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Question 1 sur 10 10:00

[{"id":14828,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x² - 5","option_c":"6x² - 5","option_d":"3x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14829,"question":"La fonction f(x) = x³ - 3x + 1 est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1, donc la fonction n'est pas strictement croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14830,"question":"Quelle est l'intégrale de f(x) = 2x entre 0 et 3 ?","option_a":"3","option_b":"6","option_c":"9","option_d":"12","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de 2x est x². Entre 0 et 3, cela donne 3² - 0² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14831,"question":"L'équation x² + 4x + 5 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0, donc pas de solution réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14832,"question":"Quelle est la limite de (sin x)\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n'existe pas","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":14833,"question":"La fonction f(x) = e^x est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Sa dérivée seconde f''(x) = e^x \u003E 0, donc la fonction est convexe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14834,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient -x \u003E 6, soit x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14835,"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, si deux vecteurs sont orthogonaux, leur produit scalaire est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14836,"question":"Quelle est la primitive de f(x) = 1\/x qui s'annule en x = 1 ?","option_a":"ln|x|","option_b":"ln|x| + C","option_c":"ln|x| - 1","option_d":"ln|x| + 1","option_e":"","option_f":"","bonne_reponse":"D","explication":"La primitive de 1\/x est ln|x| + C. Pour F(1) = 0, on a C = -1, donc F(x) = ln|x| - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14837,"question":"La suite u_n = n² + 3n est croissante pour tout n ∈ ℕ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence u_{n+1} - u_n = 2n + 4 \u003E 0 pour tout n ∈ ℕ, donc la suite est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]