Quiz Maths 3ème Année : Algèbre, Géométrie et Fonctions

Question 1 sur 10 10:00

[{"id":28488,"question":"Quelle est la solution de l'équation 2x + 5 = 11 ?","option_a":"x = 3","option_b":"x = 4","option_c":"x = 2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 5 des deux côtés, on obtient 2x = 6, puis en divisant par 2, x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28489,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28490,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2x","option_d":"f'(x) = 6x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -1 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28491,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, quelle est la nature de ce triangle ?","option_a":"Triangle rectangle en A","option_b":"Triangle rectangle en B","option_c":"Triangle rectangle en C","option_d":"Triangle quelconque","option_e":"","option_f":"","bonne_reponse":"B","explication":"On vérifie que 5² + 12² = 13² (25 + 144 = 169), donc le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28492,"question":"La fonction f(x) = x² est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = x² est décroissante pour x \u003C 0 et croissante pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28493,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≤ 2","option_c":"x ≥ 12","option_d":"x ≥ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés, on obtient x - 7 ≤ 5, puis en ajoutant 7, x ≤ 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28494,"question":"Dans un repère orthonormé, quel est le coefficient directeur de la droite passant par les points A(1, 2) et B(3, 6) ?","option_a":"2","option_b":"3","option_c":"1","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est (6 - 2) \/ (3 - 1) = 4 \/ 2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28495,"question":"La fonction f(x) = 1\/x est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28496,"question":"Quelle est la valeur de sin(30°) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La valeur de sin(30°) est 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28497,"question":"L'équation x² + 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 16 = 0, donc l'équation admet une solution double (x = -2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]