Quiz Mathématiques : Terminale — Fonctions et Équations

Question 1 sur 10 10:00

[{"id":18838,"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 d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18839,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-1, 1], donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18840,"question":"Résoudre l'équation 2^(x+1) = 8.","option_a":"x = 2","option_b":"x = 1","option_c":"x = 3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"2^(x+1) = 8 équivaut à 2^(x+1) = 2³, donc x+1 = 3 ⇒ x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18841,"question":"Soit f(x) = ln(x). Quelle est la limite de f(x) quand x tend vers 0+ ?","option_a":"0","option_b":"-∞","option_c":"+∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) tend vers -∞ lorsque x tend vers 0 par la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18842,"question":"La suite définie par uₙ = n² + 2n est minorée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite uₙ = n² + 2n est croissante et tend vers +∞, donc elle est minorée par u₀ = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18843,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce^(-2x)","option_b":"y = Ce^(2x)","option_c":"y = C","option_d":"y = Cx","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle linéaire du premier ordre a pour solution générale y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18844,"question":"Soit f(x) = sin(x). Quelle est la dérivée de f(x) ?","option_a":"cos(x)","option_b":"-cos(x)","option_c":"sin(x)","option_d":"tan(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de sin(x) est cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18845,"question":"La fonction f(x) = 1\/x est définie en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0, car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18846,"question":"Résoudre l'inéquation x² - 5x + 6 ≤ 0.","option_a":"x ∈ [2, 3]","option_b":"x ∈ ]-∞, 2] ∪ [3, +∞[","option_c":"x ∈ [1, 4]","option_d":"x ∈ ]-∞, 1] ∪ [4, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de x² - 5x + 6 sont 2 et 3. Le polynôme est négatif entre ses racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18847,"question":"Quelle est la limite de (sin(x))\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"+∞","option_d":"-∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite classique (sin(x))\/x quand x → 0 est égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]