Quiz : Testez vos connaissances en mathématiques de Terminale !

Question 1 sur 10 10:00

[{"id":31338,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2","option_d":"D. 6x + 5","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":31339,"question":"La suite définie par uₙ₊₁ = 2uₙ + 3 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 = uₙ + 3, qui n'est pas constant.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31340,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"A. 1\/6","option_b":"B. 1\/3","option_c":"C. 1\/2","option_d":"D. 2\/3","option_e":"","option_f":"","bonne_reponse":"C","explication":"Un dé a 6 faces, dont 3 sont paires (2, 4, 6). La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31341,"question":"L'équation x² + 4x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0, donc l'équation n'a pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31342,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x) \/ (x² - 1) quand x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. -1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) ≈ 3 pour x grand, donc la limite est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31343,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur l'intervalle [0, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 6x + 2 est positive sur [0, 2] (Δ' = 12 \u003E 0 et racines hors intervalle), donc f est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31344,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (2x + 1) dx ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 1,5","option_d":"D. 3","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale se calcule comme [x² + x]₀¹ = (1 + 1) - (0 + 0) = 2. La réponse correcte est 2, mais l'option C (1,5) est incorrecte. Correction : la bonne réponse est B (2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31345,"question":"Un vecteur directeur de la droite d'équation 2x - 3y + 5 = 0 est :","option_a":"A. (2, 3)","option_b":"B. (3, 2)","option_c":"C. (-3, -2)","option_d":"D. (2, -3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un vecteur directeur d'une droite ax + by + c = 0 est (-b, a). Ici, (-(-3), 2) = (3, 2). La réponse correcte est B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31346,"question":"La fonction exponentielle est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, eˣ \u003E 0. La fonction exponentielle est donc toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31347,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 \u003C 0 ?","option_a":"A. x ∈ ]2, 3[","option_b":"B. x ∈ ]-∞, 2[ ∪ ]3, +∞[","option_c":"C. x ∈ [2, 3]","option_d":"D. x ∈ ]-∞, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de x² - 5x + 6 = 0 sont 2 et 3. Le polynôme est négatif entre les racines, donc x ∈ ]2, 3[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]