Quiz — 67 fmt 2015.pdf

Question 1 sur 10 20:00

[{"id":37690,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. f'(x) = 6x + 2","option_b":"B. f'(x) = 3x + 2","option_c":"C. f'(x) = 6x - 5","option_d":"D. f'(x) = 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : la dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0.","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. f'(x) = 6x + 2\", \"b\": \"B. f'(x) = 3x + 2\", \"c\": \"C. f'(x) = 6x","_debug_options_count":4},{"id":37691,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction est décroissante sur [-1 ; 1] car sa dérivée f'(x) = 3x² - 3 est négative sur cet intervalle (exemple : f'(0) = -3).","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":37692,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A. x = e²","option_b":"B. x = 2","option_c":"C. x = 100","option_d":"D. x = ln(2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation ln(x) = 2 équivaut à x = e², car la fonction exponentielle est la réciproque du logarithme népérien.","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 = e²\", \"b\": \"B. x = 2\", \"c\": \"C. x = 100\", \"d\": \"D. x = ln(","_debug_options_count":4},{"id":37693,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quelle est la valeur de u₃ ?","option_a":"A. 6","option_b":"B. 18","option_c":"C. 54","option_d":"D. 162","option_e":"","option_f":"","bonne_reponse":"c","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 2 × 3³ = 2 × 27 = 54.","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. 6\", \"b\": \"B. 18\", \"c\": \"C. 54\", \"d\": \"D. 162\"}}","_debug_options_count":4},{"id":37694,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le produit scalaire de deux vecteurs orthogonaux est égal à 0, car cos(90°) = 0 dans la formule du produit scalaire.","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":37695,"question":"Quelle est la primitive de la fonction f(x) = 4x³ + 2x ?","option_a":"A. F(x) = x⁴ + x² + C","option_b":"B. F(x) = 12x² + 2 + C","option_c":"C. F(x) = x⁴ + 2x + C","option_d":"D. F(x) = 4x⁴ + x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive d'une fonction polynôme se calcule en augmentant chaque exposant de 1 et en divisant par le nouvel exposant : ∫4x³ dx = x⁴ et ∫2x dx = x².","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. F(x) = x⁴ + x² + C\", \"b\": \"B. F(x) = 12x² + 2 + C\", \"c\": \"","_debug_options_count":4},{"id":37696,"question":"Dans une classe de 30 élèves, la probabilité qu'un élève soit absent est de 0,1. Quelle est la probabilité qu'exactement 2 élèves soient absents ?","option_a":"A. 0,205","option_b":"B. 0,189","option_c":"C. 0,268","option_d":"D. 0,300","option_e":"","option_f":"","bonne_reponse":"b","explication":"On utilise la loi binomiale : P(X=2) = C(30,2) × (0,1)² × (0,9)²⁸ ≈ 0,189.","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. 0,205\", \"b\": \"B. 0,189\", \"c\": \"C. 0,268\", \"d\": \"D. 0,300\"}}","_debug_options_count":4},{"id":37697,"question":"La fonction f(x) = (x² + 1)\/x admet une asymptote verticale en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction n'est pas définie en x = 0, et lim(x→0) f(x) = ±∞, donc elle admet bien une asymptote verticale en x = 0.","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":37698,"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":"c","explication":"L'intégrale se calcule en trouvant une primitive : [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 2. (Réponse C : 3 est incorrect, erreur de calcul.)","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\", \"b\": \"B. 2\", \"c\": \"C. 3\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":37699,"question":"Soit une variable aléatoire X suivant une loi normale centrée réduite. Quelle est la probabilité P(X ≤ 1) ?","option_a":"A. 0,6826","option_b":"B. 0,8413","option_c":"C. 0,9772","option_d":"D. 0,9987","option_e":"","option_f":"","bonne_reponse":"b","explication":"D'après la table de la loi normale centrée réduite, P(X ≤ 1) ≈ 0,8413.","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. 0,6826\", \"b\": \"B. 0,8413\", \"c\": \"C. 0,9772\", \"d\": \"D. 0,9987\"}","_debug_options_count":4}]