Quiz : Fonctions, Équations et Géométrie — Niveau Seconde

Question 1 sur 10 10:00

[{"id":9543,"question":"Quelle est l'expression d'une fonction affine dont la représentation graphique passe par les points A(1;3) et B(2;5) ?","option_a":"f(x) = 2x + 1","option_b":"f(x) = x + 2","option_c":"f(x) = 3x - 2","option_d":"f(x) = -x + 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"La pente m = (5-3)\/(2-1) = 2. En utilisant le point A, on obtient 3 = 2*1 + b ⇒ b = 1. Donc f(x) = 2x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9544,"question":"L'équation 3x - 7 = 5x + 1 a pour solution x = -4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvons l'équation : 3x - 7 = 5x + 1 ⇒ -2x = 8 ⇒ x = -4. La solution est donc correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9545,"question":"Quelle est la solution de l'inéquation 2x + 5 ≤ 11 ?","option_a":"x ≤ 3","option_b":"x ≥ 3","option_c":"x ≤ -3","option_d":"x ≥ -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 5 ≤ 11 ⇒ 2x ≤ 6 ⇒ x ≤ 3. L'inégalité change de sens si on divise par un nombre négatif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9546,"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":"6 cm","option_c":"7 cm","option_d":"8 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":9547,"question":"La fonction f(x) = -2x + 3 est décroissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est -2 (négatif), donc la fonction est décroissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9548,"question":"Quelle est la solution de l'équation 4(x - 1) = 2x + 6 ?","option_a":"x = 5","option_b":"x = -1","option_c":"x = 3","option_d":"x = 7","option_e":"","option_f":"","bonne_reponse":"A","explication":"4x - 4 = 2x + 6 ⇒ 2x = 10 ⇒ x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9549,"question":"L'aire d'un cercle de rayon r est donnée par la formule A = πr².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule de l'aire d'un cercle est bien A = πr².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9550,"question":"Quelle est la représentation graphique d'une fonction affine de pente négative ?","option_a":"Une droite descendante","option_b":"Une droite montante","option_c":"Une parabole","option_d":"Un cercle","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une pente négative signifie que la fonction est décroissante, donc sa représentation graphique est une droite descendante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9551,"question":"Résoudre l'inéquation -3x + 2 \u003E 8.","option_a":"x \u003C -2","option_b":"x \u003E -2","option_c":"x \u003C 2","option_d":"x \u003E 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"-3x + 2 \u003E 8 ⇒ -3x \u003E 6 ⇒ x \u003C -2 (l'inégalité change de sens car on divise par -3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9552,"question":"Le volume d'un cube d'arête a est donné par V = a³.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule du volume d'un cube est bien V = a³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]