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Question 1 sur 10 10:00

[{"id":53581,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"3x² - 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53582,"question":"La limite de (sin x)\/x quand x tend vers 0 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une limite fondamentale en analyse : lim(x→0) sin(x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53583,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quel est le terme u₃ ?","option_a":"18","option_b":"54","option_c":"162","option_d":"81","option_e":"","option_f":"","bonne_reponse":"C","explication":"uₙ = u₀ × qⁿ, donc u₃ = 2 × 3³ = 2 × 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53584,"question":"Dans une expérience aléatoire, si P(A) = 0.3 et P(B) = 0.5, quelle est la valeur maximale possible de P(A ∪ B) ?","option_a":"0.8","option_b":"0.5","option_c":"0.3","option_d":"0.2","option_e":"","option_f":"","bonne_reponse":"A","explication":"P(A ∪ B) ≤ P(A) + P(B) = 0.8. La valeur maximale est atteinte si A et B sont incompatibles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53585,"question":"L'équation différentielle y' + 2y = 0 admet pour solution y = Ce^(-2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une équation différentielle linéaire du premier ordre dont la solution générale est y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53586,"question":"Quel est le module du nombre complexe z = 3 + 4i ?","option_a":"5","option_b":"7","option_c":"12","option_d":"25","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z = a + bi est √(a² + b²) = √(9 + 16) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53587,"question":"Soit f une fonction continue sur [a; b]. Si f(a) \u003C 0 et f(b) \u003E 0, alors l'équation f(x) = 0 admet au moins une solution dans [a; b].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème des valeurs intermédiaires : si f est continue et change de signe, elle s'annule au moins une fois.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53588,"question":"Quelle est la primitive de f(x) = 4x³ - 2x + 1 ?","option_a":"x⁴ - x² + x + C","option_b":"4x⁴ - 2x² + x + C","option_c":"x⁴ - x² + C","option_d":"4x⁴ - x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de f(x) = 4x³ - 2x + 1 est F(x) = x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53589,"question":"Dans l'espace, deux droites parallèles à une même troisième droite sont parallèles entre elles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale de la géométrie dans l'espace : la transitivité du parallélisme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":53590,"question":"Soit X une variable aléatoire suivant une loi normale N(μ; σ²). Quelle est la probabilité P(X ≤ μ) ?","option_a":"0.5","option_b":"0.25","option_c":"0.75","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La loi normale est symétrique autour de sa moyenne μ, donc P(X ≤ μ) = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]