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Question 1 sur 10 10:00

[{"id":80302,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"x³ + x² - 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme est obtenue en appliquant la règle de dérivation terme à terme : (3x²)' = 6x et (2x)' = 2, donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80303,"question":"La limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 est égale à 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant f(x) = (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1, la limite quand x→1 est bien 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80304,"question":"Quel est le discriminant de l'équation x² - 4x + 3 = 0 ?","option_a":"4","option_b":"16","option_c":"8","option_d":"12","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = (-4)² - 4*1*3 = 16 - 12 = 4. L'option correcte est 16 car Δ = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80305,"question":"La fonction f(x) = e^x est-elle toujours positive sur ℝ ?","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, car e^x \u003E 0 pour tout x ∈ ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80306,"question":"Quelle est la primitive de f(x) = 4x³ ?","option_a":"x⁴ + C","option_b":"12x² + C","option_c":"x⁴\/4 + C","option_d":"16x⁴ + C","option_e":"","option_f":"","bonne_reponse":"C","explication":"La primitive de 4x³ est obtenue en appliquant la règle de l'intégration : ∫4x³ dx = 4*(x⁴\/4) + C = x⁴ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80307,"question":"Le théorème des valeurs intermédiaires s'applique-t-il à toute fonction continue sur un intervalle fermé ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème des valeurs intermédiaires stipule que si une fonction est continue sur un intervalle fermé [a,b], alors elle prend toutes les valeurs intermédiaires entre f(a) et f(b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80308,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"e²","option_b":"2","option_c":"ln(2)","option_d":"1\/e²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = 2 se résout en appliquant l'exponentielle des deux côtés : x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80309,"question":"La suite définie par uₙ = n²\/(n+1) est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite uₙ = n²\/(n+1) tend vers +∞ quand n→∞, donc elle n'est pas bornée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80310,"question":"Quelle est la valeur de la somme S = 1 + 2 + 3 + ... + n ?","option_a":"n(n+1)\/2","option_b":"n²","option_c":"(n+1)²\/2","option_d":"2n","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des n premiers entiers naturels est donnée par la formule S = n(n+1)\/2, connue sous le nom de formule de Gauss.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80311,"question":"La fonction f(x) = sin(x) est-elle périodique de période 2π ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction sinus est périodique de période 2π, car sin(x + 2π) = sin(x) pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]