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[{"id":43676,"question":"Quel est le résultat de l'inégalité suivante : x² - 5x + 6 \u003C 0 ?","option_a":"A. x ∈ ]2, 3[","option_b":"B. x ∈ ]-∞, 2[ ∪ ]3, +∞[","option_c":"C. x ∈ ]-∞, +∞[","option_d":"D. x ∈ {2, 3}","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'inégalité x² - 5x + 6 \u003C 0 se résout en factorisant : (x-2)(x-3) \u003C 0. Le produit est négatif lorsque x est entre 2 et 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43677,"question":"La somme des angles intérieurs d'un pentagone convexe est égale à 540°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule générale pour un polygone à n côtés est (n-2) × 180°. Pour n=5, on obtient 540°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43678,"question":"Quel est le dernier chiffre de 7^2023 ?","option_a":"A. 1","option_b":"B. 3","option_c":"C. 7","option_d":"D. 9","option_e":"","option_f":"","bonne_reponse":"D","explication":"Les puissances de 7 cyclent tous les 4 : 7^1=7, 7^2=9, 7^3=3, 7^4=1. 2023 mod 4 = 3, donc le dernier chiffre est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43679,"question":"Soit f(x) = 3x² - 2x + 1. Quelle est la dérivée de f en x=2 ?","option_a":"A. 10","option_b":"B. 12","option_c":"C. 14","option_d":"D. 16","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de f(x) est f'(x) = 6x - 2. En x=2, f'(2) = 6×2 - 2 = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43680,"question":"Un nombre premier est toujours impair.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le nombre 2 est le seul nombre premier pair, tous les autres sont impairs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43681,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"A. x = 1","option_b":"B. x = 2","option_c":"C. x = 3","option_d":"D. x = 4","option_e":"","option_f":"","bonne_reponse":"B","explication":"8 = 2³, donc 2^(x+1) = 2³ ⇒ x+1 = 3 ⇒ x = 2. (Correction : x=2 est la réponse correcte, l'option C correspond à x=3 qui est incorrect.)","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43682,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore, une propriété fondamentale des triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43683,"question":"Quel est le PGCD de 120 et 180 ?","option_a":"A. 30","option_b":"B. 40","option_c":"C. 60","option_d":"D. 120","option_e":"","option_f":"","bonne_reponse":"A","explication":"La décomposition en facteurs premiers donne 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":43684,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle ]-∞, -1[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 est négative sur ]-1, 1[, donc la fonction est décroissante sur cet intervalle. Elle est croissante sur ]-∞, -1[ et ]1, +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43685,"question":"Quel est le résultat de la somme 1 + 2 + 3 + ... + 100 ?","option_a":"A. 5050","option_b":"B. 5000","option_c":"C. 4950","option_d":"D. 5100","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des n premiers entiers est n(n+1)\/2. Pour n=100, on obtient 100×101\/2 = 5050.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]