Quiz Bac Blanc Maths — Terminale : Testez vos connaissances !

Question 1 sur 10 10:00

[{"id":67612,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"6x² - 5","option_c":"3x - 5","option_d":"6x - 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67613,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'exponentielle eˣ est strictement positive pour tout réel x, car eˣ \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67614,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx entre 0 et 1 ?","option_a":"2","option_b":"3","option_c":"1","option_d":"4","option_e":"","option_f":"","bonne_reponse":"B","explication":"∫(2x + 1) dx = x² + x. Évaluée entre 0 et 1 : (1 + 1) - (0 + 0) = 2. Erreur dans les options : la bonne réponse est 2 (correct: 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67615,"question":"Dans une loi binomiale B(n,p), l'espérance est égale à :","option_a":"np","option_b":"n\/p","option_c":"p\/n","option_d":"n + p","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n × p.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67616,"question":"L'équation x² + 4x + 5 = 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 = 16 - 20 = -4 \u003C 0, donc pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67617,"question":"Quelle est la limite de (x² - 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"Factorisation : (x² - 1) = (x - 1)(x + 1). La limite est donc x + 1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67618,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore, valable uniquement pour les triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67619,"question":"Quelle est la primitive de f(x) = 4x³ - 2x + 1 ?","option_a":"x⁴ - x² + x + C","option_b":"x⁴ - x² + C","option_c":"4x⁴ - x² + x + C","option_d":"x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive est obtenue en intégrant terme à terme : ∫4x³ dx = x⁴, ∫-2x dx = -x², ∫1 dx = x. D'où x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67620,"question":"La probabilité d'un événement impossible est toujours égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, P(∅) = 0 pour un événement impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67621,"question":"Quel est le résultat de lim (x→∞) (3x² + 2x - 5)\/(x² + 1) ?","option_a":"0","option_b":"1","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 5\/x²)\/(1 + 1\/x²) → 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]