Quiz : Identifiez les réponses exactes en mathématiques — Terminale

Question 1 sur 10 10:00

[{"id":18418,"question":"Quelle est la solution exacte de l'équation 2x + 5 = 11 ?","option_a":"x = 3","option_b":"x = 4","option_c":"x = 2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 5 des deux côtés, on obtient 2x = 6, puis en divisant par 2, x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18419,"question":"La dérivée de la fonction f(x) = x² + 3x + 2 est f'(x) = 2x + 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de 2 est 0. Donc f'(x) = 2x + 3 est correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18420,"question":"Quelle est la solution exacte de l'inéquation -3x + 7 \u003E 1 ?","option_a":"x \u003C 2","option_b":"x \u003E 2","option_c":"x \u003C -2","option_d":"x \u003E -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 7, on obtient -3x \u003E -6, puis en divisant par -3 (changement de sens), x \u003C 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18421,"question":"La fonction f(x) = x³ est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² est toujours positive ou nulle, donc la fonction est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18422,"question":"Quelle est la solution exacte de l'équation √(x + 4) = 3 ?","option_a":"x = 5","option_b":"x = 13","option_c":"x = 9","option_d":"x = -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En élevant au carré, on obtient x + 4 = 9, donc x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18423,"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 possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18424,"question":"Quelle est la solution exacte de l'équation 4^(x-1) = 16 ?","option_a":"x = 3","option_b":"x = 2","option_c":"x = 4","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"16 = 4², donc 4^(x-1) = 4² ⇒ x - 1 = 2 ⇒ x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18425,"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 elle n'est pas définie sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18426,"question":"Quelle est la solution exacte de l'équation sin(x) = √2\/2 pour x ∈ [0, π] ?","option_a":"x = π\/4","option_b":"x = π\/3","option_c":"x = π\/6","option_d":"x = 3π\/4","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(π\/4) = √2\/2, et π\/4 est dans l'intervalle [0, π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18427,"question":"La limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 est 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 pour x ≠ 1, donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]