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Question 1 sur 10 10:00

[{"id":47221,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : la dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47222,"question":"La suite définie par uₙ = n² + 1 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout n, uₙ₊₁ - uₙ = (n+1)² + 1 - (n² + 1) = 2n + 1 \u003E 0. La suite est donc strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47223,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) quand x tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x) \/ (1 - 1\/x²), qui tend vers 2\/1 = 2 quand x tend vers l'infini.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47224,"question":"L'équation différentielle y' = 2y admet-elle une solution de la forme y = Ce^(2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de y = Ce^(2x) est y' = 2Ce^(2x) = 2y, ce qui vérifie l'équation différentielle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47225,"question":"Quel est le coefficient binomial C(5, 2) ?","option_a":"10","option_b":"20","option_c":"15","option_d":"5","option_e":"","option_f":"","bonne_reponse":"A","explication":"C(5, 2) = 5! \/ (2! * 3!) = (5×4) \/ (2×1) = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47226,"question":"La fonction f(x) = x³ - 3x est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ + 3x ≠ f(x), donc la fonction n'est pas paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47227,"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 36 combinaisons possibles (6×6), et une seule donne un double 6. La probabilité est donc 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47228,"question":"La suite géométrique de premier terme u₀ = 2 et de raison q = 3 est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique de raison |q| \u003E 1 n'est pas bornée car ses termes tendent vers l'infini ou moins l'infini.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47229,"question":"Quelle est l'intégrale de f(x) = 4x³ entre 0 et 2 ?","option_a":"16","option_b":"8","option_c":"32","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 4x³ est x⁴. Entre 0 et 2, cela donne 2⁴ - 0⁴ = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47230,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est-il toujours positif ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac peut être positif, nul ou négatif selon les valeurs de a, b et c.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]