Maths 3ème : Testez vos connaissances en fonctions et équations

Question 1 sur 10 10:00

[{"id":24338,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0.5 ou x = 2","option_c":"x = -1 ou x = -2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La solution s'obtient en factorisant l'équation : 2x² - 5x + 2 = (2x - 1)(x - 2) = 0, donc x = 0.5 ou x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24339,"question":"La fonction f(x) = x² - 4x + 3 est croissante sur l'intervalle ]2 ; +∞[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 est positive pour x \u003E 2, donc la fonction est croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24340,"question":"Quelle est la limite de la suite u_n = (3n + 1)\/(2n - 5) quand n tend vers +∞ ?","option_a":"3\/2","option_b":"1","option_c":"0","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient u_n = (3 + 1\/n)\/(2 - 5\/n), donc la limite est 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24341,"question":"Le vecteur AB a pour coordonnées (3 ; -2). Quel est le vecteur 2AB ?","option_a":"(6 ; -4)","option_b":"(3 ; -2)","option_c":"(1.5 ; -1)","option_d":"(-3 ; 2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Multiplier un vecteur par un scalaire revient à multiplier ses coordonnées par ce scalaire : 2AB = (2×3 ; 2×(-2)) = (6 ; -4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24342,"question":"La probabilité de tirer un as dans un jeu de 32 cartes est de 1\/8.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 4 as dans un jeu de 32 cartes, donc la probabilité est 4\/32 = 1\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24343,"question":"Quelle est la dérivée de la fonction f(x) = √(x² + 1) ?","option_a":"f'(x) = x\/√(x² + 1)","option_b":"f'(x) = 2x\/√(x² + 1)","option_c":"f'(x) = x\/√(x² - 1)","option_d":"f'(x) = 1\/√(x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la formule de dérivation des fonctions composées, f'(x) = (1\/2)(x² + 1)^(-1\/2) × 2x = x\/√(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24344,"question":"Un triangle a pour côtés 5 cm, 12 cm et 13 cm. Est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vérifions le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24345,"question":"Quelle est la solution de l'inéquation x² - 3x - 4 ≤ 0 ?","option_a":"x ∈ [-4 ; 1]","option_b":"x ∈ [-1 ; 4]","option_c":"x ∈ ]-∞ ; -1] ∪ [4 ; +∞[","option_d":"x ∈ ]-∞ ; -4] ∪ [1 ; +∞[","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les racines de l'équation x² - 3x - 4 = 0 sont x = -1 et x = 4. Le polynôme est négatif entre les racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24346,"question":"La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, e^x \u003E 0. La fonction exponentielle est donc toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24347,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 5 ?","option_a":"-3","option_b":"5","option_c":"3","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur d'une droite d'équation y = ax + b est le nombre a, ici a = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]