Quiz Maths 2ème Année : Algèbre, Géométrie & Analyse

Question 1 sur 10 10:00

[{"id":34213,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -5","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 2x = 7 + 5 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34214,"question":"La dérivée de f(x) = x² + 3x - 4 est f'(x) = 2x + 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -4 est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34215,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"0","option_b":"1","option_c":"Leur norme","option_d":"Indéfini","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34216,"question":"Résolvez l'inéquation 2x + 5 ≤ 11.","option_a":"x ≤ 3","option_b":"x ≥ 3","option_c":"x ≤ -3","option_d":"x ≥ -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x ≤ 6 → x ≤ 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34217,"question":"La fonction f(x) = x³ est toujours croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Sa dérivée f'(x) = 3x² est toujours positive sauf en x=0 où elle est nulle, mais la fonction reste croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34218,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 7 ?","option_a":"-4","option_b":"7","option_c":"4","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est le nombre devant x dans l'équation réduite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34219,"question":"Soit f(x) = (2x + 1)\/(x - 3). Quelle est sa limite en +∞ ?","option_a":"2","option_b":"1\/2","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En +∞, le terme dominant est 2x\/x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34220,"question":"Deux vecteurs u et v sont colinéaires si et seulement si u = kv pour un réel k.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est la définition de la colinéarité entre deux vecteurs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34221,"question":"Quelle est la dérivée de f(x) = e^(2x) ?","option_a":"2e^(2x)","option_b":"e^(2x)","option_c":"2xe^(2x-1)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^u est u'e^u, ici u=2x → u'=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34222,"question":"L'équation x² + 4x + 5 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0 → pas de solution réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]