Quiz : Maîtrisez les Maths de 4ème Année Secondaire !

Question 1 sur 10 10:00

[{"id":19438,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2x","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19439,"question":"L'équation x² - 5x + 6 = 0 a pour solutions :","option_a":"x = 2 et x = 3","option_b":"x = -2 et x = -3","option_c":"x = 1 et x = 6","option_d":"x = -1 et x = -6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant, on obtient (x-2)(x-3) = 0, donc les solutions sont x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19440,"question":"Vrai ou Faux ? La fonction f(x) = 1\/x est continue 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 continue sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19441,"question":"Quelle est la limite de (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 4\/x²), donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19442,"question":"Vrai ou Faux ? Un vecteur directeur de la droite d'équation y = 2x + 3 est u(1, 2).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur de la droite est 2, donc un vecteur directeur est bien u(1, 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19443,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ -12","option_d":"x ≥ -12","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient x ≤ 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19444,"question":"Vrai ou Faux ? La dérivée de sin(x) est cos(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de sin(x) est bien cos(x), une propriété fondamentale en analyse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19445,"question":"Quelle est l'aire sous la courbe de f(x) = x² entre x=0 et x=2 ?","option_a":"8\/3","option_b":"4","option_c":"2","option_d":"16\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire est donnée par l'intégrale ∫₀² x² dx = [x³\/3]₀² = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19446,"question":"Vrai ou Faux ? Une suite géométrique a un rapport constant entre deux termes consécutifs.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, une suite géométrique a un rapport constant r entre deux termes consécutifs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19447,"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":"En exponentiant les deux côtés, on obtient x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]