Quiz — 58.DOC

Question 1 sur 10 20:00

[{"id":11933,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. -3","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d'un rapport de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 3x²\/x² = 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. -3\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":11934,"question":"La fonction f(x) = x³ - 3x + 2 est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction n'est donc pas strictement croissante sur tout ℝ.","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":11935,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx entre 0 et 2 ?","option_a":"A. 4","option_b":"B. 6","option_c":"C. 8","option_d":"D. 10","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégrale de 2x + 1 est x² + x. Évaluée entre 0 et 2, cela donne (4 + 2) - (0 + 0) = 6. L'option C (8) est incorrecte.","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. 4\", \"b\": \"B. 6\", \"c\": \"C. 8\", \"d\": \"D. 10\"}}","_debug_options_count":4},{"id":11936,"question":"Soit une suite géométrique de premier terme u₀ = 5 et de raison q = 2. Quelle est la valeur de u₃ ?","option_a":"A. 10","option_b":"B. 20","option_c":"C. 40","option_d":"D. 80","option_e":"","option_f":"","bonne_reponse":"d","explication":"uₙ = u₀ × qⁿ. Donc u₃ = 5 × 2³ = 5 × 8 = 40. L'option D (80) est incorrecte.","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. 10\", \"b\": \"B. 20\", \"c\": \"C. 40\", \"d\": \"D. 80\"}}","_debug_options_count":4},{"id":11937,"question":"L'équation différentielle y' + 2y = 0 admet 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 réelle.","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":11938,"question":"Quelle est la valeur propre d'une matrice triangulaire supérieure ?","option_a":"A. La somme des éléments diagonaux","option_b":"B. Les éléments diagonaux","option_c":"C. Le déterminant de la matrice","option_d":"D. Le produit des éléments diagonaux","option_e":"","option_f":"","bonne_reponse":"b","explication":"Les valeurs propres d'une matrice triangulaire sont exactement ses éléments diagonaux.","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. La somme des éléments diagonaux\", \"b\": \"B. Les éléments di","_debug_options_count":4},{"id":11939,"question":"Un dé est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"A. 1\/6","option_b":"B. 1\/12","option_c":"C. 1\/36","option_d":"D. 1\/2","option_e":"","option_f":"","bonne_reponse":"c","explication":"La probabilité d'obtenir un 6 est 1\/6. Pour deux lancers indépendants, c'est (1\/6) × (1\/6) = 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\/2\"}}","_debug_options_count":4},{"id":11940,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","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":11941,"question":"Quel est le module du nombre complexe z = 3 + 4i ?","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 de z = a + bi est √(a² + b²). Ici, √(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":11942,"question":"L'intervalle de fluctuation asymptotique d'une proportion p au seuil de 95% est donné par [p - 1,96√(p(1-p)\/n), p + 1,96√(p(1-p)\/n)].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la formule standard de l'intervalle de fluctuation asymptotique pour une proportion au seuil de 95%.","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}]