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Question 1 sur 10 10:00

[{"id":42666,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2x","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42667,"question":"L'intégrale de 0 à 1 de la fonction f(x) = x² est égale à 1\/3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x² entre 0 et 1 se calcule avec la primitive F(x) = x³\/3. F(1) - F(0) = 1\/3 - 0 = 1\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42668,"question":"Quelle est la solution de l'équation 2x - 7 = 3x + 1 ?","option_a":"x = -8","option_b":"x = 6","option_c":"x = -6","option_d":"x = 8","option_e":"","option_f":"","bonne_reponse":"C","explication":"En isolant x : 2x - 3x = 1 + 7 → -x = 8 → x = -8. La solution est donc x = -8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42669,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement impossible est 0, tandis que celle d'un événement certain est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42670,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, la limite devient (2 + 1\/n)\/(1 + 3\/n) → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42671,"question":"Le déterminant d'une matrice 2x2 [[a, b], [c, d]] est égal à ad - bc.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le déterminant d'une matrice 2x2 se calcule bien avec la formule ad - bc.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42672,"question":"Quelle est la forme exponentielle du nombre complexe z = -1 + i√3 ?","option_a":"2e^(iπ\/3)","option_b":"2e^(i2π\/3)","option_c":"√2 e^(iπ\/4)","option_d":"2e^(iπ)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le module de z est √((-1)² + (√3)²) = 2, et l'argument θ vérifie cosθ = -1\/2 et sinθ = √3\/2, soit θ = 2π\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42673,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, eˣ \u003E 0. La fonction exponentielle est strictement positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42674,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 \u003C 0 ?","option_a":"x ∈ ]2; 3[","option_b":"x ∈ ]-∞; 2[ ∪ ]3; +∞[","option_c":"x ∈ ℝ","option_d":"x ∈ ]-∞; 2[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le polynôme x² - 5x + 6 se factorise en (x-2)(x-3). Le signe est négatif entre les racines, soit x ∈ ]2; 3[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42675,"question":"La somme des angles d'un triangle est toujours égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle plan, la somme des angles est toujours de 180°, qu'il soit rectangle, isocèle ou quelconque.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]