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Question 1 sur 10 10:00

[{"id":49711,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = ax^n est f'(x) = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49712,"question":"La suite (u_n) définie par u_n = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, u_{n+1} - u_n = 2, donc elle est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49713,"question":"Quelle est la limite de la fonction f(x) = (2x² - 3x + 1)\/(x² + 1) quand x tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (2 - 3\/x + 1\/x²)\/(1 + 1\/x²). Quand x→∞, f(x)→2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49714,"question":"L'équation différentielle y' + y = 0 a pour solution générale :","option_a":"y = Ce^x","option_b":"y = Ce^{-x}","option_c":"y = Cx","option_d":"y = C","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation y' + y = 0 est une équation différentielle linéaire du premier ordre. Sa solution générale est y = Ce^{-x}, où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49715,"question":"Dans un repère orthonormé, le produit scalaire de deux vecteurs u et v est nul si et seulement si :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit scalaire u·v = 0 si et seulement si les vecteurs u et v sont orthogonaux (perpendiculaires).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49716,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 6×6 = 36 issues possibles. Un seul cas favorable (6,6), donc la probabilité est 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49717,"question":"La fonction f(x) = x³ - 3x² + 2x est croissante sur l'intervalle :","option_a":"]-∞; 0[","option_b":"[0; 2]","option_c":"[2; +∞[","option_d":"]-∞; +∞[","option_e":"","option_f":"","bonne_reponse":"C","explication":"La dérivée f'(x) = 3x² - 6x + 2. Le discriminant Δ = 36 - 24 = 12 \u003E 0, donc f'(x) \u003E 0 pour x \u003E 2 (car le coefficient de x² est positif).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49718,"question":"Une loi normale centrée réduite a pour moyenne :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une loi normale centrée réduite (N(0,1)) a une moyenne μ = 0 et un écart-type σ = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49719,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2; 3]","option_b":"x ∈ ]-∞; 2] ∪ [3; +∞[","option_c":"x ∈ ]2; 3[","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de x² - 5x + 6 = 0 sont x = 2 et x = 3. Le trinôme est négatif entre ses racines, donc x ∈ [2; 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49720,"question":"La fonction f(x) = ln(x) est définie pour :","option_a":"x \u003E 0","option_b":"x ≥ 0","option_c":"x ∈ ℝ","option_d":"x \u003C 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction logarithme népérien ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]