Quiz — Examen bac blanc - Bouhouch.pdf

Question 1 sur 10 20:00

[{"id":24414,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A) 2","option_b":"B) 0","option_c":"C) -∞","option_d":"D) +∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d’un quotient de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 2x²\/x² = 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) 2\", \"b\": \"B) 0\", \"c\": \"C) -∞\", \"d\": \"D) +∞\"}}","_debug_options_count":4},{"id":24415,"question":"Soit une suite (Un) définie par U0 = 1 et Un+1 = 2Un + 3. Cette suite est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite est croissante car Un+1 - Un = Un + 3 \u003E 0 pour tout n ≥ 0.","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":24416,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 1) ?","option_a":"A) f'(x) = 6x\/(3x² + 1)","option_b":"B) f'(x) = 3x\/(3x² + 1)","option_c":"C) f'(x) = 6x","option_d":"D) f'(x) = 1\/(3x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u’\/u. Ici, u = 3x² + 1, donc u’ = 6x. Ainsi, f'(x) = 6x\/(3x² + 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\": \"A) f'(x) = 6x\/(3x² + 1)\", \"b\": \"B) f'(x) = 3x\/(3x² + 1)\", \"c\": ","_debug_options_count":4},{"id":24417,"question":"Soit X une variable aléatoire suivant une loi normale N(0, 1). Quelle est la probabilité P(-1 ≤ X ≤ 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, environ 68,26% des valeurs sont dans l’intervalle [-1, 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) 0,3413\", \"b\": \"B) 0,6826\", \"c\": \"C) 0,9544\", \"d\": \"D) 0,9974\"}","_debug_options_count":4},{"id":24418,"question":"L’équation x³ - 3x + 2 = 0 admet-elle trois solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En étudiant la fonction f(x) = x³ - 3x + 2, on trouve f(-2) = -8 + 6 + 2 = 0, f(1) = 1 - 3 + 2 = 0 et f(2) = 8 - 6 + 2 = 4. La fonction s’annule donc en x = -2 et x = 1 (double racine).","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":24419,"question":"Quelle est la primitive de la fonction f(x) = e^(2x) ?","option_a":"A) F(x) = e^(2x) + C","option_b":"B) F(x) = (1\/2)e^(2x) + C","option_c":"C) F(x) = 2e^(2x) + C","option_d":"D) F(x) = e^(x) + C","option_e":"","option_f":"","bonne_reponse":"b","explication":"La primitive de e^(ax) est (1\/a)e^(ax) + C. Ici, a = 2, donc F(x) = (1\/2)e^(2x) + C.","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) F(x) = e^(2x) + C\", \"b\": \"B) F(x) = (1\/2)e^(2x) + C\", \"c\": \"C)","_debug_options_count":4},{"id":24420,"question":"Soit un plan P d’équation x + 2y - z + 3 = 0. Quel est le vecteur normal à ce plan ?","option_a":"A) (1, 2, -1)","option_b":"B) (1, 2, 1)","option_c":"C) (1, -2, 1)","option_d":"D) (-1, -2, 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le vecteur normal à un plan d’équation ax + by + cz + d = 0 est (a, b, c). Ici, le vecteur normal est (1, 2, -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\": \"A) (1, 2, -1)\", \"b\": \"B) (1, 2, 1)\", \"c\": \"C) (1, -2, 1)\", \"d\": \"","_debug_options_count":4},{"id":24421,"question":"La suite (Un) définie par Un = (-1)^n \/ n converge-t-elle vers 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"D’après le théorème des gendarmes, comme |Un| = 1\/n tend vers 0, Un converge vers 0.","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":24422,"question":"Quelle est la valeur de l’intégrale ∫(0 à 1) x² dx ?","option_a":"A) 1\/3","option_b":"B) 1\/2","option_c":"C) 1","option_d":"D) 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de x² est x³\/3. Ainsi, ∫(0 à 1) x² dx = [x³\/3](0 à 1) = 1\/3.","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) 1\/3\", \"b\": \"B) 1\/2\", \"c\": \"C) 1\", \"d\": \"D) 2\"}}","_debug_options_count":4},{"id":24423,"question":"Soit f une fonction deux fois dérivable sur ℝ. Si f''(x) \u003E 0 pour tout x, alors f est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction est convexe sur un intervalle si sa dérivée seconde est positive sur cet intervalle. Ici, f''(x) \u003E 0 implique que f est convexe sur ℝ.","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}]