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Question 1 sur 10 10:00

[{"id":64702,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 5","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64703,"question":"La limite de 1\/x quand x tend vers 0+ est-elle infinie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Quand x tend vers 0 par valeurs positives, 1\/x tend vers +∞. Donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64704,"question":"Quel est le résultat de l'intégrale ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x + C","option_c":"3x³ + x² + C","option_d":"x³ + 2x² + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale de 3x² est x³ et celle de 2x est x², avec une constante d'intégration C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64705,"question":"L'équation x² + y² = 25 représente-t-elle un cercle de rayon 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² + y² = r² représente un cercle de centre (0,0) et de rayon r. Ici r² = 25, donc r = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64706,"question":"Quelle est la forme trigonométrique du nombre complexe z = 1 + i√3 ?","option_a":"2(cos(π\/3) + i sin(π\/3))","option_b":"√2(cos(π\/4) + i sin(π\/4))","option_c":"2(cos(π\/6) + i sin(π\/6))","option_d":"√3(cos(π\/3) + i sin(π\/3))","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z est √(1² + (√3)²) = 2. L'argument θ vérifie tan(θ) = √3\/1 = √3, donc θ = π\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64707,"question":"La suite uₙ = n\/(n+1) est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite de uₙ quand n tend vers +∞ est 1. La suite est donc convergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64708,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"Leur norme","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64709,"question":"La fonction f(x) = e^x est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^x est e^x, qui est toujours positive. Donc f est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64710,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 6×6 = 36 issues possibles. Une seule issue correspond à (6,6). Donc P = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64711,"question":"La fonction f(x) = |x| est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée à gauche est -1 et à droite est 1. Les limites ne sont pas égales, donc f n'est pas dérivable en 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]