Quiz interactif : Maîtrisez les Maths de Terminale !

Question 1 sur 10 10:00

[{"id":16648,"question":"Quelle est la limite de la suite définie par uₙ = (3n² + 2n - 1)\/(2n² + 5) lorsque n tend vers l'infini ?","option_a":"A. 0","option_b":"B. 1,5","option_c":"C. 3\/2","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"La limite d'une suite rationnelle est le rapport des coefficients dominants : ici, 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16649,"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] (discriminant négatif), donc la fonction est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16650,"question":"Quel est le discriminant de l'équation 2x² - 5x + 3 = 0 ?","option_a":"A. 1","option_b":"B. 49","option_c":"C. 25","option_d":"D. 16","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = (-5)² - 4*2*3 = 25 - 24 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16651,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est-elle de 1\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16652,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x+1) ?","option_a":"A. e^(2x+1)","option_b":"B. 2e^(2x+1)","option_c":"C. e^(2x)","option_d":"D. 2e^(x+1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^u est u'e^u, ici u = 2x+1 donc u' = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16653,"question":"Le théorème des valeurs intermédiaires s'applique-t-il à toute fonction continue sur un intervalle fermé ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème des valeurs intermédiaires s'applique aux fonctions continues sur un intervalle fermé [a ; b].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16654,"question":"Quelle est la solution générale de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(-2x)","option_b":"B. y = Cx²","option_c":"C. y = Ce^(2x)","option_d":"D. y = C\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation y' + 2y = 0 a pour solution y = Ce^(-2x) (solution de l'équation homogène).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16655,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est-il égal à la somme des carrés des deux autres côtés ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore : dans un triangle rectangle, a² + b² = c² où c est l'hypoténuse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16656,"question":"Quelle est la valeur de ∫(3x² + 2x) dx ?","option_a":"A. x³ + x² + C","option_b":"B. x³ + x + C","option_c":"C. 6x + 2 + C","option_d":"D. x³ + 2x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x² est x³ et celle de 2x est x², donc la réponse est x³ + x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16657,"question":"La fonction f(x) = 1\/x est-elle 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}]