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[{"id":75562,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A. 2x + 3","option_b":"B. x² + 3","option_c":"C. 2x - 5","option_d":"D. 3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation : f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75563,"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":"La fonction exponentielle e^x est strictement positive pour tout x réel, car e^x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75564,"question":"Quelle est la limite de (sin x)\/x lorsque x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. -1","option_d":"D. ∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"Par le théorème des gendarmes ou le développement limité, on sait que lim(x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75565,"question":"Dans une suite géométrique de raison q ≠ 1, la somme des n premiers termes est donnée par :","option_a":"A. S_n = u_1 * (1 - q^n)","option_b":"B. S_n = u_1 * (q^n - 1)\/(q - 1)","option_c":"C. S_n = u_1 * q^n","option_d":"D. S_n = u_1 * n","option_e":"","option_f":"","bonne_reponse":"B","explication":"La formule de la somme des n premiers termes d'une suite géométrique est S_n = u_1 * (q^n - 1)\/(q - 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75566,"question":"L'équation différentielle y' = 2y admet pour solution générale y = C * e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution générale de y' = 2y est bien y = C * e^(2x), où C est une constante réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75567,"question":"Quelle est la valeur de l'intégrale ∫(0 à 1) x² dx ?","option_a":"A. 1\/2","option_b":"B. 1\/3","option_c":"C. 1","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale de x² entre 0 et 1 vaut [x³\/3] de 0 à 1 = 1\/3 - 0 = 1\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75568,"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 : dans un triangle rectangle, AB² + AC² = BC² si BC est l'hypoténuse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75569,"question":"Quelle est la probabilité d'obtenir un 6 en lançant un dé équilibré ?","option_a":"A. 1\/2","option_b":"B. 1\/6","option_c":"C. 1\/3","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un dé équilibré a 6 faces, donc la probabilité d'obtenir un 6 est 1\/6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75570,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75571,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"A. x = -6","option_b":"B. x = 6","option_c":"C. x = -4","option_d":"D. x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 5 = 3x + 1, on obtient x = -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]