Quiz — مقاييس اصلاح ح1_تطبيقي_شعب علمية_2026.pdf

Question 1 sur 5 10:00

[{"id":267,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"f'(x) = 3x² - 4x + 5","option_b":"f'(x) = 3x² - 4x - 1","option_c":"f'(x) = x² - 2x + 5","option_d":"f'(x) = 3x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynomiale s'obtient en appliquant la règle de dérivation : (x^n)' = n*x^(n-1). Ainsi, f'(x) = 3x² - 4x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 3x² - 4x + 5\", \"b\": \"f'(x) = 3x² - 4x - 1\", \"c\": \"f'(x)","_debug_options_count":4},{"id":268,"question":"Dans l'espace muni d'un repère orthonormé, quelle est l'équation du plan passant par le point A(1, 2, 3) et de vecteur normal n(2, -1, 4) ?","option_a":"2x - y + 4z - 12 = 0","option_b":"2x - y + 4z + 12 = 0","option_c":"2x + y - 4z - 12 = 0","option_d":"x - 2y + 3z - 12 = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation d'un plan de vecteur normal n(a,b,c) passant par A(x0,y0,z0) est a(x-x0) + b(y-y0) + c(z-z0) = 0. Ici, cela donne 2(x-1) -1(y-2) +4(z-3) = 0, soit 2x - y + 4z - 12 = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2x - y + 4z - 12 = 0\", \"b\": \"2x - y + 4z + 12 = 0\", \"c\": \"2x + y ","_debug_options_count":4},{"id":269,"question":"Soit X une variable aléatoire suivant une loi normale N(μ=10, σ=2). Quelle est la probabilité P(X ≤ 12) ?","option_a":"P(X ≤ 12) ≈ 0.8413","option_b":"P(X ≤ 12) ≈ 0.1587","option_c":"P(X ≤ 12) ≈ 0.6915","option_d":"P(X ≤ 12) ≈ 0.3085","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale N(μ,σ), P(X ≤ μ + σ) ≈ 0.8413. Ici, 12 = μ + σ, donc P(X ≤ 12) ≈ 0.8413.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"P(X ≤ 12) ≈ 0.8413\", \"b\": \"P(X ≤ 12) ≈ 0.1587\", \"c\": \"P(X","_debug_options_count":4},{"id":270,"question":"Quel algorithme permet de calculer la somme des n premiers entiers naturels ?","option_a":"S = n(n+1)\/2","option_b":"S = n²","option_c":"S = 2^n","option_d":"S = n!","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule de la somme des n premiers entiers naturels est S = n(n+1)\/2, dérivée de la suite arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"S = n(n+1)\/2\", \"b\": \"S = n²\", \"c\": \"S = 2^n\", \"d\": \"S = n!\"}}","_debug_options_count":4},{"id":271,"question":"Soit f une fonction continue sur [a,b]. Le théorème des valeurs intermédiaires garantit que :","option_a":"f prend toutes les valeurs comprises entre f(a) et f(b)","option_b":"f est dérivable sur [a,b]","option_c":"f est constante sur [a,b]","option_d":"f s'annule sur [a,b]","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème des valeurs intermédiaires stipule que si f est continue sur [a,b], alors elle prend toutes les valeurs comprises entre f(a) et f(b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f prend toutes les valeurs comprises entre f(a) et f(b)\", \"b\": \"f","_debug_options_count":4}]