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Question 1 sur 10 10:00

[{"id":66292,"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},{"id":66293,"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},{"id":66294,"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},{"id":66295,"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},{"id":66296,"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},{"id":66297,"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},{"id":66298,"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},{"id":66299,"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},{"id":66300,"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},{"id":66301,"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}]