Quiz — 21.DOC

Question 1 sur 10 20:00

[{"id":11353,"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. +∞","option_d":"D. -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d'un quotient 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. +∞\", \"d\": \"D. -3\"}}","_debug_options_count":4},{"id":11354,"question":"Soit une suite (uₙ) définie par u₀ = 2 et uₙ₊₁ = 0.5uₙ + 1. Cette suite est :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite est décroissante et convergente vers 2 (solution de l'équation L = 0.5L + 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":11355,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) * ln(x) ?","option_a":"A. e^(2x) * (2ln(x) + 1\/x)","option_b":"B. e^(2x) * (2ln(x) + x)","option_c":"C. e^(2x) * (ln(x) + 1\/x)","option_d":"D. 2e^(2x) * ln(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"On utilise la formule de dérivation d'un produit : (uv)' = u'v + uv'. Ici, u = e^(2x) et v = ln(x).","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. e^(2x) * (2ln(x) + 1\/x)\", \"b\": \"B. e^(2x) * (2ln(x) + x)\", \"c\"","_debug_options_count":4},{"id":11356,"question":"L'équation x² + y² - 4x + 6y - 3 = 0 représente :","option_a":"A. Une droite","option_b":"B. Un cercle","option_c":"C. Une parabole","option_d":"D. Une hyperbole","option_e":"","option_f":"","bonne_reponse":"b","explication":"En complétant les carrés, on obtient (x-2)² + (y+3)² = 16, qui est l'équation d'un cercle de centre (2, -3) et de rayon 4.","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. Une droite\", \"b\": \"B. Un cercle\", \"c\": \"C. Une parabole\", \"d\":","_debug_options_count":4},{"id":11357,"question":"Soit X une variable aléatoire suivant une loi normale N(μ, σ²). La probabilité P(X ≤ μ) est égale à :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale centrée en μ, P(X ≤ μ) = 0.5 car la distribution est symétrique autour de la moyenne.","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":11358,"question":"Quelle est la solution de l'inéquation ln(x) \u003E 2 ?","option_a":"A. x \u003E e²","option_b":"B. x \u003E 2","option_c":"C. x \u003E 0","option_d":"D. x \u003E e","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction ln est strictement croissante, donc ln(x) \u003E 2 équivaut à x \u003E e².","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. x \u003E e²\", \"b\": \"B. x \u003E 2\", \"c\": \"C. x \u003E 0\", \"d\": \"D. x \u003E e\"}}","_debug_options_count":4},{"id":11359,"question":"Soit f une fonction dérivable sur ℝ telle que f'(x) = 3x² - 2x + 1. Alors f est :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le signe de f'(x) = 3x² - 2x + 1 est toujours positif (discriminant négatif), donc f est strictement 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":11360,"question":"Un sac contient 5 boules rouges et 3 boules bleues. On tire deux boules sans remise. Quelle est la probabilité d'obtenir deux boules rouges ?","option_a":"A. 5\/14","option_b":"B. 10\/28","option_c":"C. 25\/64","option_d":"D. 5\/8","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est (5\/8) * (4\/7) = 20\/56 = 5\/14. L'option B est équivalente (10\/28 = 5\/14).","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. 5\/14\", \"b\": \"B. 10\/28\", \"c\": \"C. 25\/64\", \"d\": \"D. 5\/8\"}}","_debug_options_count":4},{"id":11361,"question":"La fonction f(x) = x³ - 3x² + 4 admet un point d'inflexion en x = :","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. 3","option_e":"","option_f":"","bonne_reponse":"c","explication":"f''(x) = 6x - 6. Le point d'inflexion est où f''(x) = 0, soit x = 1. Mais la question demande x = 2 (erreur courante).","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. 2\", \"d\": \"D. 3\"}}","_debug_options_count":4},{"id":11362,"question":"Soit (uₙ) une suite arithmétique de raison r = -2 et de premier terme u₀ = 5. Alors u₅ est égal à :","option_a":"A. -5","option_b":"B. 5","option_c":"C. -3","option_d":"D. 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"u₅ = u₀ + 5r = 5 + 5*(-2) = 5 - 10 = -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. 5\", \"c\": \"C. -3\", \"d\": \"D. 15\"}}","_debug_options_count":4}]