Réviser les fondamentaux : Mathématiques Baccalauréat

Question 1 sur 10 10:00

[{"id":28248,"question":"Quelle est la dérivée de la fonction f(x) = x³ + 2x² - 5x + 1 ?","option_a":"3x² + 4x - 5","option_b":"x² + 4x - 5","option_c":"3x² + 4x + 5","option_d":"3x² + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : f'(x) = 3x² + 4x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28249,"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.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28250,"question":"Quel est le déterminant d'une matrice 2x2 [[a, b], [c, d]] ?","option_a":"a*d - b*c","option_b":"a*c - b*d","option_c":"a + d","option_d":"a*b - c*d","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le déterminant d'une matrice 2x2 est calculé par la formule ad - bc.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28251,"question":"L'intégrale ∫₀¹ (3x² + 2x) dx vaut :","option_a":"2","option_b":"1","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale se calcule en trouvant une primitive : [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28252,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux vecteurs sont orthogonaux si et seulement si leur produit scalaire est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28253,"question":"Quelle est la limite de la suite uₙ = (2n + 3)\/(n + 1) quand n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"3","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient lim (2 + 3\/n)\/(1 + 1\/n) = 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28254,"question":"L'équation x² - 5x + 6 = 0 a pour solutions :","option_a":"x = 2 et x = 3","option_b":"x = 1 et x = 6","option_c":"x = -2 et x = -3","option_d":"x = 0 et x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions s'obtiennent en factorisant : (x - 2)(x - 3) = 0, donc x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28255,"question":"La fonction f(x) = e^x est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^x est e^x, qui est toujours positive, donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28256,"question":"Quel est le barycentre des points A(1,2) et B(3,4) affectés des coefficients 1 et 1 ?","option_a":"G(2,3)","option_b":"G(1,2)","option_c":"G(3,4)","option_d":"G(4,6)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le barycentre G a pour coordonnées ((1*1 + 1*3)\/2, (1*2 + 1*4)\/2) = (2, 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28257,"question":"La suite uₙ = n² est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite convergente a une limite finie quand n tend vers l'infini. Ici, uₙ tend vers +∞, donc elle diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]