Maths Terminale : Testez vos connaissances en séries d'exercices

Question 1 sur 10 10:00

[{"id":19088,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"D","explication":"En simplifiant f(x) = (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1, on obtient lim(x→1) f(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19089,"question":"Soit une suite définie par u₀ = 2 et uₙ₊₁ = 3uₙ - 1. Cette suite 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 termes. Ici, u₁ - u₀ = 3 et u₂ - u₁ = 6, donc elle n'est pas arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19090,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) * ln(x) ?","option_a":"A. e^(2x) * (2ln(x) + 1\/x)","option_b":"B. e^(2x) * (2ln(x) - 1\/x)","option_c":"C. 2e^(2x) * ln(x)","option_d":"D. e^(2x) * (ln(x) + 2\/x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la dérivée d'un produit et la règle de la chaîne : f'(x) = 2e^(2x)ln(x) + e^(2x)\/x = e^(2x)(2ln(x) + 1\/x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19091,"question":"L'intégrale ∫₀¹ (3x² + 2x) dx est égale à :","option_a":"A. 2","option_b":"B. 1","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons : ∫(3x² + 2x)dx = x³ + x² + C. Évaluée entre 0 et 1, cela donne (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19092,"question":"Soit A = [[1, 2], [3, 4]]. Le déterminant de A est égal à :","option_a":"A. -2","option_b":"B. 2","option_c":"C. -1","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"det(A) = (1*4) - (2*3) = 4 - 6 = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19093,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"f'(x) = 3x² - 3. f'(x) \u003C 0 pour x ∈ ]-1, 1[, donc la fonction n'est pas croissante sur [-2, 2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19094,"question":"Résoudre l'équation différentielle y' + 2y = 0 avec y(0) = 1.","option_a":"A. y = e^(-2x)","option_b":"B. y = e^(2x)","option_c":"C. y = 1 - 2x","option_d":"D. y = e^(-x\/2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Solution générale : y = Ce^(-2x). Avec y(0)=1, on obtient C=1, donc y = e^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19095,"question":"Soit Z = 3 + 4i un nombre complexe. Son module est égal à :","option_a":"A. 5","option_b":"B. 7","option_c":"C. 25","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Module = √(3² + 4²) = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19096,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est :","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":"Il y a 3 nombres pairs (2,4,6) sur 6 faces, donc P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19097,"question":"Soit f une fonction continue sur [a, b]. Le théorème des valeurs intermédiaires garantit que :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si f(a) \u003C 0 et f(b) \u003E 0, alors il existe c ∈ ]a, b[ tel que f(c) = 0 (théorème des valeurs intermédiaires).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]