Quiz — 647cb5edb4b20_Enoncé Sujet de révision N°6.pdf

Question 1 sur 10 20:00

[{"id":79564,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 3","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"La limite d'un polynôme de degré n lorsque x tend vers l'infini est donnée par le terme de plus haut degré. Ici, le terme dominant est 3x²\/x² = 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. 0\", \"b\": \"B. 1\", \"c\": \"C. 3\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":79565,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 1\/2. Quelle est la valeur de u₃ ?","option_a":"A. 1\/4","option_b":"B. 1\/2","option_c":"C. 1","option_d":"D. 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 2 × (1\/2)³ = 2 × 1\/8 = 1\/4.","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\/4\", \"b\": \"B. 1\/2\", \"c\": \"C. 1\", \"d\": \"D. 2\"}}","_debug_options_count":4},{"id":79566,"question":"Vrai ou Faux ? La fonction exponentielle est strictement décroissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction exponentielle est strictement croissante sur ℝ, car sa dérivée f'(x) = eˣ est toujours positive.","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":79567,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 1) ?","option_a":"A. 3\/(3x + 1)","option_b":"B. 1\/(3x + 1)","option_c":"C. 3x\/(3x + 1)","option_d":"D. 1\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x + 1, donc u' = 3. Ainsi, f'(x) = 3\/(3x + 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. 3\/(3x + 1)\", \"b\": \"B. 1\/(3x + 1)\", \"c\": \"C. 3x\/(3x + 1)\", \"d\":","_debug_options_count":4},{"id":79568,"question":"Vrai ou Faux ? Si une suite est majorée et croissante, alors elle converge.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de convergence monotone, une suite croissante et majorée converge vers sa borne supérieure.","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":79569,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"A. 1\/6","option_b":"B. 1\/12","option_c":"C. 1\/36","option_d":"D. 1\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 36 issues possibles (6 × 6). Un seul cas favorable : (6,6). Donc P = 1\/36.","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\/6\", \"b\": \"B. 1\/12\", \"c\": \"C. 1\/36\", \"d\": \"D. 1\/18\"}}","_debug_options_count":4},{"id":79570,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ceˣ","option_b":"B. y = Ce⁻²ˣ","option_c":"C. y = C + eˣ","option_d":"D. y = Cx","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation différentielle linéaire du premier ordre y' + ay = 0 a pour solution y = Ce⁻ᵃˣ. Ici, a = 2, donc y = Ce⁻²ˣ.","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. y = Ceˣ\", \"b\": \"B. y = Ce⁻²ˣ\", \"c\": \"C. y = C + eˣ\", \"d\"","_debug_options_count":4},{"id":79571,"question":"Vrai ou Faux ? La fonction f(x) = x³ - 3x est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = (-x)³ - 3(-x) = -x³ + 3x ≠ f(x). Elle est donc impaire.","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":79572,"question":"Quelle est la valeur 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":"b","explication":"L'intégrale se calcule comme suit : [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 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. 1\", \"b\": \"B. 2\", \"c\": \"C. 3\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":79573,"question":"Quelle est la probabilité qu'une variable aléatoire X suivant une loi normale N(0,1) soit supérieure à 1,96 ?","option_a":"A. 0,025","option_b":"B. 0,05","option_c":"C. 0,95","option_d":"D. 0,975","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après les tables de la loi normale centrée réduite, P(X \u003E 1,96) ≈ 0,025.","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. 0,025\", \"b\": \"B. 0,05\", \"c\": \"C. 0,95\", \"d\": \"D. 0,975\"}}","_debug_options_count":4}]