Quiz Maths 4M : Fonctions, Équations et Probabilités

Question 1 sur 10 10:00

[{"id":49701,"question":"Quelle est l'image de 3 par la fonction f(x) = 2x + 1 ?","option_a":"5","option_b":"7","option_c":"6","option_d":"8","option_e":"","option_f":"","bonne_reponse":"C","explication":"En remplaçant x par 3 dans f(x) = 2x + 1, on obtient f(3) = 2*3 + 1 = 7. L'image de 3 est donc 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49702,"question":"L'équation 3x - 5 = 10 a pour solution x = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant 3x - 5 = 10, on obtient 3x = 15, donc x = 5. L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49703,"question":"Quelle est la représentation graphique d'une fonction affine ?","option_a":"Une droite","option_b":"Une parabole","option_c":"Un cercle","option_d":"Une hyperbole","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine de la forme f(x) = ax + b est représentée graphiquement par une droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49704,"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 union est bien la somme de leurs probabilités individuelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49705,"question":"Résoudre l'inéquation 2x - 3 \u003E 7.","option_a":"x \u003E 5","option_b":"x \u003E 2","option_c":"x \u003C 5","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 3 \u003E 7, on obtient 2x \u003E 10, donc x \u003E 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49706,"question":"La fonction f(x) = x² est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine est de la forme f(x) = ax + b, or f(x) = x² est une fonction du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49707,"question":"Quelle est la probabilité d'obtenir un 6 en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé équilibré a 6 faces, donc la probabilité d'obtenir un 6 est de 1\/6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49708,"question":"L'équation x² - 4x + 4 = 0 a deux solutions distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette équation se factorise en (x - 2)² = 0, donc elle a une solution double x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49709,"question":"Quelle est la pente de la droite d'équation y = -3x + 2 ?","option_a":"3","option_b":"-3","option_c":"2","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l'équation y = ax + b, a représente la pente. Ici, a = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49710,"question":"Si P(A) = 0,2 et P(B) = 0,3, alors P(A ∩ B) = 0,06 si A et B sont indépendants.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) * P(B) = 0,2 * 0,3 = 0,06.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]