Quiz : Les fondamentaux des mathématiques en Terminale

Question 1 sur 10 10:00

[{"id":25838,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"f'(x) = 2x + 3","option_b":"f'(x) = x² + 3","option_c":"f'(x) = 2x - 5","option_d":"f'(x) = 3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (x²)' = 2x et (3x)' = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25839,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25840,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(π\/6) = sin(30°) = 1\/2, valeur à connaître par cœur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25841,"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},{"id":25842,"question":"Quelle est la limite de (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En factorisant, (x² - 1)\/(x - 1) = (x - 1)(x + 1)\/(x - 1) = x + 1. La limite est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25843,"question":"L'intégrale de 0 à 1 de x² dx est-elle égale à 1\/3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x² de 0 à 1 est [x³\/3]₀¹ = 1\/3 - 0 = 1\/3. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25844,"question":"Quelle est la solution de l'équation ln(x) = 1 ?","option_a":"x = 0","option_b":"x = 1","option_c":"x = e","option_d":"x = π","option_e":"","option_f":"","bonne_reponse":"C","explication":"ln(x) = 1 ⇒ x = e¹ = e. La solution est donc x = e.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25845,"question":"La fonction f(x) = x³ 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 ≠ x³ = f(x). La fonction est donc impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25846,"question":"Quelle est la valeur de cos(π\/3) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"cos(π\/3) = cos(60°) = 1\/2, valeur à connaître par cœur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25847,"question":"L'équation e^x = 0 admet-elle une solution réelle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction exponentielle e^x est toujours strictement positive pour tout x réel. L'équation n'a donc pas de solution.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]