Quiz : Maîtrisez les suites et fonctions en Seconde !

Question 1 sur 10 10:00

[{"id":77932,"question":"Quelle est la raison d'une suite géométrique dont les termes sont 3, 6, 12, 24 ?","option_a":"2","option_b":"3","option_c":"1.5","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"La raison q est obtenue en divisant un terme par le précédent : 6\/3 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77933,"question":"Une suite est définie par u(n+1) = 2u(n) + 1 avec u(0) = 0. Cette suite est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite arithmétique a une différence constante entre termes. Ici, u(1) = 1, u(2) = 3, la différence n'est pas constante (2 ≠ 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77934,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 4x + 3 ?","option_a":"(x - 2)² - 1","option_b":"(x - 1)² + 2","option_c":"2(x - 1)² - 1","option_d":"(x - 2)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est f(x) = (x - α)² + β avec α = -b\/(2a) = 2 et β = f(α) = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77935,"question":"Résoudre l'inéquation 2x - 5 \u003E 3x + 1.","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 5 \u003E 3x + 1 ⇒ -x \u003E 6 ⇒ x \u003C -6 (en divisant par -1, l'inégalité change de sens).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77936,"question":"La fonction f(x) = -3x² + 6x - 2 admet-elle un maximum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient a = -3 \u003C 0, donc la parabole est tournée vers le bas et admet un maximum en son sommet.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77937,"question":"Quelle est la somme des 5 premiers termes d'une suite arithmétique de premier terme 2 et de raison 3 ?","option_a":"40","option_b":"45","option_c":"50","option_d":"55","option_e":"","option_f":"","bonne_reponse":"B","explication":"S5 = (5\/2) * (2*2 + (5-1)*3) = 2.5 * (4 + 12) = 2.5 * 16 = 40. La bonne réponse est 40 (option A).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77938,"question":"La fonction f(x) = 4x + 7 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur 4 \u003E 0, donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77939,"question":"Résoudre 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":"Les solutions sont obtenues en factorisant : (x - 2)(x - 3) = 0 ⇒ x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77940,"question":"Une suite est définie par u(n) = 5n - 2. Cette suite est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence entre deux termes consécutifs est constante : u(n+1) - u(n) = 5, donc la suite est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77941,"question":"Quelle est l'image de 2 par la fonction f(x) = -x² + 4x - 1 ?","option_a":"3","option_b":"1","option_c":"5","option_d":"7","option_e":"","option_f":"","bonne_reponse":"A","explication":"f(2) = -(2)² + 4*2 - 1 = -4 + 8 - 1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]