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Question 1 sur 10 10:00

[{"id":65692,"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":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2 et (-5)' = 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65693,"question":"L'intégrale de 2x entre 0 et 3 est égale à 9.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x est x². Entre 0 et 3, cela donne 3² - 0² = 9. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65694,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x = 2","option_b":"x = 1","option_c":"x = 3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"B","explication":"2^(x+1) = 8 équivaut à 2^(x+1) = 2³. Donc x+1 = 3, soit x = 2. La bonne réponse est x = 2 (option A).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65695,"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 entre -1 et 1. L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65696,"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":65697,"question":"L'équation x² + y² + 2x - 4y + 5 = 0 représente un cercle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En complétant les carrés : (x+1)² + (y-2)² = 0. C'est un cercle de rayon 0 (un point). L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65698,"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. Une seule correspond à (6,6). La probabilité est donc 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65699,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0. L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65700,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 1 ?","option_a":"x \u003E 8","option_b":"x \u003E 6","option_c":"x \u003C 8","option_d":"x \u003C 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 7 \u003E 2x + 1 ⇒ x \u003E 8. La bonne réponse est x \u003E 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65701,"question":"La dérivée seconde d'une fonction linéaire est toujours nulle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction linéaire f(x) = ax + b a pour dérivée f'(x) = a et f''(x) = 0. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]