Quiz Mathématiques : Équations, Fonctions et Problèmes — 3ème Année Secondaire

Question 1 sur 10 10:00

[{"id":25138,"question":"Quelle est la solution de l’équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = -4","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25139,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s’écrit sous la forme f(x) = ax + b, ce qui est le cas ici avec a = 2 et b = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25140,"question":"Quel est le discriminant de l’équation x² - 4x + 4 = 0 ?","option_a":"Δ = 0","option_b":"Δ = 4","option_c":"Δ = -4","option_d":"Δ = 16","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25141,"question":"Si f(x) = 5x - 2, alors f(3) = ?","option_a":"13","option_b":"17","option_c":"15","option_d":"10","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 3 dans f(x) = 5x - 2, on obtient f(3) = 5*3 - 2 = 15 - 2 = 13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25142,"question":"L’inéquation 2x + 1 \u003E 5 a pour solution x \u003E 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"2x + 1 \u003E 5 ⇒ 2x \u003E 4 ⇒ x \u003E 2. La solution est donc x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25143,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25144,"question":"Si une droite a pour équation y = -2x + 5, quel est son coefficient directeur ?","option_a":"5","option_b":"-2","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l’équation y = ax + b, a est le coefficient directeur. Ici, a = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25145,"question":"L’équation x² + 4x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0. Il n’y a donc pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25146,"question":"Quelle est la solution de l’inéquation -3x + 6 ≤ 0 ?","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x \u003E 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"-3x + 6 ≤ 0 ⇒ -3x ≤ -6 ⇒ x ≥ 2 (en divisant par un nombre négatif, on inverse le sens de l’inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25147,"question":"La fonction f(x) = x² - 4x + 4 admet-elle un minimum ? Si oui, quelle est sa valeur ?","option_a":"Oui, minimum = 0","option_b":"Oui, minimum = 4","option_c":"Non, pas de minimum","option_d":"Oui, minimum = -4","option_e":"","option_f":"","bonne_reponse":"A","explication":"f(x) = (x - 2)², qui est toujours ≥ 0. Le minimum est donc 0, atteint en x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]