Quiz Maths : Algèbre, Analyse et Géométrie — Niveau 4ème Année Secondaire

Question 1 sur 10 10:00

[{"id":51751,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² - 5x","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51752,"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, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51753,"question":"Quelle est l'intégrale de la fonction f(x) = 4x³ entre 0 et 2 ?","option_a":"16","option_b":"8","option_c":"32","option_d":"64","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x³ est x⁴\/4. Entre 0 et 2 : (2⁴\/4) - (0⁴\/4) = 16\/4 = 4. Donc 4 * 4 = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51754,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, si deux vecteurs sont orthogonaux, leur produit scalaire est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51755,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51756,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","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 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51757,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. Donc P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51758,"question":"L'équation cos(x) = 0 admet des solutions dans l'intervalle [0, π].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"cos(x) = 0 ⇒ x = π\/2 dans l'intervalle [0, π]. Donc la réponse est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51759,"question":"Quelle est la limite de la fonction f(x) = (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":"B","explication":"Factorisons : (x² - 1)\/(x - 1) = (x - 1)(x + 1)\/(x - 1) = x + 1. Donc la limite est 1 + 1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51760,"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":"B","explication":"La dérivée f'(x) = 3x² - 3. Sur [-2, 2], f'(x) change de signe (négative entre -1 et 1, positive ailleurs). Donc la fonction n'est pas croissante sur tout l'intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]