Quiz Mathématiques : Fonctions, Équations et Géométrie pour la Seconde

Question 1 sur 10 10:00

[{"id":33093,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = 2","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés puis on divise par 3 : 3x = 12 → x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33094,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction s'annule en x = 1 et x = 3, et est négative entre ces deux valeurs. Elle n'est donc pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33095,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"1","option_b":"25","option_c":"4","option_d":"16","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33096,"question":"Dans un triangle rectangle, si les côtés de l'angle droit mesurent 3 cm et 4 cm, quelle est la longueur de l'hypoténuse ?","option_a":"5 cm","option_b":"7 cm","option_c":"6 cm","option_d":"4,5 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore : hypoténuse² = 3² + 4² = 9 + 16 = 25 → hypoténuse = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33097,"question":"La fonction f(x) = 2x + 1 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur de la fonction affine est positif (2), donc la fonction est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33098,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E 5","option_c":"x \u003E -2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"On soustrait 3 des deux côtés : 2x \u003E 4 → x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33099,"question":"Dans un cercle de rayon 5 cm, quelle est la longueur d'un arc correspondant à un angle au centre de 60° ?","option_a":"5π\/3 cm","option_b":"5π cm","option_c":"10π\/3 cm","option_d":"π\/3 cm","option_e":"","option_f":"","bonne_reponse":"C","explication":"La longueur de l'arc L = (θ\/360) × 2πr = (60\/360) × 2π × 5 = (1\/6) × 10π = 5π\/3 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33100,"question":"La fonction f(x) = -x² + 4x - 3 admet-elle un maximum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient de x² est négatif (-1), donc la parabole est tournée vers le bas et admet un maximum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33101,"question":"Résoudre le système : { 2x + y = 5 ; x - y = 1 }","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En additionnant les deux équations : 3x = 6 → x = 2. En remplaçant dans la 2ème équation : 2 - y = 1 → y = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33102,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]