Quiz Mathématiques Bac : Série 5 — Exercices et Concepts Clés

Question 1 sur 10 10:00

[{"id":10853,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"5 - 6x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10854,"question":"L'équation x² - 4x + 3 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = (-4)² - 4*1*3 = 4 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10855,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) quand x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x, on obtient f(x) ≈ 2x\/x = 2, donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10856,"question":"La suite définie par uₙ = 2uₙ₋₁ + 3 est une suite géométrique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette suite est arithmético-géométrique, pas géométrique pure, car elle combine une multiplication et une addition.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10857,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x³ - 2x² en x = 1 ?","option_a":"-1","option_b":"1","option_c":"2","option_d":"0","option_e":"","option_f":"","bonne_reponse":"C","explication":"La dérivée f'(x) = 3x² - 4x donne f'(1) = 3 - 4 = -1. Le coefficient directeur est donc -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10858,"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":"Les nombres pairs sur un dé sont 2, 4, 6, soit 3 issues favorables sur 6 possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10859,"question":"Résoudre l'inéquation 2x - 5 ≤ 3x + 1.","option_a":"x ≥ -6","option_b":"x ≤ -6","option_c":"x ≥ 6","option_d":"x ≤ 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"En simplifiant, on obtient -x ≤ 6, soit x ≥ -6. L'inégalité change de sens car on divise par un nombre négatif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10860,"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 tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10861,"question":"Quelle est la somme des 5 premiers termes d'une suite arithmétique de premier terme 2 et de raison 3 ?","option_a":"35","option_b":"40","option_c":"45","option_d":"50","option_e":"","option_f":"","bonne_reponse":"C","explication":"La somme S₅ = (5\/2)*(2*2 + (5-1)*3) = (5\/2)*(4 + 12) = 5\/2 * 16 = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10862,"question":"L'espérance d'une variable aléatoire suivant une loi binomiale B(n,p) est égale à np.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, l'espérance d'une loi binomiale B(n,p) est bien E(X) = np.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]