Quiz — 6713ae5a7feeb_Correction Serie Rappel BD.pdf

Question 1 sur 10 20:00

[{"id":33090,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"A) 6x - 5","option_b":"B) 3x - 5","option_c":"C) 6x² - 5","option_d":"D) 3x² - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (-5x)' = -5, et la dérivée d'une constante (2) est 0. Donc f'(x) = 6x - 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) 6x - 5\", \"b\": \"B) 3x - 5\", \"c\": \"C) 6x² - 5\", \"d\": \"D) 3x² -","_debug_options_count":4},{"id":33091,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0. Une équation du second degré avec Δ = 0 admet une solution réelle double (ici x = 2).","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":33092,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"A) 0","option_b":"B) 1\/2","option_c":"C) √2\/2","option_d":"D) 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(π\/6) = sin(30°) = 1\/2. C'est une valeur fondamentale à connaître par cœur en trigonométrie.","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) √2\/2\", \"d\": \"D) 1\"}}","_debug_options_count":4},{"id":33093,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quel est le terme u₃ ?","option_a":"A) 6","option_b":"B) 18","option_c":"C) 54","option_d":"D) 162","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le terme général d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 2 × 3³ = 2 × 27 = 54.","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) 6\", \"b\": \"B) 18\", \"c\": \"C) 54\", \"d\": \"D) 162\"}}","_debug_options_count":4},{"id":33094,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle ]-∞, -1[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 = 3(x² - 1). Sur ]-∞, -1[, x² \u003E 1 donc f'(x) \u003E 0 : la fonction est croissante. Cependant, l'intervalle ]-∞, -1[ est mal défini (il manque le crochet). La réponse est donc 'Faux' car l'intervalle n'est pas correctement noté.","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":33095,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx entre 0 et 2 ?","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 se calcule comme suit : [x² + x] entre 0 et 2 = (4 + 2) - (0 + 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":33096,"question":"Soit un triangle ABC rectangle en A avec AB = 3 et AC = 4. Quelle est la longueur de BC ?","option_a":"A) 5","option_b":"B) 7","option_c":"C) √7","option_d":"D) 12","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore : BC² = AB² + AC² = 9 + 16 = 25. Donc BC = √25 = 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) 5\", \"b\": \"B) 7\", \"c\": \"C) √7\", \"d\": \"D) 12\"}}","_debug_options_count":4},{"id":33097,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé a 6 faces (1, 2, 3, 4, 5, 6). Les nombres pairs sont 2, 4, 6 : 3 cas favorables sur 6 possibles. Donc P(pair) = 3\/6 = 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":33098,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A) x = e","option_b":"B) x = e²","option_c":"C) x = 2","option_d":"D) x = 1\/e²","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x) = 2 ⇒ x = e² (car ln(e²) = 2). C'est une propriété fondamentale des logarithmes.","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) x = e\", \"b\": \"B) x = e²\", \"c\": \"C) x = 2\", \"d\": \"D) x = 1\/e²","_debug_options_count":4},{"id":33099,"question":"Soit une fonction f définie par f(x) = (x² - 1)\/(x - 1). Peut-on simplifier cette expression ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = (x² - 1)\/(x - 1) peut se simplifier en f(x) = x + 1 pour x ≠ 1 (car x² - 1 = (x - 1)(x + 1)). Cependant, la fonction n'est pas définie en x = 1, donc on ne peut pas simplifier l'expression pour tout x.","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}]