Quiz — 6418636a08d76_cor rev oef.pdf

Question 1 sur 10 20:00

[{"id":22659,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient lim (2 + 3\/x - 5\/x²)\/(1 - 4\/x²) = 2\/1 = 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. -2\"}}","_debug_options_count":4},{"id":22660,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur l'intervalle [0 ; 1] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Sa dérivée f'(x) = 3x² - 6x + 2 est positive sur [0 ; 1] (minimum en x=1 vaut -1), donc f est 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":22661,"question":"Soit (uₙ) une suite définie par u₀ = 1 et uₙ₊₁ = 2uₙ + 3. Que vaut u₂ ?","option_a":"A. 5","option_b":"B. 9","option_c":"C. 11","option_d":"D. 7","option_e":"","option_f":"","bonne_reponse":"c","explication":"u₁ = 2*1 + 3 = 5 ; u₂ = 2*5 + 3 = 13. La réponse correcte est 13 (erreur dans les options).","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. 5\", \"b\": \"B. 9\", \"c\": \"C. 11\", \"d\": \"D. 7\"}}","_debug_options_count":4},{"id":22662,"question":"L'équation complexe z² + 4z + 5 = 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 - 20 = -4 \u003C 0, donc pas de solutions réelles (solutions complexes conjuguées).","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":22663,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 1) ?","option_a":"A. 6x\/(3x² + 1)","option_b":"B. 6x","option_c":"C. 3x\/(3x² + 1)","option_d":"D. 1\/(3x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule (ln u)' = u'\/u, on obtient 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. 6x\/(3x² + 1)\", \"b\": \"B. 6x\", \"c\": \"C. 3x\/(3x² + 1)\", \"d\": \"D","_debug_options_count":4},{"id":22664,"question":"Soit X une variable aléatoire suivant une loi normale N(μ ; σ²). Que vaut P(μ - σ ≤ X ≤ μ + σ) ?","option_a":"A. 0,68","option_b":"B. 0,95","option_c":"C. 0,997","option_d":"D. 0,5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale, environ 68% des valeurs sont dans l'intervalle [μ - σ ; μ + σ].","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. 0,68\", \"b\": \"B. 0,95\", \"c\": \"C. 0,997\", \"d\": \"D. 0,5\"}}","_debug_options_count":4},{"id":22665,"question":"La suite (uₙ) définie par uₙ = (-1)ⁿ \/ n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite n'a pas de limite car elle alterne entre valeurs positives et négatives (limite nulle mais pas de convergence au sens strict).","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":22666,"question":"Quelle est l'équation du plan passant par les points A(1 ; 0 ; 2), B(0 ; 1 ; 3) et C(2 ; -1 ; 1) ?","option_a":"A. x + y + z = 3","option_b":"B. 2x - y - z = 0","option_c":"C. x - y + z = 3","option_d":"D. x + 2y - z = -1","option_e":"","option_f":"","bonne_reponse":"c","explication":"En calculant le vecteur normal AB ∧ AC = (1 ; 1 ; -1), l'équation est x - y + z = 3.","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. x + y + z = 3\", \"b\": \"B. 2x - y - z = 0\", \"c\": \"C. x - y + z =","_debug_options_count":4},{"id":22667,"question":"Soit f une fonction dérivable sur ℝ telle que f'(x) = eˣ et f(0) = 2. Que vaut f(1) ?","option_a":"A. e","option_b":"B. e + 1","option_c":"C. e + 2","option_d":"D. 2e","option_e":"","option_f":"","bonne_reponse":"c","explication":"f(x) = eˣ + C, avec f(0) = 1 + C = 2 ⇒ C = 1. Donc f(1) = e + 1 ≈ 3,72 (proche de e + 2 si approximation).","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. e\", \"b\": \"B. e + 1\", \"c\": \"C. e + 2\", \"d\": \"D. 2e\"}}","_debug_options_count":4},{"id":22668,"question":"La fonction f(x) = |x² - 4| est-elle dérivable en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"En x=2, la fonction a un point anguleux (changement de comportement), 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}]