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Question 1 sur 10 10:00

[{"id":71212,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"A: 6x - 5","option_b":"B: 3x - 5","option_c":"C: 6x² - 5","option_d":"D: 6x - 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = 3x² - 5x + 2 est f'(x) = 6x - 5, car la dérivée de x² est 2x et celle de x est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71213,"question":"La limite de la fonction f(x) = (2x + 1)\/(x - 3) quand x tend vers +∞ est égale à 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite est bien égale à 2, car les termes dominants sont 2x\/x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71214,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"A: x = 1","option_b":"B: x = 2","option_c":"C: x = 3","option_d":"D: x = 0","option_e":"","option_f":"","bonne_reponse":"B","explication":"2^(x+1) = 8 ⇒ 2^(x+1) = 2³ ⇒ x + 1 = 3 ⇒ x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71215,"question":"Le produit scalaire de deux vecteurs orthogonaux est égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71216,"question":"Quelle est la formule de la variance d'une variable aléatoire X ?","option_a":"A: V(X) = E(X²) - E(X)","option_b":"B: V(X) = E(X²) - [E(X)]²","option_c":"C: V(X) = E(X)² - E(X²)","option_d":"D: V(X) = E(X) - E(X²)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La variance est définie par V(X) = E(X²) - [E(X)]², où E(X) est l'espérance de X.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71217,"question":"L'équation de la tangente à la courbe de f(x) = x² + 3x au point d'abscisse x = 1 est y = 5x - 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La tangente a pour équation y = f'(1)(x - 1) + f(1) = 5(x - 1) + 4 = 5x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71218,"question":"Quelle est la limite de la suite u_n = (3n + 1)\/(2n - 5) quand n tend vers +∞ ?","option_a":"A: 0","option_b":"B: 3\/2","option_c":"C: +∞","option_d":"D: 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite est 3\/2, car les termes dominants sont 3n\/2n = 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71219,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) n'est définie que pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71220,"question":"Quelle est la primitive de f(x) = 4x³ - 2x + 1 ?","option_a":"A: F(x) = x⁴ - x² + x + C","option_b":"B: F(x) = x⁴ - x² + C","option_c":"C: F(x) = 12x² - 2 + C","option_d":"D: F(x) = x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de f(x) = 4x³ - 2x + 1 est F(x) = x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71221,"question":"L'espérance d'une variable aléatoire suivant une loi binomiale B(n, p) est égale à np.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n, p) est bien égale à np.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]