Quiz Maths Bac : Équations, Fonctions et Suites

Question 1 sur 10 10:00

[{"id":3294,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisons l'équation : (x-2)(x-3)=0. Les solutions sont donc x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3295,"question":"La fonction f(x) = x³ - 3x² + 2x est croissante sur l'intervalle [0, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Calculons la dérivée f'(x) = 3x² - 6x + 2. f'(x) = 0 pour x=1±√(1\/3). La fonction n'est pas croissante sur tout l'intervalle [0,2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3296,"question":"Quelle est la limite de (2x² + 3x - 1)\/(x² - 4) quand x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Divisons numérateur et dénominateur par x² : (2 + 3\/x - 1\/x²)\/(1 - 4\/x²) → 2\/1 = 2 quand x→∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3297,"question":"La suite définie par uₙ = 2n² - 3n + 1 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, uₙ₊₁ - uₙ = 4n - 1, qui dépend de n.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3298,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x+1) ?","option_a":"f'(x) = e^(2x+1)","option_b":"f'(x) = 2e^(2x+1)","option_c":"f'(x) = (2x+1)e^(2x)","option_d":"f'(x) = e^(2x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la règle de dérivation des fonctions exponentielles : f'(x) = 2e^(2x+1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3299,"question":"La suite uₙ = (1 + 1\/n)^n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette suite converge vers e (nombre d'Euler) quand n tend vers l'infini, d'après la définition de la limite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3300,"question":"Résolvez l'inéquation : x² - 4x + 3 \u003E 0.","option_a":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_b":"x ∈ ]1, 3[","option_c":"x ∈ ]-∞, 3[","option_d":"x ∈ ]-1, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines sont x=1 et x=3. Le polynôme est positif à l'extérieur des racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3301,"question":"La fonction f(x) = ln(x) est définie pour x \u003E 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction logarithme népérien est définie uniquement pour les valeurs positives de x, donc x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3302,"question":"Quelle est la valeur de la limite de (1 + 1\/n)^n quand n tend vers l'infini ?","option_a":"1","option_b":"e","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette limite est la définition du nombre d'Euler e ≈ 2,71828.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":3303,"question":"La suite uₙ = 3*2ⁿ est-elle géométrique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le rapport entre deux termes consécutifs est constant : uₙ₊₁\/uₙ = 2, donc la suite est géométrique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]