Quiz Mathématiques Bac Sciences : Teste tes connaissances !

Question 1 sur 10 10:00

[{"id":75912,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2","option_d":"D. 6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75913,"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 = 25 - 24 = 1 \u003E 0, donc deux solutions réelles distinctes : x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75914,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) quand x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) ≈ 2 pour x grand, donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75915,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75916,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 1 ?","option_a":"A. x \u003E 6","option_b":"B. x \u003C 8","option_c":"C. x \u003E 8","option_d":"D. x \u003C 6","option_e":"","option_f":"","bonne_reponse":"C","explication":"3x - 7 \u003E 2x + 1 ⇒ x \u003E 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75917,"question":"La fonction f(x) = x³ est strictement 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 ≥ 0 et ne s'annule qu'en x=0, donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75918,"question":"Quelle est l'intégrale de f(x) = 4x³ entre 0 et 2 ?","option_a":"A. 8","option_b":"B. 16","option_c":"C. 32","option_d":"D. 64","option_e":"","option_f":"","bonne_reponse":"C","explication":"∫4x³ dx = x⁴, donc ∫₀² 4x³ dx = 2⁴ - 0⁴ = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75919,"question":"Deux événements A et B sont indépendants si P(A ∩ B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est la définition de l'indépendance de deux événements.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75920,"question":"Quelle est la valeur de cos(π\/3) ?","option_a":"A. 0","option_b":"B. 1\/2","option_c":"C. √2\/2","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"cos(π\/3) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75921,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution générale de y' + 2y = 0 est y = Ce^(-2x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]