Quiz Maths Lycée : Algèbre, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":28948,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 aux deux membres : 3x = 15, puis on divise par 3 : x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28949,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = x² - 4x + 3 est une parabole tournée vers le haut. Son sommet (minimum) se situe en x = -b\/(2a) = 4\/2 = 2. Donc c'est vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28950,"question":"Quel est le résultat de (2x + 3)(x - 1) ?","option_a":"2x² + x - 3","option_b":"2x² + x + 3","option_c":"2x² - x - 3","option_d":"2x² + 5x - 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant (2x + 3)(x - 1) = 2x² - 2x + 3x - 3 = 2x² + x - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28951,"question":"Le théorème de Pythagore s'applique-t-il uniquement aux triangles rectangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore est valable uniquement pour les triangles rectangles. Il relie les longueurs des côtés de l'angle droit à l'hypoténuse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28952,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + 5 ?","option_a":"f'(x) = 9x² - 4x","option_b":"f'(x) = 6x² - 4x","option_c":"f'(x) = 9x² - 4x + 5","option_d":"f'(x) = 3x² - 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x³ est 9x², celle de -2x² est -4x, et celle de 5 est 0. Donc f'(x) = 9x² - 4x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28953,"question":"L'inéquation 2x + 7 ≤ 15 a pour solution x ≤ 4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 7 des deux côtés : 2x ≤ 8, puis en divisant par 2 : x ≤ 4. Donc c'est vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28954,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"√3\/2","option_b":"1\/2","option_c":"√2\/2","option_d":"0","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(π\/6) = 1\/2, car π\/6 correspond à 30° et sin(30°) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28955,"question":"La fonction f(x) = 1\/x est-elle définie en 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 interdite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28956,"question":"Quel est le résultat de √(16) + √(9) ?","option_a":"7","option_b":"5","option_c":"10","option_d":"13","option_e":"","option_f":"","bonne_reponse":"A","explication":"√(16) = 4 et √(9) = 3, donc √(16) + √(9) = 4 + 3 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28957,"question":"L'équation x² + 4x + 4 = 0 admet-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation x² + 4x + 4 = 0 peut s'écrire (x + 2)² = 0, donc elle admet une solution double : x = -2. Ce n'est pas deux solutions distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]