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Question 1 sur 10 10:00

[{"id":48811,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48812,"question":"La suite définie par u₀ = 2 et uₙ₊₁ = 3uₙ - 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, u₁ = 5, u₂ = 14, donc u₂ - u₁ ≠ u₁ - u₀.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48813,"question":"Quel est le domaine de définition de la fonction f(x) = √(x² - 4) ?","option_a":"x ∈ ℝ","option_b":"x ≤ -2 ou x ≥ 2","option_c":"x ≥ 2","option_d":"x ∈ [-2 ; 2]","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction racine carrée est définie lorsque l'expression sous la racine est positive ou nulle : x² - 4 ≥ 0 ⇒ x ≤ -2 ou x ≥ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48814,"question":"La probabilité d'un événement A est P(A) = 0,3. Quelle est la probabilité de l'événement contraire A̅ ?","option_a":"0,3","option_b":"0,7","option_c":"0,5","option_d":"0,2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 1 - 0,3 = 0,7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48815,"question":"Le nombre complexe z = 3 + 4i a pour module |z| = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module d'un nombre complexe z = a + bi est |z| = √(a² + b²). Ici, |z| = √(3² + 4²) = 5, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48816,"question":"Quelle est la limite de la fonction f(x) = (x² + 1)\/x lorsque x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"+∞","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par x, on obtient f(x) = x + 1\/x. Lorsque x → 0⁺, 1\/x → +∞, donc f(x) → +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48817,"question":"Dans un triangle ABC, si cos(A) = 0,5, alors l'angle A mesure :","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"A","explication":"cos(30°) = √3\/2 ≈ 0,866, cos(45°) = √2\/2 ≈ 0,707, cos(60°) = 0,5, cos(90°) = 0. Donc A = 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48818,"question":"La fonction f(x) = e^(2x) 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 de f(x) = e^(2x) est f'(x) = 2e^(2x), qui est toujours positive sur ℝ. Donc f est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48819,"question":"Quel est le résultat de l'intégrale ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x²","option_c":"6x + 2 + C","option_d":"x³ + x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale d'une somme est la somme des intégrales. ∫3x² dx = x³ + C₁ et ∫2x dx = x² + C₂. Donc ∫(3x² + 2x) dx = x³ + x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48820,"question":"Dans une expérience aléatoire, si P(A ∪ B) = 0,7 et P(A ∩ B) = 0,2, alors P(A) + P(B) = ?","option_a":"0,5","option_b":"0,9","option_c":"1,2","option_d":"0,7","option_e":"","option_f":"","bonne_reponse":"B","explication":"D'après la formule P(A ∪ B) = P(A) + P(B) - P(A ∩ B), on a 0,7 = P(A) + P(B) - 0,2 ⇒ P(A) + P(B) = 0,9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]