Quiz Mathématiques : Équations, Fonctions et Géométrie pour la 4ème année secondaire

Question 1 sur 5 10:00

[{"id":2260,"question":"Quelle est la solution de l'équation du second degré 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":2261,"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) = 3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2262,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"4 cm","option_c":"12 cm","option_d":"5 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant le théorème de Pythagore : 6² + x² = 10² → x² = 64 → x = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2263,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 1) lorsque x tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x → ∞, on divise chaque terme par x² : f(x) ≈ (2x²)\/(x²) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2264,"question":"Quel est le volume d'un cylindre de rayon 3 cm et de hauteur 5 cm ? (π ≈ 3,14)","option_a":"141,3 cm³","option_b":"47,1 cm³","option_c":"94,2 cm³","option_d":"282,6 cm³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le volume d'un cylindre est donné par V = πr²h = 3,14 × 3² × 5 ≈ 141,3 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]