Quiz Mathématiques Terminale : Algèbre, Analyse et Géométrie

Question 1 sur 10 10:00

[{"id":74392,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation se factorise en (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":74393,"question":"La dérivée de la fonction f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En dérivant terme à terme, on obtient bien f'(x) = 3x² - 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74394,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"2","option_b":"1\/2","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74395,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74396,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"F(x) = x⁴ - x² + x + C","option_b":"F(x) = x⁴ - x² + 1 + C","option_c":"F(x) = 12x² - 2 + C","option_d":"F(x) = x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive est obtenue en intégrant terme à terme : F(x) = x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74397,"question":"L'équation de la tangente à la courbe y = x² au point d'abscisse x = 1 est y = 2x - 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La tangente a pour équation y = f'(1)(x-1) + f(1) = 2(x-1) + 1 = 2x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74398,"question":"Quelle est la valeur de l'intégrale ∫(0 à 1) (3x² + 2x) dx ?","option_a":"2","option_b":"3","option_c":"1","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale vaut [x³ + x²] de 0 à 1 = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74399,"question":"La fonction f(x) = 1\/x est définie et continue sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction n'est pas définie en x=0 et présente une discontinuité en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74400,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant l'inéquation, on obtient 2x - 3x \u003E 1 + 5 → -x \u003E 6 → x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74401,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule du discriminant est bien Δ = b² - 4ac.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]