Quiz : Maîtrisez les fonctions dérivées et les équations en Terminale Math

Question 1 sur 10 10:00

[{"id":66902,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"A : 6x - 5","option_b":"B : 3x - 5","option_c":"C : 6x² - 5","option_d":"D : 3x² - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66903,"question":"L'équation x² - 4x + 3 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = (-4)² - 4×1×3 = 4 \u003E 0, donc deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66904,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) lorsque x tend vers l'infini ?","option_a":"A : 0","option_b":"B : 2","option_c":"C : +∞","option_d":"D : -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) ≈ 2 pour x grand.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66905,"question":"La fonction f(x) = x³ - 3x² + 4 est croissante sur l'intervalle [-1, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x est négative sur [-1, 0] et positive sur [0, 2], donc la fonction n'est pas croissante sur tout l'intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66906,"question":"Quelle est la solution de l'inéquation (x - 1)(x + 2) \u003E 0 ?","option_a":"A : x ∈ ]-∞, -2[ ∪ ]1, +∞[","option_b":"B : x ∈ ]-2, 1[","option_c":"C : x ∈ ]-∞, 1[","option_d":"D : x ∈ ]-2, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit est positif lorsque les deux facteurs sont de même signe, donc x \u003C -2 ou x \u003E 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66907,"question":"La suite définie par uₙ = 2n + 1 est arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence entre deux termes consécutifs est constante : uₙ₊₁ - uₙ = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66908,"question":"Quelle est la dérivée de la fonction g(x) = ln(3x + 1) ?","option_a":"A : 3 \/ (3x + 1)","option_b":"B : 1 \/ (3x + 1)","option_c":"C : 3x \/ (3x + 1)","option_d":"D : 1 \/ x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u) est u'\/u, donc g'(x) = 3 \/ (3x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66909,"question":"L'espérance d'une variable aléatoire suivant une loi binomiale B(n, p) est np.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n, p) est bien E(X) = np.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66910,"question":"Quelle est la solution de l'équation e^(2x) = 5 ?","option_a":"A : x = ln(5)\/2","option_b":"B : x = 5\/2","option_c":"C : x = e^5","option_d":"D : x = ln(2)\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En prenant le logarithme des deux côtés, on obtient 2x = ln(5), donc x = ln(5)\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66911,"question":"La fonction f(x) = x^4 - 4x³ admet un extremum local en x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 4x³ - 12x² s'annule en x = 0 et x = 3. En x = 3, la dérivée change de signe, donc c'est un extremum local.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]