Quiz Mathématiques : Série 9 — Teste tes connaissances !

Question 1 sur 10 10:00

[{"id":23788,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0.5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation se résout avec 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":23789,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur ]-1, 1[ et croissante ailleurs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23790,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² en x = 3 ?","option_a":"3","option_b":"6","option_c":"9","option_d":"0","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur est f'(3) = 2*3 = 6. La tangente a pour équation y = 6x - 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23791,"question":"L'inéquation x² - 4x + 3 \u003E 0 a pour solution :","option_a":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_b":"x ∈ ]1, 3[","option_c":"x ∈ ]-∞, 3[","option_d":"x ∈ ]0, 4[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le trinôme x² - 4x + 3 se factorise en (x-1)(x-3). Il est positif en dehors des racines, soit x \u003C 1 ou x \u003E 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23792,"question":"La fonction sinus est-elle 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). Or sin(-x) = -sin(x), donc la fonction sinus est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23793,"question":"Quel est le résultat de ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale se calcule terme par terme : ∫2x dx = x² et ∫1 dx = x, d'où x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23794,"question":"L'équation cos(x) = 0.5 a pour solutions dans [0, 2π] :","option_a":"π\/3 et 5π\/3","option_b":"π\/6 et 11π\/6","option_c":"π\/3 et 2π\/3","option_d":"π\/4 et 3π\/4","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les solutions sont x = π\/3 + 2kπ ou x = 5π\/3 + 2kπ. Dans [0, 2π], on a π\/3 et 5π\/3 (ou 11π\/6).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23795,"question":"La droite d'équation y = 2x + 1 est-elle parallèle à y = 2x - 3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites sont parallèles si elles ont le même coefficient directeur. Ici, les deux droites ont un coefficient de 2, donc elles sont parallèles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23796,"question":"Quel est le produit scalaire de vecteurs u(2, -1) et v(3, 4) ?","option_a":"10","option_b":"5","option_c":"0","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit scalaire se calcule par u·v = (2*3) + (-1*4) = 6 - 4 = 2. (Note : la bonne réponse est 2, mais l'option 5 est incorrecte.)","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23797,"question":"La fonction f(x) = 1\/x est-elle définie en 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}]