Quiz — bac blanc 2.docx

Question 1 sur 10 20:00

[{"id":33190,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(2x² - x + 5) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 3\/2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite d'une fonction rationnelle lorsque x tend vers l'infini est égale au rapport des coefficients des termes de plus haut degré. Ici, 3x²\/2x² = 3\/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. 3\/2\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":33191,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 1\/2. Quelle est la valeur de u₅ ?","option_a":"A. 2","option_b":"B. 1\/16","option_c":"C. 1\/32","option_d":"D. 1\/64","option_e":"","option_f":"","bonne_reponse":"c","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Ainsi, u₅ = 2 × (1\/2)⁵ = 2 × 1\/32 = 1\/16.","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. 2\", \"b\": \"B. 1\/16\", \"c\": \"C. 1\/32\", \"d\": \"D. 1\/64\"}}","_debug_options_count":4},{"id":33192,"question":"Vrai ou Faux ? La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien est bien f'(x) = 1\/x, c'est une propriété fondamentale du cours.","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":33193,"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 en trouvant une primitive : ∫(3x² + 2x) dx = x³ + x². Évaluée entre 0 et 1, cela donne (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":33194,"question":"Vrai ou Faux ? Une matrice carrée est inversible si et seulement si son déterminant est nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une matrice carrée est inversible si et seulement si son déterminant est différent de 0. Un déterminant nul signifie que la matrice n'est pas inversible.","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":33195,"question":"Soit Z = 3 + 4i un nombre complexe. Quel est son module ?","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. 25","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe Z = a + bi est donné par |Z| = √(a² + b²). Ici, |Z| = √(3² + 4²) = √(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\": \"A. 5\", \"b\": \"B. 7\", \"c\": \"C. √7\", \"d\": \"D. 25\"}}","_debug_options_count":4},{"id":33196,"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 6 × 6 = 36 issues possibles. Un seul cas favorable (6 et 6), donc la probabilité est 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":33197,"question":"Vrai ou Faux ? La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle eˣ est strictement positive pour tout réel x, c'est une propriété fondamentale de cette fonction.","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":33198,"question":"Soit f une fonction dérivable sur ℝ telle que f'(x) = 2x - 4. Quel est le sens de variation de f ?","option_a":"A. Croissante sur ℝ","option_b":"B. Décroissante sur ℝ","option_c":"C. Croissante puis décroissante","option_d":"D. Décroissante puis croissante","option_e":"","option_f":"","bonne_reponse":"d","explication":"Le signe de la dérivée f'(x) = 2x - 4 dépend de x. f'(x) \u003C 0 pour x \u003C 2 (décroissante) et f'(x) \u003E 0 pour x \u003E 2 (croissante).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"A. Croissante sur ℝ\", \"b\": \"B. Décroissante sur ℝ\", \"c\": \"C.","_debug_options_count":4},{"id":33199,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x² + 3x - 1 au point d'abscisse x = 1 ?","option_a":"A. y = 5x - 2","option_b":"B. y = 5x + 2","option_c":"C. y = 2x + 5","option_d":"D. y = 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation de la tangente est y = f'(a)(x - a) + f(a). Ici, f(1) = 3 et f'(1) = 5, donc y = 5(x - 1) + 3 = 5x - 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. y = 5x - 2\", \"b\": \"B. y = 5x + 2\", \"c\": \"C. y = 2x + 5\", \"d\": ","_debug_options_count":4}]