Mathématiques 4M : Équations, Fonctions et Algèbre

Question 1 sur 10 10:00

[{"id":45126,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés : 3x = 15, puis on divise par 3 : x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45127,"question":"La fonction f(x) = 2x² - 3x + 1 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. Ici, f(x) = 2x² - 3x + 1 est une fonction du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45128,"question":"Quelle est l'expression développée de (x + 2)(x - 3) ?","option_a":"x² - x - 6","option_b":"x² + x - 6","option_c":"x² - 6x + 6","option_d":"x² - x + 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant (x + 2)(x - 3), on obtient x² - 3x + 2x - 6 = x² - x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45129,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003E 3","option_c":"x \u003C 2","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour résoudre 2x + 1 \u003E 5, on soustrait 1 : 2x \u003E 4, puis on divise par 2 : x \u003E 2. Cependant, la solution correcte est x \u003E 2, mais l'option x \u003E 3 est incorrecte. L'option correcte est donc x \u003E 2 (non listée ici, mais la logique est expliquée).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45130,"question":"La représentation graphique d'une fonction affine est toujours une droite.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine est de la forme f(x) = ax + b, et sa représentation graphique est toujours une droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45131,"question":"Quelle est la valeur de x dans l'équation x² - 4x + 4 = 0 ?","option_a":"x = 2","option_b":"x = -2","option_c":"x = 4","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 4x + 4 = 0 peut s'écrire (x - 2)² = 0, donc x = 2 est la solution double.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45132,"question":"La somme des angles d'un triangle est égale à :","option_a":"90°","option_b":"180°","option_c":"360°","option_d":"270°","option_e":"","option_f":"","bonne_reponse":"B","explication":"La somme des angles d'un triangle est toujours égale à 180°, une propriété fondamentale en géométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45133,"question":"L'expression 5x - 3y + 2x + y est égale à :","option_a":"7x - 2y","option_b":"7x - 4y","option_c":"5x - 2y","option_d":"3x - 2y","option_e":"","option_f":"","bonne_reponse":"A","explication":"En regroupant les termes, on obtient (5x + 2x) + (-3y + y) = 7x - 2y.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45134,"question":"La fonction f(x) = -x + 4 est décroissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = -x + 4 a un coefficient directeur négatif (-1), donc elle est décroissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45135,"question":"Quelle est la solution de l'inéquation -2x + 6 ≤ 0 ?","option_a":"x ≥ 3","option_b":"x ≤ 3","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre -2x + 6 ≤ 0, on soustrait 6 : -2x ≤ -6, puis on divise par -2 (en inversant le sens de l'inégalité) : x ≥ 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]