Quiz Mathématiques Terminale : Concepts, Preuves et Exercices

Question 1 sur 10 10:00

[{"id":52941,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 2x + 5 ?","option_a":"6x - 2","option_b":"3x² - 2","option_c":"6x² - 2x","option_d":"3x - 2","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":52942,"question":"La suite définie par uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite alterne entre -1 et 1, elle n'a pas de limite finie, donc elle est divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52943,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e²","option_b":"x = 2","option_c":"x = e","option_d":"x = ln(2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = 2 équivaut à x = e², car ln(e²) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52944,"question":"Le théorème des valeurs intermédiaires s'applique-t-il à toute fonction continue sur un intervalle ?","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 à toute fonction continue sur un intervalle fermé [a, b].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52945,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/n quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"+∞","option_d":"n","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = 1 + 1\/n², donc la limite est +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52946,"question":"La fonction f(x) = x³ - 3x est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ + 3x ≠ f(x), donc elle n'est pas paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52947,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 36 issues possibles, dont une seule correspond à un double 6, donc la probabilité est 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52948,"question":"Le produit scalaire de deux vecteurs orthogonaux est-il toujours nul ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52949,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"x⁴ - x² + x + C","option_b":"x⁴ - x + x² + C","option_c":"4x⁴ - x² + x + C","option_d":"x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive se calcule en intégrant terme par terme : ∫(4x³ - 2x + 1)dx = x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":52950,"question":"La fonction exponentielle est-elle 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}]