Quiz — pb128.pdf

Question 1 sur 10 20:00

[{"id":82277,"question":"Quelle est la limite de la suite définie par uₙ = (2n² + 3n - 1)\/(n² + 5) quand n tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite d'une suite rationnelle s'obtient en comparant les termes de plus haut degré. Ici, uₙ ≈ 2n²\/n² = 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. 2\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":82278,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle strictement 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) = 3x² - 6x + 2 s'annule en x = 1 ± √(1\/3), donc la fonction n'est pas strictement croissante partout.","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":82279,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = eˣ en x = 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. e","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la tangente est f'(0) = e⁰ = 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. e\", \"d\": \"D. -1\"}}","_debug_options_count":4},{"id":82280,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc P = 3\/6 = 1\/2. L'affirmation est vraie.","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":82281,"question":"Soit une suite géométrique de raison q = -2 et de premier terme u₀ = 3. Quelle est la valeur de u₃ ?","option_a":"A. -24","option_b":"B. 24","option_c":"C. -12","option_d":"D. 12","option_e":"","option_f":"","bonne_reponse":"a","explication":"u₃ = u₀ × q³ = 3 × (-2)³ = 3 × (-8) = -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\": \"A. -24\", \"b\": \"B. 24\", \"c\": \"C. -12\", \"d\": \"D. 12\"}}","_debug_options_count":4},{"id":82282,"question":"La fonction f(x) = ln(x) est définie pour tout x ∈ ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0.","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":82283,"question":"Quel est le résultat de l'intégrale ∫₀¹ (3x² + 2x) dx ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégrale vaut [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 2. L'option C est incorrecte, la bonne réponse est B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 1\", \"b\": \"B. 2\", \"c\": \"C. 3\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":82284,"question":"Une suite arithmétique de raison r = 5 a pour premier terme u₀ = 2. Quel est u₁₀ ?","option_a":"A. 50","option_b":"B. 52","option_c":"C. 55","option_d":"D. 60","option_e":"","option_f":"","bonne_reponse":"b","explication":"u₁₀ = u₀ + 10r = 2 + 50 = 52.","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. 50\", \"b\": \"B. 52\", \"c\": \"C. 55\", \"d\": \"D. 60\"}}","_debug_options_count":4},{"id":82285,"question":"La fonction f(x) = 1\/x est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction 1\/x n'est pas définie en x = 0, donc elle n'est pas dérivable en ce point.","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":82286,"question":"Quel est le discriminant de l'équation x² - 4x + 3 = 0 ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. 16","option_d":"D. -4","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = 16 - 12 = 4.","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. 4\", \"c\": \"C. 16\", \"d\": \"D. -4\"}}","_debug_options_count":4}]