Quiz Mathématiques : 3ème année secondaire — 1er trimestre

Question 1 sur 10 10:00

[{"id":47121,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A) x = 2 ou x = 3","option_b":"B) x = -2 ou x = -3","option_c":"C) x = 1 ou x = 6","option_d":"D) x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47122,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle dérivable en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction polynôme est dérivable sur ℝ, donc f(x) est dérivable en x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47123,"question":"Quelle est la dérivée de la fonction f(x) = (2x + 1)\/(x - 3) ?","option_a":"A) f'(x) = 2\/(x-3)","option_b":"B) f'(x) = -7\/(x-3)²","option_c":"C) f'(x) = (2x-5)\/(x-3)²","option_d":"D) f'(x) = (2x+7)\/(x-3)²","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation d'un quotient, f'(x) = [2(x-3) - (2x+1)(1)] \/ (x-3)² = -7\/(x-3)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47124,"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 si et seulement si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc la suite diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47125,"question":"Quelle est la solution de l'inéquation 2x - 5 ≤ 3x + 1 ?","option_a":"A) x ≥ -6","option_b":"B) x ≤ -6","option_c":"C) x ≥ 6","option_d":"D) x ≤ 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 5 ≤ 3x + 1, on obtient -x ≤ 6, soit x ≥ -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47126,"question":"La fonction f(x) = x² - 4x + 5 admet-elle un minimum en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2, et f''(x) = 2 \u003E 0, donc f admet un minimum en x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47127,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"A) 1\/6","option_b":"B) 1\/3","option_c":"C) 1\/2","option_d":"D) 2\/3","option_e":"","option_f":"","bonne_reponse":"C","explication":"Un dé équilibré 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":47128,"question":"La suite définie par uₙ = n² - 3n + 2 est-elle croissante à partir de n = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite est croissante si uₙ₊₁ - uₙ \u003E 0. Ici, uₙ₊₁ - uₙ = 2n - 2, qui est positif pour n ≥ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47129,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (3x² + 2x) dx ?","option_a":"A) 1","option_b":"B) 2","option_c":"C) 3","option_d":"D) 4","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale vaut [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47130,"question":"Une fonction affine f(x) = ax + b est-elle toujours dérivable ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction affine est dérivable sur ℝ, avec f'(x) = a pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]