Maths 3ème année secondaire : Testez vos connaissances en synthèse

Question 1 sur 10 10:00

[{"id":19848,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19849,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19850,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) quand x tend vers +∞ ?","option_a":"2","option_b":"1\/2","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"On divise le numérateur et le dénominateur par x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 4\/x²). Quand x tend vers +∞, les termes en 1\/x tendent vers 0, donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19851,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est l'énoncé du théorème de Pythagore, valable uniquement pour les triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19852,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ 2","option_d":"x ≥ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"On soustrait 2x des deux côtés : x - 7 ≤ 5, puis on ajoute 7 : x ≤ 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19853,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x), donc elle n'est pas paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19854,"question":"Quelle est l'aire d'un cercle de rayon r = 5 cm ?","option_a":"25π cm²","option_b":"10π cm²","option_c":"50π cm²","option_d":"100π cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un cercle est donnée par A = πr². Avec r = 5 cm, A = 25π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19855,"question":"La fonction f(x) = 1\/x est-elle continue 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, donc elle n'est pas continue en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19856,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x = 1","option_b":"x = 2","option_c":"x = 3","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"B","explication":"On écrit 8 comme 2³, donc 2^(x+1) = 2³. Par identification, x + 1 = 3, donc x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19857,"question":"Le vecteur u(2; -3) et le vecteur v(-4; 6) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux vecteurs sont colinéaires si l'un est multiple de l'autre. Ici, v = -2u, donc ils sont colinéaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]