Maths Bac : Testez vos connaissances en série d'exercices

Question 1 sur 10 10:00

[{"id":58316,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme est obtenue en appliquant la règle de dérivation terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58317,"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 = (-4)² - 4*1*4 = 0, donc l'équation admet une solution réelle double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58318,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé a 6 faces (1, 2, 3, 4, 5, 6). Les nombres pairs sont 2, 4 et 6, soit 3 cas favorables sur 6 possibles : P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58319,"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":58320,"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":"Résolvons l'inéquation : 2x - 3 \u003E 5 → 2x \u003E 8 → x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58321,"question":"La dérivée de la fonction f(x) = e^x est f'(x) = e^x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de la fonction exponentielle e^x est bien e^x, car sa dérivée est égale à elle-même.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58322,"question":"Quelle est la valeur de la limite lim(x→∞) (3x² + 2x) \/ (x² + 1) ?","option_a":"3","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient lim(x→∞) (3 + 2\/x) \/ (1 + 1\/x²) = 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58323,"question":"La fonction f(x) = x³ est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = (-x)³ = -x³ ≠ f(x), donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58324,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e²","option_b":"x = 2","option_c":"x = 100","option_d":"x = ln(2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = 2 équivaut à x = e², car ln(e²) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58325,"question":"La probabilité de tirer un as dans un jeu de 52 cartes est de 1\/13.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un jeu de 52 cartes contient 4 as, donc la probabilité est 4\/52 = 1\/13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]