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Question 1 sur 10 10:00

[{"id":27948,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"3x² - 4x + 5","option_b":"x² - 2x + 5","option_c":"3x² - 4x + 1","option_d":"x³ - 4x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme s'obtient en appliquant la règle de dérivation terme à terme : (x^n)' = n*x^(n-1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27949,"question":"Une suite croissante est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite croissante n'est pas nécessairement convergente (exemple : la suite u_n = n).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27950,"question":"Quelle est l'intégrale de f(x) = 3x² entre 0 et 2 ?","option_a":"8","option_b":"4","option_c":"12","option_d":"6","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x² est x³. Évaluée entre 0 et 2, cela donne 8 - 0 = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27951,"question":"Dans une loi normale centrée réduite, quelle est la probabilité P(-1 ≤ X ≤ 1) ?","option_a":"≈ 0.68","option_b":"≈ 0.95","option_c":"≈ 0.34","option_d":"≈ 0.5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale centrée réduite, environ 68% des valeurs se situent entre -1 et 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27952,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27953,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce^(-2x)","option_b":"y = Ce^(2x)","option_c":"y = Cx + D","option_d":"y = Cx² + D","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle linéaire du premier ordre y' + ay = 0 a pour solution y = Ce^(-ax).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27954,"question":"Dans un triangle ABC, si AB = 5, AC = 7 et BC = 8, quel est le cosinus de l'angle A ?","option_a":"0.5","option_b":"0.6","option_c":"0.7","option_d":"0.8","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule du cosinus : cos(A) = (AB² + AC² - BC²) \/ (2 * AB * AC) = (25 + 49 - 64) \/ 70 = 10\/70 ≈ 0.6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27955,"question":"La fonction exponentielle est toujours positive.","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.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27956,"question":"Quelle est la limite de (sin(x))\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est un résultat fondamental en analyse : lim (x→0) sin(x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27957,"question":"Dans une urne contenant 3 boules rouges et 2 boules bleues, quelle est la probabilité de tirer deux boules rouges sans remise ?","option_a":"3\/10","option_b":"6\/25","option_c":"1\/5","option_d":"3\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La probabilité est (3\/5) * (2\/4) = 6\/20 = 3\/10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]