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Question 1 sur 10 10:00

[{"id":13693,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 7 ?","option_a":"3x² - 4x + 5","option_b":"3x² - 4x + 5x","option_c":"x² - 2x + 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 : (x^n)' = n*x^(n-1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13694,"question":"La limite de (sin x)\/x quand x tend vers 0 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une limite fondamentale en analyse : lim(x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13695,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce^(-2x)","option_b":"y = Ce^(2x)","option_c":"y = Cx^2","option_d":"y = C\/x^2","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une équation différentielle linéaire du premier ordre. La solution générale est y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13696,"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 sont orthogonaux si et seulement si leur produit scalaire est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13697,"question":"Quelle est la primitive de f(x) = 4x³ - 3x² + 2x - 1 ?","option_a":"x⁴ - x³ + x² - x + C","option_b":"x⁴ - x³ + x² - x","option_c":"4x⁴ - 3x³ + 2x² - x + C","option_d":"x⁴ - x³ + x² - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive s'obtient en intégrant terme à terme : ∫4x³dx = x⁴, ∫-3x²dx = -x³, etc.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13698,"question":"La suite définie par uₙ = (2n + 1)\/(n + 3) est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En calculant la limite quand n tend vers l'infini, on trouve lim uₙ = 2, donc la suite est convergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13699,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (3x² + 2x) dx ?","option_a":"2","option_b":"1","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons l'intégrale : [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13700,"question":"L'équation x² + y² + z² = 1 représente une sphère de centre O et de rayon 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est l'équation cartésienne d'une sphère centrée à l'origine avec un rayon de 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13701,"question":"Quelle est la solution de 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":"En résolvant : 2x - 5 \u003E 3x + 1 ⇒ -x \u003E 6 ⇒ x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13702,"question":"La fonction f(x) = e^(-x²) est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Puisque e^(-x²) \u003E 0 pour tout x réel (exponentielle toujours positive), la fonction est toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]