Quiz — 67d01dd5d8ae0_-_Correction Série N° 23 Révision DS2-Img.pdf

Question 1 sur 10 20:00

[{"id":5656,"question":"Soit la fonction f définie par f(x) = x² - 4x + 3. Quelle est la dérivée f'(x) ?","option_a":"A) f'(x) = 2x - 4","option_b":"B) f'(x) = x² - 4","option_c":"C) f'(x) = 2x + 3","option_d":"D) f'(x) = x - 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, la dérivée de -4x est -4, et la dérivée de 3 est 0. Donc f'(x) = 2x - 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) f'(x) = 2x - 4\", \"b\": \"B) f'(x) = x² - 4\", \"c\": \"C) f'(x) = 2","_debug_options_count":4},{"id":5657,"question":"L'intégrale ∫(2x + 1) dx entre 0 et 2 est égale à :","option_a":"A) 4","option_b":"B) 6","option_c":"C) 8","option_d":"D) 10","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 2x est x² et celle de 1 est x. Évaluée entre 0 et 2 : (2² + 2) - (0² + 0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) 4\", \"b\": \"B) 6\", \"c\": \"C) 8\", \"d\": \"D) 10\"}}","_debug_options_count":4},{"id":5658,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général :","option_a":"A) uₙ = 3 + 2n","option_b":"B) uₙ = 3 × 2ⁿ","option_c":"C) uₙ = 3 × n²","option_d":"D) uₙ = 2 × 3ⁿ","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le terme général d'une suite géométrique est uₙ = u₀ × qⁿ. Ici, uₙ = 3 × 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) uₙ = 3 + 2n\", \"b\": \"B) uₙ = 3 × 2ⁿ\", \"c\": \"C) uₙ = 3 ","_debug_options_count":4},{"id":5659,"question":"Vrai ou Faux ? La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle eˣ est strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":5660,"question":"Soit une variable aléatoire X suivant une loi normale N(μ=5, σ=2). Quelle est la probabilité P(X ≤ 7) ?","option_a":"A) 0,5","option_b":"B) 0,6915","option_c":"C) 0,8413","option_d":"D) 0,9772","option_e":"","option_f":"","bonne_reponse":"c","explication":"En standardisant : Z = (7-5)\/2 = 1. P(Z ≤ 1) ≈ 0,8413 (table de la loi normale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A) 0,5\", \"b\": \"B) 0,6915\", \"c\": \"C) 0,8413\", \"d\": \"D) 0,9772\"}}","_debug_options_count":4},{"id":5661,"question":"Vrai ou Faux ? Une suite croissante est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite croissante peut diverger vers +∞ (exemple : uₙ = n).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":5662,"question":"Quelle est la solution de l'équation différentielle y' = 3y avec y(0) = 2 ?","option_a":"A) y = 2e³ˣ","option_b":"B) y = 2eˣ","option_c":"C) y = 3e²ˣ","option_d":"D) y = e³ˣ + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale est y = Ce³ˣ. Avec y(0)=2, on trouve C=2. Donc y=2e³ˣ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) y = 2e³ˣ\", \"b\": \"B) y = 2eˣ\", \"c\": \"C) y = 3e²ˣ\", \"d\": \"D","_debug_options_count":4},{"id":5663,"question":"Vrai ou Faux ? La somme des probabilités d'une loi de probabilité discrète est toujours égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, la somme des probabilités d'une loi discrète vaut 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":5664,"question":"Soit une matrice A = [[1, 2], [3, 4]]. Quel est son déterminant ?","option_a":"A) -2","option_b":"B) 0","option_c":"C) 2","option_d":"D) -1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le déterminant de A est (1×4) - (2×3) = 4 - 6 = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) -2\", \"b\": \"B) 0\", \"c\": \"C) 2\", \"d\": \"D) -1\"}}","_debug_options_count":4},{"id":5665,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/(2n² - 3) quand n tend vers +∞ ?","option_a":"A) 0","option_b":"B) 1\/2","option_c":"C) 1","option_d":"D) +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n² : uₙ = (1 + 1\/n²)\/(2 - 3\/n²) → 1\/2 quand n→+∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) 0\", \"b\": \"B) 1\/2\", \"c\": \"C) 1\", \"d\": \"D) +∞\"}}","_debug_options_count":4}]