Quiz : Les fondamentaux des mathématiques en 2ème année secondaire (Lettres)

Question 1 sur 10 10:00

[{"id":53521,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 15","option_d":"x = 5\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés : 3x = 15, puis on divise par 3 : x = 5. La réponse correcte est donc x = 15\/3 (équivalent à 5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53522,"question":"L'intervalle ]-2 ; 4] contient-il le nombre 4 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intervalle ]-2 ; 4] inclut tous les nombres strictement supérieurs à -2 et inférieurs ou égaux à 4. Le nombre 4 est donc inclus.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53523,"question":"Quelle est l'image de 2 par la fonction f(x) = 3x + 1 ?","option_a":"f(2) = 4","option_b":"f(2) = 7","option_c":"f(2) = 5","option_d":"f(2) = 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour calculer l'image de 2 par f(x) = 3x + 1, on remplace x par 2 : f(2) = 3*2 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53524,"question":"La distance entre les points A(1 ; 2) et B(4 ; 6) est-elle égale à 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La distance est calculée par la formule √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53525,"question":"Quelle est la forme réduite de l'expression 2(x + 3) - 4x ?","option_a":"-2x + 6","option_b":"2x + 6","option_c":"6 - 2x","option_d":"4x + 6","option_e":"","option_f":"","bonne_reponse":"C","explication":"En développant 2(x + 3) - 4x, on obtient 2x + 6 - 4x = -2x + 6, soit 6 - 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53526,"question":"Le milieu du segment [AB] avec A(-1 ; 3) et B(5 ; -1) a pour coordonnées (2 ; 1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le milieu a pour coordonnées ((-1+5)\/2 ; (3-1)\/2) = (2 ; 1). L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53527,"question":"Quelle est la solution de l'inéquation 2x + 7 ≤ 3x - 1 ?","option_a":"x ≥ 8","option_b":"x ≤ 8","option_c":"x ≥ -8","option_d":"x ≤ -8","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés : 7 ≤ x - 1, puis en ajoutant 1 : 8 ≤ x, soit x ≥ 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53528,"question":"La fonction f(x) = -2x + 5 est-elle décroissante ?","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 -2 (négatif), donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53529,"question":"Quelle est la valeur de x dans l'équation |x - 3| = 5 ?","option_a":"x = 8 ou x = -2","option_b":"x = 2 ou x = -8","option_c":"x = 5 ou x = -5","option_d":"x = 3 ou x = -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation |x - 3| = 5 a deux solutions : x - 3 = 5 (x = 8) ou x - 3 = -5 (x = -2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53530,"question":"Le point C(3 ; 4) appartient-il à la droite d'équation y = 2x - 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 3 dans l'équation : y = 2*3 - 2 = 4. Le point C(3 ; 4) vérifie donc l'équation de la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]