Quiz — 628def422fb9e_._Prototype-dExamen-Bac-N3-ML-correction.pdf

Question 1 sur 10 20:00

[{"id":59874,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"A. 3x² - 4x + 5","option_b":"B. 3x² - 4x + 5x","option_c":"C. x² - 2x + 5","option_d":"D. 3x² - 4x - 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : 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\": \"A. 3x² - 4x + 5\", \"b\": \"B. 3x² - 4x + 5x\", \"c\": \"C. x² - 2x + ","_debug_options_count":4},{"id":59875,"question":"La limite de la suite uₙ = (2n² + 3n) \/ (n² + 1) quand n tend vers l'infini est égale à 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n², on obtient lim(uₙ) = 2 \/ 1 = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":59876,"question":"Quel est le produit scalaire de deux vecteurs u et v de coordonnées respectives (1, 2, -1) et (3, -1, 2) ?","option_a":"A. 3","option_b":"B. -3","option_c":"C. 0","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le produit scalaire se calcule par : 1×3 + 2×(-1) + (-1)×2 = 3 - 2 - 2 = -1.","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. 3\", \"b\": \"B. -3\", \"c\": \"C. 0\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":59877,"question":"La fonction f(x) = e^(2x) est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2e^(2x) est toujours positive, donc f est strictement croissante.","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":59878,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"A. 1\/6","option_b":"B. 1\/12","option_c":"C. 1\/36","option_d":"D. 1\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 6×6 = 36 issues possibles, et une seule issue favorable (6,6), donc P = 1\/36.","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. 1\/6\", \"b\": \"B. 1\/12\", \"c\": \"C. 1\/36\", \"d\": \"D. 1\/18\"}}","_debug_options_count":4},{"id":59879,"question":"L'équation x² + 4x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0, donc pas de solutions réelles.","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":59880,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. ∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En simplifiant f(x) = (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1, donc lim(x→1) f(x) = 2.","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\", \"b\": \"B. 1\", \"c\": \"C. 2\", \"d\": \"D. ∞\"}}","_debug_options_count":4},{"id":59881,"question":"La suite uₙ définie par u₀ = 1 et uₙ₊₁ = 2uₙ + 3 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une suite arithmétique, uₙ₊₁ - uₙ doit être constant. Ici, uₙ₊₁ - uₙ = uₙ + 3, qui n'est pas constant.","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":59882,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = ln(x) au point d'abscisse 1 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. e","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(x) est f'(x) = 1\/x, donc f'(1) = 1.","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\", \"c\": \"C. e\", \"d\": \"D. -1\"}}","_debug_options_count":4},{"id":59883,"question":"L'intégrale ∫₀¹ (3x² + 2x) dx est-elle égale à 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale vaut [x³ + x²]₀¹ = 1 + 1 = 2, donc l'affirmation est vraie.","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}]