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Question 1 sur 10 10:00

[{"id":59117,"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":59118,"question":"La fonction f(x) = x³ est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Sa dérivée f'(x) = 3x² est toujours positive (sauf en x=0 où elle est nulle), donc la fonction est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59119,"question":"Quelle est la limite de (sin x)\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"Non définie","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une limite fondamentale en analyse : lim(x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59120,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique converge si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc elle diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59121,"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":59122,"question":"La fonction f(x) = e^x est-elle sa propre dérivée ?","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, donc la fonction est bien sa propre dérivée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59123,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e²","option_b":"x = 2","option_c":"x = 1\/e²","option_d":"x = √e","option_e":"","option_f":"","bonne_reponse":"A","explication":"En exponentiant les deux côtés, on obtient x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59124,"question":"Un événement impossible a une probabilité de 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, la probabilité d'un événement impossible est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59125,"question":"Quelle est la primitive de f(x) = 2x + 1 ?","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 2x est x² et celle de 1 est x, donc F(x) = x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59126,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 1\/x n'est pas définie en x = 0, car la division par zéro est interdite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]