Maths 3ème année secondaire : Équations, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":43966,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x - 2)(x - 3) = 0. Les solutions sont donc x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43967,"question":"La fonction f(x) = 3x + 2 est une fonction affine.","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. Ici, a = 3 et b = 2, donc f(x) = 3x + 2 est bien une fonction affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43968,"question":"Quelle est la pente de la droite d'équation y = -2x + 5 ?","option_a":"-2","option_b":"2","option_c":"5","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'équation d'une droite y = ax + b, a représente la pente. Ici, a = -2, donc la pente est -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43969,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est l'énoncé du théorème de Pythagore, qui s'applique uniquement dans un triangle rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43970,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 3 \u003E 5, on obtient 2x \u003E 8, puis x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43971,"question":"La fonction f(x) = x² est une fonction paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = (-x)² = x² = f(x), donc f(x) = x² est une fonction paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43972,"question":"Dans un triangle ABC, si AB = 5 cm, AC = 12 cm et BC = 13 cm, alors le triangle est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En vérifiant avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle en A.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43973,"question":"Quelle est la forme factorisée de l'expression 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":"L'expression x² - 9 est une différence de carrés, donc elle se factorise en (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43974,"question":"La droite d'équation y = 4x - 1 passe par le point (1, 3).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 1 dans l'équation, on obtient y = 4(1) - 1 = 3. Le point (1, 3) appartient donc à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43975,"question":"Quelle est la solution de l'équation 3(x - 2) = 2(x + 1) ?","option_a":"x = 8","option_b":"x = 4","option_c":"x = -8","option_d":"x = -4","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant, on obtient 3x - 6 = 2x + 2. En isolant x, on trouve x = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]