Quiz : Maîtrisez les bases des Mathématiques pour le Bac !

Question 1 sur 10 10:00

[{"id":58466,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x - 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":58467,"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. L’équation admet donc une solution double (x=2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58468,"question":"Quelle est l’expression factorisée de x² - 9 ?","option_a":"(x-3)(x+3)","option_b":"(x-9)(x+1)","option_c":"(x-3)²","option_d":"(x+3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"C’est une identité remarquable : a² - b² = (a-b)(a+b). Ici, a=x et b=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58469,"question":"La limite de (2x² + 3x - 1)\/(x² - 1) quand x tend vers +∞ est égale à :","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 - 1\/x²) → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58470,"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 est paire si f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x). Elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58471,"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":58472,"question":"La probabilité d’obtenir un nombre pair en lançant un dé équilibré est :","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Il y a 3 nombres pairs (2,4,6) sur 6 faces possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58473,"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 (division par zéro).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58474,"question":"Quelle est la primitive de f(x) = 4x³ ?","option_a":"x⁴ + C","option_b":"x⁴","option_c":"12x² + C","option_d":"4x⁴ + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de xⁿ est x^(n+1)\/(n+1). Ici, ∫4x³ dx = 4×(x⁴\/4) + C = x⁴ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58475,"question":"L’équation cos(x) = 0 admet une solution dans l’intervalle [0, π\/2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"cos(π\/2) = 0, donc x=π\/2 est une solution dans l’intervalle [0, π\/2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]