Quiz Math Bac : Testez vos connaissances en algèbre et analyse

Question 1 sur 10 10:00

[{"id":60407,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 0.5","option_c":"x = -1 ou x = -2","option_d":"x = 0.5 ou x = 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60408,"question":"La fonction f(x) = x³ - 3x² + 2 est croissante sur l'intervalle [0 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x = 3x(x - 2) est négative sur [0 ; 2], donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60409,"question":"Quel est le résultat de l'intégrale ∫(2x + 1)dx ?","option_a":"x² + x + C","option_b":"x² + 2x + C","option_c":"2x² + x + C","option_d":"x² + x","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x est x² et celle de 1 est x. On ajoute la constante d'intégration C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60410,"question":"La suite définie par uₙ = 2n - 1 est arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60411,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2)\/(x² - 1) quand x tend vers l'infini ?","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 f(x) = (3 + 2\/x²)\/(1 - 1\/x²), donc la limite est 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60412,"question":"L'équation eˣ = 5 a pour solution x = ln(5).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la fonction logarithme népérien des deux côtés, on obtient x = ln(5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60413,"question":"Quelle est la dérivée de la fonction f(x) = sin(2x) ?","option_a":"cos(2x)","option_b":"2cos(2x)","option_c":"-2cos(2x)","option_d":"sin(2x)cos(2x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation des fonctions composées, f'(x) = 2cos(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60414,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60415,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 5x + 1 ?","option_a":"x \u003C -4","option_b":"x \u003E -4","option_c":"x \u003C 4","option_d":"x \u003E 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant, on obtient -7 - 1 \u003E 5x - 3x → -8 \u003E 2x → x \u003C -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60416,"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}]