Maths 4M : Révisons les fondamentaux avant l'examen !

Question 1 sur 5 10:00

[{"id":1585,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = -0,5","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvons l'équation 2x² - 5x + 2 = 0 en utilisant le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± √9)\/4, soit x = 2 ou x = 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1586,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 3x² + 2x - 1 ?","option_a":"f'(x) = 3x² - 6x + 2","option_b":"f'(x) = 3x² - 6x + 1","option_c":"f'(x) = x² - 3x + 2","option_d":"f'(x) = 3x² - 3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (xⁿ)' = n·xⁿ⁻¹. Ainsi, f'(x) = 3x² - 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1587,"question":"Dans un triangle ABC rectangle en A, si AB = 6 cm et BC = 10 cm, quelle est la longueur de AC ?","option_a":"8 cm","option_b":"4 cm","option_c":"√(100-36) cm","option_d":"6√3 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, AC² = BC² - AB² = 100 - 36 = 64. Donc AC = √64 = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1588,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"2","option_c":"∞","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"D","explication":"En x = 1, le dénominateur s'annule, tandis que le numérateur vaut 0. On a donc une forme indéterminée 0\/0. Après simplification, on obtient f(x) = (2x + 5)(x - 1)\/(x - 1) = 2x + 5 pour x ≠ 1. La limite est donc 2·1 + 5 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1589,"question":"Quel est le volume d'un cône de rayon 3 cm et de hauteur 5 cm ?","option_a":"15π cm³","option_b":"45π cm³","option_c":"9π cm³","option_d":"30π cm³","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le volume d'un cône se calcule avec la formule V = (1\/3)·π·r²·h. Ici, V = (1\/3)·π·9·5 = 15π cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]