Quiz : Maîtrisez les fonctions dérivées et la trigonométrie

Question 1 sur 10 10:00

[{"id":68692,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2x","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68693,"question":"L'équation sin(x) = 0,5 admet-elle une solution dans l'intervalle [0, π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car sin(π\/6) = 0,5 et π\/6 ∈ [0, π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68694,"question":"Quelle est l'équation de la droite passant par les points A(1, 2) et B(3, 4) ?","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x - 1","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. L'équation est y = x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68695,"question":"La dérivée de cos(x) est égale à -sin(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale de la dérivée des fonctions trigonométriques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68696,"question":"Quelle est la valeur de cos(π\/3) ?","option_a":"0,5","option_b":"√3\/2","option_c":"1\/√2","option_d":"√2\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"cos(π\/3) = 0,5 est une valeur connue des angles remarquables.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68697,"question":"La tangente à la courbe de f(x) = x² au point d'abscisse 1 a pour équation y = 2x - 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée en x=1 est f'(1)=2. L'équation de la tangente est y = 2x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68698,"question":"Quelle est la solution de l'équation 2sin(x) - 1 = 0 dans [0, 2π] ?","option_a":"π\/6 et 5π\/6","option_b":"π\/3 et 2π\/3","option_c":"π\/4 et 3π\/4","option_d":"π\/2 et 3π\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(x) = 0,5 ⇒ x = π\/6 ou 5π\/6 dans l'intervalle donné.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68699,"question":"La distance entre les points A(2, 3) et B(-1, 1) est égale à √13.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La distance est √[(2-(-1))² + (3-1)²] = √(9 + 4) = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68700,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"2e^(2x)","option_b":"e^(2x)","option_c":"2xe^(2x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(u(x)) est u'(x)e^(u(x)). Ici, u(x)=2x ⇒ u'(x)=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68701,"question":"L'équation de la droite d'équation y = -3x + 5 a un coefficient directeur égal à -3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est le coefficient de x dans l'équation réduite y = mx + p.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]