Maîtrisez les exercices de Terminale en Mathématiques !

Question 1 sur 10 10:00

[{"id":53731,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2x","option_c":"6x - 5","option_d":"x² + 2x - 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":53732,"question":"La limite de la fonction f(x) = (x² - 1)\/(x - 1) en x = 1 est égale à 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, f(x) = (x - 1)(x + 1)\/(x - 1) = x + 1 pour x ≠ 1. Ainsi, lim(x→1) f(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53733,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53734,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-1, 1], donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53735,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/n en +∞ ?","option_a":"0","option_b":"1","option_c":"2","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = 2 + 1\/n. Ainsi, lim(n→+∞) uₙ = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53736,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est 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":53737,"question":"Quelle est l'équation de la tangente à la courbe f(x) = x² au point d'abscisse x = 1 ?","option_a":"y = 2x + 1","option_b":"y = 2x - 1","option_c":"y = x + 1","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La tangente a pour équation y = f'(1)(x - 1) + f(1) = 2(x - 1) + 1 = 2x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53738,"question":"La fonction f(x) = 1\/x est définie sur ℝ.","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, donc son ensemble de définition est ℝ*.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53739,"question":"Quelle est la somme des 5 premiers termes de la suite géométrique de premier terme 2 et de raison 3 ?","option_a":"242","option_b":"243","option_c":"121","option_d":"122","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme S₅ = 2(3⁵ - 1)\/(3 - 1) = 2(243 - 1)\/2 = 242.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53740,"question":"La fonction f(x) = eˣ est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle eˣ est strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]