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Question 1 sur 10 10:00

[{"id":65592,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 2 ou x = 1\/2","option_b":"x = -2 ou x = -1\/2","option_c":"x = 1\/2 ou x = 2","option_d":"x = -1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"C","explication":"La résolution de l'équation du second degré donne deux solutions réelles : x = 2 et x = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65593,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","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. La fonction est décroissante sur [-1, 1] et croissante ailleurs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65594,"question":"Quel est le produit scalaire de deux vecteurs u(2, -3) et v(-1, 4) ?","option_a":"10","option_b":"-10","option_c":"14","option_d":"-14","option_e":"","option_f":"","bonne_reponse":"D","explication":"Le produit scalaire se calcule par u·v = (2)(-1) + (-3)(4) = -2 -12 = -14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65595,"question":"La limite de la suite uₙ = (n² + 1)\/n quand n tend vers l'infini est :","option_a":"0","option_b":"1","option_c":"+∞","option_d":"n'existe pas","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = 1 + 1\/n² → 1 + 0 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65596,"question":"Une probabilité peut être supérieure à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une probabilité est toujours comprise entre 0 et 1, inclus.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65597,"question":"Quelle est la dérivée de la fonction f(x) = ln(x² + 1) ?","option_a":"f'(x) = 2x\/(x² + 1)","option_b":"f'(x) = 1\/(x² + 1)","option_c":"f'(x) = 2x","option_d":"f'(x) = x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la formule de dérivation d'une fonction composée, f'(x) = (2x)\/(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65598,"question":"Dans un triangle ABC, si AB = 5, AC = 7 et BC = 8, alors l'angle BÂC mesure environ :","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"C","explication":"En utilisant la loi des cosinus, cos(BÂC) = (5² + 7² - 8²)\/(2*5*7) ≈ 0,5 → BÂC ≈ 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65599,"question":"La fonction f(x) = e^x 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":65600,"question":"Quel est le développement limité de sin(x) à l'ordre 3 autour de 0 ?","option_a":"sin(x) ≈ x - x³\/6","option_b":"sin(x) ≈ x + x³\/6","option_c":"sin(x) ≈ x - x²\/2","option_d":"sin(x) ≈ 1 - x²\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le développement limité de sin(x) à l'ordre 3 est sin(x) ≈ x - x³\/6 + o(x³).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65601,"question":"Si une variable aléatoire X suit une loi normale N(μ, σ²), alors P(μ - σ ≤ X ≤ μ + σ) est environ égal à :","option_a":"0,68","option_b":"0,95","option_c":"0,997","option_d":"0,5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale, environ 68% des valeurs sont dans l'intervalle [μ - σ, μ + σ].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]