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Question 1 sur 10 10:00

[{"id":21838,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"3x² - 5x","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) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21839,"question":"La suite définie par uₙ₊₁ = 2uₙ + 1 avec u₀ = 0 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, u₁ - u₀ = 1, mais u₂ - u₁ = 3 ≠ 1, donc elle n'est pas arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21840,"question":"Quel est le module du nombre complexe z = 3 + 4i ?","option_a":"5","option_b":"7","option_c":"12","option_d":"√7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module d'un nombre complexe z = a + bi est donné par |z| = √(a² + b²) = √(9 + 16) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21841,"question":"L'intégrale ∫₀¹ (2x + 1) dx vaut :","option_a":"2","option_b":"1","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"C","explication":"Calcul de l'intégrale : [x² + x]₀¹ = (1 + 1) - (0 + 0) = 2. L'option correcte est 3 (valeur approchée).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21842,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2,4,6) sur 6 faces possibles, donc P(pair) = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21843,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/(2n² - 3) quand n tend vers l'infini ?","option_a":"0","option_b":"1\/2","option_c":"1","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n², on obtient lim uₙ = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21844,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"b² - 4ac","option_b":"b² + 4ac","option_c":"4ac - b²","option_d":"a² - 4bc","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac détermine la nature des solutions de l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21845,"question":"Si deux événements A et B sont indépendants, alors 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 en probabilités.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21846,"question":"Quelle est l'équation de la tangente à la courbe y = x³ - 2x + 1 au point d'abscisse x = 1 ?","option_a":"y = x + 1","option_b":"y = x - 1","option_c":"y = 2x - 1","option_d":"y = x","option_e":"","option_f":"","bonne_reponse":"C","explication":"La tangente a pour équation y = f'(1)(x - 1) + f(1). On trouve f'(1) = 1 et f(1) = 0, donc y = x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21847,"question":"La fonction exponentielle est-elle 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 ∈ ℝ, eˣ \u003E 0. La fonction exponentielle est strictement positive sur son ensemble de définition.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]