Quiz : Maîtrisez les fonctions et la géométrie en 4ème Math

Question 1 sur 10 10:00

[{"id":49881,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49882,"question":"L'équation de la tangente à la courbe de f en x = 1 est y = 4x + 1. Quelle est la valeur de f'(1) ?","option_a":"2","option_b":"4","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur de la tangente en un point est égal à la dérivée de la fonction en ce point. Ici, f'(1) = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49883,"question":"Deux événements A et B sont indépendants si P(A ∩ B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est la définition de l'indépendance de deux événements en probabilités.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49884,"question":"Quelle est l'équation réduite de la droite passant par les points A(1, 3) et B(2, 5) ?","option_a":"y = 2x + 1","option_b":"y = x + 2","option_c":"y = 2x - 1","option_d":"y = x - 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est (5-3)\/(2-1) = 2. L'équation est y = 2x + b. En remplaçant A(1,3), on trouve b = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49885,"question":"Si f'(x) \u003E 0 sur un intervalle, alors f est décroissante sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Si f'(x) \u003E 0, la fonction f est croissante. Si f'(x) \u003C 0, elle est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49886,"question":"Quelle est la probabilité de tirer un as dans un jeu de 52 cartes ?","option_a":"1\/13","option_b":"1\/4","option_c":"4\/52","option_d":"1\/52","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 4 as dans un jeu de 52 cartes. La probabilité est donc 4\/52 = 1\/13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49887,"question":"La distance entre les points A(2, -1) et B(-3, 4) est :","option_a":"√50","option_b":"√26","option_c":"√74","option_d":"√10","option_e":"","option_f":"","bonne_reponse":"C","explication":"La distance se calcule avec la formule √[(xB-xA)² + (yB-yA)²] = √[(-5)² + 5²] = √50.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49888,"question":"Si A et B sont deux événements incompatibles, alors P(A ∪ B) = P(A) + P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements incompatibles, la probabilité de leur réunion est la somme de leurs probabilités.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49889,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"2e^(2x)","option_b":"e^(2x)","option_c":"2x e^(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, donc u'(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49890,"question":"L'équation x² + y² - 4x + 6y + 9 = 0 représente :","option_a":"Une droite","option_b":"Un cercle","option_c":"Une parabole","option_d":"Une hyperbole","option_e":"","option_f":"","bonne_reponse":"B","explication":"En complétant le carré, on obtient (x-2)² + (y+3)² = 4, ce qui est l'équation d'un cercle de centre (2, -3) et de rayon 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]