Quiz — 22-38.doc

Question 1 sur 10 20:00

[{"id":116637,"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. -∞","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 le 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. +∞\"}}","_debug_options_count":4},{"id":116638,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 5 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique est convergente uniquement si |q| \u003C 1. Ici, q = 2, donc elle diverge.","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":116639,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 2) ?","option_a":"A. 3\/(3x + 2)","option_b":"B. 1\/(3x + 2)","option_c":"C. 3x\/(3x + 2)","option_d":"D. 1\/(x + 2\/3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x + 2, donc u' = 3. Ainsi, f'(x) = 3\/(3x + 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. 3\/(3x + 2)\", \"b\": \"B. 1\/(3x + 2)\", \"c\": \"C. 3x\/(3x + 2)\", \"d\":","_debug_options_count":4},{"id":116640,"question":"La probabilité d'un événement A est P(A) = 0,4. Quelle est la probabilité de l'événement contraire A̅ ?","option_a":"A. 0,6","option_b":"B. 0,4","option_c":"C. 0,8","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 1 - 0,4 = 0,6.","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. 0,6\", \"b\": \"B. 0,4\", \"c\": \"C. 0,8\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":116641,"question":"Une fonction continue sur un intervalle fermé [a, b] est-elle toujours dérivable sur cet intervalle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction continue n'est pas nécessairement dérivable. Par exemple, f(x) = |x| est continue mais non dérivable en x = 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":116642,"question":"Quelle est la solution générale de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(-2x)","option_b":"B. y = Cx²","option_c":"C. y = C\/(x+2)","option_d":"D. y = Ce^(2x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle y' + 2y = 0 est une équation linéaire du premier ordre. Sa solution générale est 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\": \"A. y = Ce^(-2x)\", \"b\": \"B. y = Cx²\", \"c\": \"C. y = C\/(x+2)\", \"d\":","_debug_options_count":4},{"id":116643,"question":"Soit une variable aléatoire X suivant une loi normale N(μ, σ²). Que vaut P(μ - σ ≤ X ≤ μ + σ) ?","option_a":"A. 0,68","option_b":"B. 0,95","option_c":"C. 0,997","option_d":"D. 0,5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale, environ 68% des valeurs se situent dans l'intervalle [μ - σ, μ + σ].","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. 0,997\", \"d\": \"D. 0,5\"}}","_debug_options_count":4},{"id":116644,"question":"La fonction f(x) = x³ - 3x + 2 est-elle 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 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":116645,"question":"Quelle est la valeur de l'intégrale ∫(0 à 1) e^(-x) dx ?","option_a":"A. 1 - 1\/e","option_b":"B. e - 1","option_c":"C. 1\/e","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de e^(-x) est -e^(-x). Ainsi, ∫(0 à 1) e^(-x) dx = [-e^(-x)] de 0 à 1 = -1\/e + 1 = 1 - 1\/e.","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 - 1\/e\", \"b\": \"B. e - 1\", \"c\": \"C. 1\/e\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":116646,"question":"Soit une suite définie par uₙ₊₁ = 0,5uₙ + 3 avec u₀ = 4. Que vaut la limite de cette suite ?","option_a":"A. 6","option_b":"B. 3","option_c":"C. 0","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si la suite converge vers L, alors L = 0,5L + 3. Résolvant cette équation, on obtient L = 6.","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. 6\", \"b\": \"B. 3\", \"c\": \"C. 0\", \"d\": \"D. 4\"}}","_debug_options_count":4}]