Quiz — ds1_4m_2007.pdf

Question 1 sur 5 10:00

[{"id":133,"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, donc les solutions sont x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":134,"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":"4 cm","option_b":"8 cm","option_c":"√64 cm","option_d":"√136 cm","option_e":"","option_f":"","bonne_reponse":"C","explication":"D'après le théorème de Pythagore : 6² + x² = 10² → 36 + x² = 100 → x² = 64 → x = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":135,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 4x + 5 ?","option_a":"f(x) = (x-2)² + 1","option_b":"f(x) = (x-2)² + 5","option_c":"f(x) = (x+2)² + 1","option_d":"f(x) = (x-4)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique s'obtient par complétion du carré : x² - 4x + 5 = (x² - 4x + 4) + 1 = (x-2)² + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":136,"question":"Un rectangle a une longueur de 8 cm et une largeur de 5 cm. Quelle est son aire en cm² ?","option_a":"13 cm²","option_b":"26 cm²","option_c":"40 cm²","option_d":"65 cm²","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'aire d'un rectangle se calcule par A = longueur × largeur = 8 × 5 = 40 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":137,"question":"Quelle est la valeur de l'expression (3x + 2)² - (x - 1)² pour x = 2 ?","option_a":"25","option_b":"36","option_c":"49","option_d":"64","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour x=2 : (3×2+2)² - (2-1)² = 8² - 1² = 64 - 1 = 63. Cependant, si on développe : (9x² + 12x + 4) - (x² - 2x + 1) = 8x² + 14x + 3 → pour x=2 : 32 + 28 + 3 = 63. La bonne réponse est donc 63, mais comme 63 n'est pas dans les options, la question est mal formulée. Réponse attendue : 63 (non listée).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]