Quiz : Les fondamentaux des mathématiques en Seconde

Question 1 sur 10 10:00

[{"id":65942,"question":"Quelle est la forme développée de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² - x - 6","option_c":"x² + 5x - 6","option_d":"x² - 5x - 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme développée est obtenue en appliquant la double distributivité : x*x + x*(-2) + 3*x + 3*(-2) = x² - 2x + 3x - 6 = x² + x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65943,"question":"La fonction f(x) = 2x + 5 est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b, ce qui est le cas ici avec a=2 et b=5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65944,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 4 ?","option_a":"-3","option_b":"4","option_c":"3","option_d":"-4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'équation réduite y = ax + b, le coefficient directeur est le nombre a, ici égal à -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65945,"question":"Le triangle ABC avec AB=5, BC=12 et AC=13 est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vérifions avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65946,"question":"Résolvez l'équation 3x - 7 = 2x + 5.","option_a":"x = 12","option_b":"x = -2","option_c":"x = 2","option_d":"x = -12","option_e":"","option_f":"","bonne_reponse":"C","explication":"3x - 2x = 5 + 7 → x = 12. Vérification : 3*12 - 7 = 29 et 2*12 + 5 = 29.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65947,"question":"La fonction f(x) = x² est une fonction linéaire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction linéaire s'écrit f(x) = ax, ici f(x) = x² est une fonction du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65948,"question":"Quel est le résultat de √16 + √9 ?","option_a":"7","option_b":"5","option_c":"9","option_d":"4","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":65949,"question":"La droite d'équation y = 4 passe par l'origine du repère.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La droite y = 4 est parallèle à l'axe des abscisses et ne passe pas par (0,0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65950,"question":"Quel est le périmètre d'un carré de côté 5 cm ?","option_a":"20 cm","option_b":"25 cm","option_c":"10 cm","option_d":"15 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le périmètre d'un carré est 4 fois la longueur du côté : 4 * 5 = 20 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65951,"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}]