit scalaire est nul.","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":30829,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce^(-2x)","option_b":"y = Ce^(2x)","option_c":"y = Cx + C","option_d":"y = Cx² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale d'une équation différentielle linéaire du premier ordre 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\": \"y = Ce^(-2x)\", \"b\": \"y = Ce^(2x)\", \"c\": \"y = Cx + C\", \"d\": \"y = C","_debug_options_count":4}]