Quiz interactif : Maths Bac – Testez vos connaissances en 10 questions

Question 1 sur 10 10:00

[{"id":31508,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"A. 6x - 5","option_b":"B. 3x - 5","option_c":"C. 6x² - 5","option_d":"D. 6x - 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : si f(x) = axⁿ, alors f'(x) = naxⁿ⁻¹. Ici, f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31509,"question":"L'équation x² - 4x + 4 = 0 admet 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. Une seule solution réelle double : x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31510,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. -∞","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x, on obtient f(x) = (2 + 1\/x)\/(1 - 3\/x). Lorsque x → +∞, 1\/x → 0, donc f(x) → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31511,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. Sur [-2, -1] et [1, 2], f est croissante, mais décroissante sur [-1, 1].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31512,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"A. x \u003C -6","option_b":"B. x \u003E -6","option_c":"C. x \u003C 6","option_d":"D. x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 5 \u003E 3x + 1, on obtient -x \u003E 6, soit x \u003C -6 (en multipliant par -1, l'inégalité change de sens).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31513,"question":"Le nombre complexe z = 3 + 4i a pour module |z| = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module d'un nombre complexe z = a + bi est |z| = √(a² + b²). Ici, |z| = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31514,"question":"Quelle est la somme des 5 premiers termes de la suite géométrique de premier terme u₁ = 2 et de raison q = 3 ?","option_a":"A. 62","option_b":"B. 242","option_c":"C. 121","option_d":"D. 364","option_e":"","option_f":"","bonne_reponse":"B","explication":"La somme des n premiers termes d'une suite géométrique est Sₙ = u₁(qⁿ - 1)\/(q - 1). Ici, S₅ = 2(3⁵ - 1)\/2 = 242.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31515,"question":"La fonction f(x) = eˣ est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée seconde f''(x) = eˣ est toujours positive, donc f est convexe sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31516,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","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":"Les nombres pairs sont 2, 4, 6. Il y a 3 issues favorables sur 6 possibles, donc P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31517,"question":"L'équation cos(x) = 0 admet une solution dans l'intervalle [0, π\/2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"cos(0) = 1 et cos(π\/2) = 0. L'équation cos(x) = 0 admet une solution unique dans [0, π\/2] : x = π\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]