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[{"id":60027,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"3x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60028,"question":"La suite définie par uₙ = 2ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique de raison |r| \u003E 1 diverge vers l'infini. Ici, r = 2 \u003E 1, donc la suite diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60029,"question":"Résolvez l'équation différentielle y' + 2y = 0.","option_a":"y = Ce^(-2x)","option_b":"y = Ce^(2x)","option_c":"y = Cx + 2","option_d":"y = 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle linéaire du premier ordre y' + ay = 0 a pour solution y = Ce^(-ax). Ici, a = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60030,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/36","option_b":"1\/12","option_c":"1\/6","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 6 × 6 = 36 issues possibles. Un seul cas favorable : (6,6). La probabilité est donc 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60031,"question":"La fonction f(x) = ln(x) est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction logarithme népérien est définie uniquement pour x \u003E 0. Elle n'est pas définie en x = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60032,"question":"Quel est le terme général d'une suite arithmétique de premier terme u₀ = 3 et de raison r = 4 ?","option_a":"uₙ = 3 + 4n","option_b":"uₙ = 4 + 3n","option_c":"uₙ = 3n + 4","option_d":"uₙ = 4n + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une suite arithmétique, uₙ = u₀ + r × n. Ici, uₙ = 3 + 4n.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60033,"question":"La fonction f(x) = e^(-x²) est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction f est paire si f(-x) = f(x). Ici, f(-x) = e^(-(-x)²) = e^(-x²) = f(x). Donc f est paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60034,"question":"Résolvez l'inéquation x² - 5x + 6 ≤ 0.","option_a":"x ∈ [2, 3]","option_b":"x ∈ ]-∞, 2] ∪ [3, +∞[","option_c":"x ∈ ]2, 3[","option_d":"x ∈ {2, 3}","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de l'équation x² - 5x + 6 = 0 sont x = 2 et x = 3. Le trinôme est négatif entre ces racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60035,"question":"La dérivée de la fonction f(x) = cos(2x) est-elle f'(x) = -2sin(2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la formule de dérivation des fonctions composées, f'(x) = -sin(2x) × 2 = -2sin(2x). L'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60036,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/(2n² - 3) lorsque n tend vers l'infini ?","option_a":"1\/2","option_b":"0","option_c":"+∞","option_d":"2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = (1 + 1\/n²)\/(2 - 3\/n²). La limite est donc 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]