Quiz Maths Seconde : Équations, Fonctions et Suites

Question 1 sur 10 10:00

[{"id":77482,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = -4","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 7 ⇒ 3x = 12 ⇒ x = 4. Solution : x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77483,"question":"La fonction f(x) = 2x² + 3x - 5 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine est de la forme f(x) = ax + b. Ici, le terme x² indique qu'il s'agit d'une fonction polynôme du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77484,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 8 ?","option_a":"f(x) = (x - 3)² - 1","option_b":"f(x) = (x - 2)² + 4","option_c":"f(x) = (x - 4)²","option_d":"f(x) = (x - 1)² + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique s'obtient par f(x) = (x - 3)² - 1 après complétion du carré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77485,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77486,"question":"Quelle est la solution de l'inéquation -2x + 5 ≥ 1 ?","option_a":"x ≤ 2","option_b":"x ≥ 2","option_c":"x ≤ -2","option_d":"x ≥ -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"-2x + 5 ≥ 1 ⇒ -2x ≥ -4 ⇒ x ≤ 2 (en divisant par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77487,"question":"La fonction f(x) = 1\/x est-elle 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},{"id":77488,"question":"Quelle est la valeur de la somme S = 1 + 2 + 3 + ... + 10 ?","option_a":"55","option_b":"45","option_c":"66","option_d":"100","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des n premiers entiers naturels est donnée par la formule S = n(n+1)\/2. Pour n = 10, S = 10×11\/2 = 55.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77489,"question":"La fonction f(x) = |x| est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction valeur absolue n'est pas dérivable en x = 0 car sa courbe présente un point anguleux à cet endroit.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77490,"question":"Quelle est la solution de l'équation x² - 4x + 4 = 0 ?","option_a":"x = 2 (double)","option_b":"x = -2","option_c":"x = 4","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation se factorise en (x - 2)² = 0, donc x = 2 est une solution double.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77491,"question":"La suite uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite uₙ = (-1)ⁿ alterne entre -1 et 1 et ne tend pas vers une limite finie. Elle est donc divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]