Quiz — 43828939_715779958786858_7129097935526035456_n.pdf

Question 1 sur 10 20:00

[{"id":42285,"question":"Quelle est la limite de la suite définie par u_n = (3n + 1) \/ (2n - 5) lorsque n tend vers l'infini ?","option_a":"A. 3\/2","option_b":"B. 0","option_c":"C. -1\/5","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d'une suite rationnelle est égale au rapport des coefficients des termes de plus haut degré. Ici, 3n\/2n = 3\/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\/2\", \"b\": \"B. 0\", \"c\": \"C. -1\/5\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":42286,"question":"La fonction f(x) = x^3 - 3x^2 + 2 est croissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x^2 - 6x est négative sur [-1, 1] (ex: f'(0) = 0, f'(1) = -3), donc la fonction est décroissante.","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":42287,"question":"Quelle est la solution générale de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^{-2x}","option_b":"B. y = Ce^{2x}","option_c":"C. y = Cx^2","option_d":"D. y = C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation est de la forme y' + ay = 0. La solution générale est y = Ce^{-ax}, ici a = 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 = Ce^{-2x}\", \"b\": \"B. y = Ce^{2x}\", \"c\": \"C. y = Cx^2\", \"d\":","_debug_options_count":4},{"id":42288,"question":"Si A et B sont deux événements indépendants avec P(A) = 0.4 et P(B) = 0.3, alors P(A ∩ B) est égale à :","option_a":"A. 0.12","option_b":"B. 0.7","option_c":"C. 0.1","option_d":"D. 0.07","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.","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. 0.12\", \"b\": \"B. 0.7\", \"c\": \"C. 0.1\", \"d\": \"D. 0.07\"}}","_debug_options_count":4},{"id":42289,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire nul.","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":42290,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"A. 2\/(2x + 1)","option_b":"B. 1\/(2x + 1)","option_c":"C. 2x\/(2x + 1)","option_d":"D. 1\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici u = 2x + 1, donc u' = 2. Ainsi f'(x) = 2\/(2x + 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. 2\/(2x + 1)\", \"b\": \"B. 1\/(2x + 1)\", \"c\": \"C. 2x\/(2x + 1)\", \"d\":","_debug_options_count":4},{"id":42291,"question":"Un dé équilibré est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"A. 1\/6","option_b":"B. 1\/36","option_c":"C. 1\/12","option_d":"D. 1\/18","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'obtenir un 6 est 1\/6. Pour deux lancers indépendants, P(6 et 6) = (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\": \"b\", \"options\": {\"a\": \"A. 1\/6\", \"b\": \"B. 1\/36\", \"c\": \"C. 1\/12\", \"d\": \"D. 1\/18\"}}","_debug_options_count":4},{"id":42292,"question":"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":"Pour tout x réel, e^x \u003E 0. La fonction exponentielle est strictement positive.","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":42293,"question":"Quelle est l'intégrale de la fonction f(x) = 3x^2 entre 0 et 2 ?","option_a":"A. 6","option_b":"B. 8","option_c":"C. 4","option_d":"D. 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 3x^2 est x^3. Évaluée entre 0 et 2, on obtient 2^3 - 0^3 = 8.","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. 6\", \"b\": \"B. 8\", \"c\": \"C. 4\", \"d\": \"D. 2\"}}","_debug_options_count":4},{"id":42294,"question":"Si une droite a pour équation y = -2x + 5, alors son coefficient directeur est :","option_a":"A. 5","option_b":"B. -2","option_c":"C. 2","option_d":"D. -5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans l'équation réduite y = mx + p, m est le coefficient directeur. Ici m = -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. 5\", \"b\": \"B. -2\", \"c\": \"C. 2\", \"d\": \"D. -5\"}}","_debug_options_count":4}]