Mathématiques 3ème année : Testez vos connaissances !

Question 1 sur 10 10:00

[{"id":25988,"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":25989,"question":"La dérivée de la fonction f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","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 est correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25990,"question":"Quel est le résultat de l'expression C(5,2) (combinaison de 5 éléments pris 2 à 2) ?","option_a":"10","option_b":"20","option_c":"5","option_d":"15","option_e":"","option_f":"","bonne_reponse":"A","explication":"C(5,2) = 5! \/ (2! * (5-2)!) = 10. C'est le nombre de façons de choisir 2 éléments parmi 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25991,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore, une propriété fondamentale en géométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25992,"question":"Quelle est la forme canonique de l'expression x² - 4x + 3 ?","option_a":"(x-2)² - 1","option_b":"(x-1)² - 4","option_c":"(x-3)² - 2","option_d":"(x-4)² + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 4x + 3 = (x² - 4x + 4) - 1 = (x-2)² - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25993,"question":"La fonction f(x) = x³ est une fonction paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x). C'est une fonction impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25994,"question":"Quel est le discriminant de l'équation 2x² - 3x + 1 = 0 ?","option_a":"1","option_b":"9","option_c":"17","option_d":"7","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = (-3)² - 4*2*1 = 9 - 8 = 1. L'option correcte est donc 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25995,"question":"Dans un repère orthonormé, la distance entre les points A(1,2) et B(4,6) est égale à 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La distance AB = √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25996,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 5 \u003E 3 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25997,"question":"La fonction f(x) = 1\/x est 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}]