Quiz — exam_RO.pdf

Question 1 sur 10 20:00

[{"id":26209,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. -1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d’un polynôme de même degré au numérateur et au dénominateur est égale au rapport des coefficients dominants, soit 3\/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. 3\", \"b\": \"B. 0\", \"c\": \"C. -1\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":26210,"question":"La dérivée de la fonction f(x) = x³ - 2x² + 5x - 7 est f'(x) = 3x² - 4x + 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée est correcte : f'(x) = 3x² - 4x + 5.","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":26211,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quel est le terme u₅ ?","option_a":"A. 486","option_b":"B. 162","option_c":"C. 54","option_d":"D. 18","option_e":"","option_f":"","bonne_reponse":"a","explication":"u₅ = u₀ × q⁵ = 2 × 3⁵ = 2 × 243 = 486.","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. 486\", \"b\": \"B. 162\", \"c\": \"C. 54\", \"d\": \"D. 18\"}}","_debug_options_count":4},{"id":26212,"question":"L’équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale de y' + 2y = 0 est bien y = Ce^(-2x), où C est une constante.","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":26213,"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 combinaisons possibles, et une seule donne un double 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":26214,"question":"Le nombre complexe z = 3 - 4i a pour module |z| = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module de z = a + bi est √(a² + b²) = √(9 + 16) = √25 = 5.","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":26215,"question":"Soit la fonction f définie par f(x) = ln(x² + 1). Quelle est sa dérivée f'(x) ?","option_a":"A. 2x\/(x² + 1)","option_b":"B. 1\/(x² + 1)","option_c":"C. 2x","option_d":"D. x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la dérivée d’une fonction composée, f'(x) = (2x)\/(x² + 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. 2x\/(x² + 1)\", \"b\": \"B. 1\/(x² + 1)\", \"c\": \"C. 2x\", \"d\": \"D. x","_debug_options_count":4},{"id":26216,"question":"La fonction exponentielle vérifie la propriété : exp(a + b) = exp(a) × exp(b).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C’est une propriété fondamentale de la fonction exponentielle.","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":26217,"question":"Quelle est l’équation de la tangente à la courbe y = x² + 3x - 2 au point d’abscisse x = 1 ?","option_a":"A. y = 5x - 3","option_b":"B. y = 5x + 3","option_c":"C. y = 3x - 5","option_d":"D. y = 5x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La tangente a pour équation y = f'(1)(x - 1) + f(1) = 5(x - 1) + 2 = 5x - 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. y = 5x - 3\", \"b\": \"B. y = 5x + 3\", \"c\": \"C. y = 3x - 5\", \"d\": ","_debug_options_count":4},{"id":26218,"question":"Soit une variable aléatoire X suivant une loi normale N(0, 1). Quelle est la probabilité P(-1 ≤ X ≤ 1) ?","option_a":"A. 0,68","option_b":"B. 0,95","option_c":"C. 0,99","option_d":"D. 0,34","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale centrée réduite, P(-1 ≤ X ≤ 1) ≈ 0,6826.","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. 0,99\", \"d\": \"D. 0,34\"}}","_debug_options_count":4}]