Quiz Maths Terminale : Dérivées, Suites et Géométrie

Question 1 sur 10 10:00

[{"id":51671,"question":"Soit f une fonction dérivable sur ℝ telle que f'(x) = 2x + 3. Quelle est la fonction f si f(0) = 1 ?","option_a":"f(x) = x² + 3x + 1","option_b":"f(x) = x² + 3x","option_c":"f(x) = 2x² + 3x + 1","option_d":"f(x) = x² + 3x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de f'(x) = 2x + 3 est f(x) = x² + 3x + C. Avec f(0) = 1, on trouve C = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51672,"question":"Une suite (uₙ) est définie par u₀ = 2 et uₙ₊₁ = 3uₙ - 1. Cette suite est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, uₙ₊₁ - uₙ = 2uₙ - 1, qui n'est pas constant.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51673,"question":"Soit X une variable aléatoire suivant une loi binomiale B(10 ; 0,3). Quelle est l'espérance de X ?","option_a":"3","option_b":"0,3","option_c":"10","option_d":"7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi binomiale B(n ; p), l'espérance est E(X) = n × p = 10 × 0,3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51674,"question":"Dans l'espace, l'équation x + 2y - z + 3 = 0 représente :","option_a":"Une droite","option_b":"Un plan","option_c":"Une sphère","option_d":"Un cercle","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation x + 2y - z + 3 = 0 est de la forme ax + by + cz + d = 0, ce qui définit un plan dans l'espace.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51675,"question":"Soit f(x) = x³ - 3x² + 2. La dérivée f'(x) est égale à :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"f'(x) = 3x² - 6x, ce qui est différent de x³ - 3x² + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51676,"question":"Soit (uₙ) une suite géométrique de raison q = 2 et de premier terme u₀ = 5. Quelle est la valeur de u₃ ?","option_a":"20","option_b":"40","option_c":"10","option_d":"80","option_e":"","option_f":"","bonne_reponse":"B","explication":"uₙ = u₀ × qⁿ, donc u₃ = 5 × 2³ = 5 × 8 = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51677,"question":"Soit A(1 ; 2 ; 3) et B(4 ; 5 ; 6) deux points de l'espace. Quelle est la distance AB ?","option_a":"3√3","option_b":"√3","option_c":"9","option_d":"√27","option_e":"","option_f":"","bonne_reponse":"A","explication":"AB = √[(4-1)² + (5-2)² + (6-3)²] = √(9 + 9 + 9) = √27 = 3√3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51678,"question":"Soit X une variable aléatoire suivant une loi normale N(0 ; 1). Quelle est P(X ≤ 1) ?","option_a":"0,8413","option_b":"0,1587","option_c":"0,5","option_d":"0,9772","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale centrée réduite, P(X ≤ 1) ≈ 0,8413 (valeur lue dans la table).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51679,"question":"Soit f(x) = ln(x) + x². La dérivée f'(x) est égale à :","option_a":"1\/x + 2x","option_b":"1\/x + x","option_c":"x + 2x","option_d":"1\/x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x et celle de x² est 2x, donc f'(x) = 1\/x + 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51680,"question":"Soit (uₙ) une suite définie par uₙ = 2n + 1. Cette suite est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite bornée est majorée et minorée. Ici, uₙ = 2n + 1 tend vers +∞ quand n tend vers +∞, donc elle n'est pas bornée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]