Quiz — 100_correction-série1.pdf

Question 1 sur 5 10:00

[{"id":738,"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":739,"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 à terme : (3x²)' = 6x, (-2x)' = -2, et (1)' = 0. Donc f'(x) = 6x - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":740,"question":"Quel est le théorème qui permet de calculer la longueur d'un côté dans un triangle rectangle ?","option_a":"Théorème de Pythagore","option_b":"Théorème de Thalès","option_c":"Théorème des milieux","option_d":"Théorème de l'angle inscrit","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore stipule que dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":741,"question":"Si sin(x) = 0.5, quelle est la valeur de x dans l'intervalle [0, π] ?","option_a":"x = π\/6","option_b":"x = π\/4","option_c":"x = π\/3","option_d":"x = π\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'intervalle [0, π], sin(x) = 0.5 admet une solution unique : x = π\/6 (ou 30°).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":742,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) quand 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 tendant vers l'infini, on divise chaque terme par x² : f(x) ≈ (2x²)\/(x²) = 2. La limite est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]