Quiz — série30_arithmétiques_aptimisation.pdf

Question 1 sur 10 20:00

[{"id":38240,"question":"Quel est le reste de la division de 2023 par 17 ?","option_a":"10","option_b":"11","option_c":"12","option_d":"13","option_e":"","option_f":"","bonne_reponse":"b","explication":"2023 ÷ 17 = 119 avec un reste de 11, car 17 × 119 = 2023 - 11.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"10\", \"b\": \"11\", \"c\": \"12\", \"d\": \"13\"}}","_debug_options_count":4},{"id":38241,"question":"Si a ≡ 3 [mod 5] et b ≡ 2 [mod 5], alors a + b ≡ ? [mod 5]","option_a":"0","option_b":"1","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"c","explication":"a + b ≡ 3 + 2 ≡ 5 ≡ 0 [mod 5]. L'option '5' est équivalente à 0 modulo 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"4\", \"d\": \"5\"}}","_debug_options_count":4},{"id":38242,"question":"Vrai ou Faux : Tout nombre premier supérieur à 2 est impair.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, un nombre premier supérieur à 2 ne peut pas être pair (sauf 2 lui-même).","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":38243,"question":"Quel est le PGCD de 120 et 180 ?","option_a":"30","option_b":"40","option_c":"60","option_d":"120","option_e":"","option_f":"","bonne_reponse":"c","explication":"120 = 2³ × 3 × 5 et 180 = 2² × 3² × 5. Le PGCD est 2² × 3 × 5 = 60.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"30\", \"b\": \"40\", \"c\": \"60\", \"d\": \"120\"}}","_debug_options_count":4},{"id":38244,"question":"Vrai ou Faux : L'inégalité x² ≥ 0 est toujours vraie pour tout réel x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le carré d'un nombre réel est toujours positif ou nul, donc l'inégalité est toujours vraie.","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":38245,"question":"Si f(x) = 3x + 2, quelle est la valeur minimale de f(x) sur l'intervalle [0, 5] ?","option_a":"2","option_b":"5","option_c":"15","option_d":"17","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = 3x + 2 est croissante. Sa valeur minimale sur [0, 5] est f(0) = 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\": \"2\", \"b\": \"5\", \"c\": \"15\", \"d\": \"17\"}}","_debug_options_count":4},{"id":38246,"question":"Quel est le nombre de solutions entières de l'équation 2x + 3y = 12 ?","option_a":"2","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"c","explication":"Les solutions sont (x, y) = (0,4), (3,2), (6,0). Il y a donc 3 solutions entières.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"2\", \"b\": \"3\", \"c\": \"4\", \"d\": \"5\"}}","_debug_options_count":4},{"id":38247,"question":"Vrai ou Faux : La fonction f(x) = x² - 4x + 5 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2, et f''(x) = 2 \u003E 0, donc c'est un minimum.","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":38248,"question":"Si a et b sont deux entiers tels que a ≡ 1 [mod 4] et b ≡ 3 [mod 4], alors a × b ≡ ? [mod 4]","option_a":"0","option_b":"1","option_c":"2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"d","explication":"a × b ≡ 1 × 3 ≡ 3 [mod 4].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"3\"}}","_debug_options_count":4},{"id":38249,"question":"Vrai ou Faux : La programmation linéaire permet de résoudre des problèmes d'optimisation avec des contraintes linéaires.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La programmation linéaire est une méthode d'optimisation pour maximiser ou minimiser une fonction linéaire sous contraintes linéaires.","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}]