Quiz : Maîtrisez les fondamentaux de la Terminale Mathématiques

Question 1 sur 10 10:00

[{"id":20348,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2x","option_d":"f'(x) = 9x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20349,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique converge uniquement si |q| \u003C 1. Ici, q = 2, donc la suite diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20350,"question":"Quelle est la solution générale de l'équation différentielle y' = 3y ?","option_a":"y = Ce^(3x)","option_b":"y = 3x + C","option_c":"y = Ce^(-3x)","option_d":"y = 3Ce^x","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle y' = ky a pour solution générale y = Ce^(kx). Ici, k = 3, donc y = Ce^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20351,"question":"Dans une loi normale centrée réduite, quelle est la probabilité P(-1 ≤ Z ≤ 1) ?","option_a":"≈ 0.68","option_b":"≈ 0.95","option_c":"≈ 0.997","option_d":"≈ 0.34","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale centrée réduite, environ 68% des valeurs sont dans l'intervalle [-1, 1].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20352,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur l'intervalle [-2, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur [-1, 1] et croissante ailleurs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20353,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n), donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20354,"question":"L'équation différentielle y'' + 4y = 0 a-t-elle pour solution y = sin(2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée seconde de sin(2x) est -4sin(2x), donc y'' + 4y = 0 est vérifiée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20355,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"C","explication":"Un dé 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":20356,"question":"La fonction f(x) = e^(2x) est-elle solution de l'équation différentielle y' - 2y = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(2x) est 2e^(2x), donc y' - 2y = 2e^(2x) - 2e^(2x) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20357,"question":"Quelle est la somme des 10 premiers termes de la suite arithmétique de premier terme u₀ = 5 et de raison r = 3 ?","option_a":"175","option_b":"200","option_c":"195","option_d":"180","option_e":"","option_f":"","bonne_reponse":"C","explication":"La somme des n premiers termes d'une suite arithmétique est Sₙ = n\/2 * (2u₀ + (n-1)r). Ici, S₁₀ = 10\/2 * (10 + 27) = 195.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]