Quiz Mathématiques Terminale : Testez vos connaissances en analyse et algèbre !

Question 1 sur 10 10:00

[{"id":62332,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"2x + 5","option_c":"x² + 3","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62333,"question":"La fonction f(x) = 1\/x est dérivable en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 1\/x n'est pas définie en x = 0, donc elle n'est pas dérivable en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62334,"question":"Quelle est la limite de (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"0","option_b":"2","option_c":"4","option_d":"Indéterminée","option_e":"","option_f":"","bonne_reponse":"D","explication":"La limite est de la forme 0\/0, mais après simplification (x² - 4) = (x - 2)(x + 2), on obtient lim (x + 2) = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62335,"question":"Soit une suite géométrique de premier terme u₀ = 3 et de raison q = 2. Quel est le terme u₃ ?","option_a":"6","option_b":"12","option_c":"24","option_d":"48","option_e":"","option_f":"","bonne_reponse":"C","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 3 × 2³ = 3 × 8 = 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62336,"question":"L'équation x² + 2x + 5 = 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 = b² - 4ac = 4 - 20 = -16 \u003C 0. Donc l'équation n'a pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62337,"question":"Quelle est la primitive de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"x³ + x² - x + C","option_b":"6x + 2 + C","option_c":"x³ + x - x + C","option_d":"x³ + x² - 1 + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 3x² est x³, celle de 2x est x², et celle de -1 est -x. Donc F(x) = x³ + x² - x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62338,"question":"Soit une variable aléatoire X suivant une loi normale N(0,1). Quelle est P(X ≤ 1) ?","option_a":"0.6826","option_b":"0.8413","option_c":"0.9772","option_d":"0.9974","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi normale centrée réduite, P(X ≤ 1) ≈ 0.8413 (valeur lue dans la table de la loi normale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62339,"question":"La fonction f(x) = |x| est dérivable en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction valeur absolue n'est pas dérivable en x = 0 car elle présente un point anguleux (dérivée à gauche ≠ dérivée à droite).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62340,"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":"2x - 5 \u003E 3x + 1 ⇒ -5 - 1 \u003E 3x - 2x ⇒ -6 \u003E x ⇒ x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62341,"question":"Soit un nombre complexe z = 3 + 4i. Quel est son module ?","option_a":"5","option_b":"7","option_c":"1","option_d":"√7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module d'un nombre complexe z = a + bi est |z| = √(a² + b²) = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]