Quiz — Corrigé-2_Serie-Révision_N°1_(Vacance mars).pdf

Question 1 sur 10 20:00

[{"id":34310,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A) x = 2 ou x = 3","option_b":"B) x = -2 ou x = -3","option_c":"C) x = 1 ou x = 6","option_d":"D) x = -1 ou x = -6","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3)=0, donc les solutions sont x=2 et x=3.","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) x = 2 ou x = 3\", \"b\": \"B) x = -2 ou x = -3\", \"c\": \"C) x = 1 ou","_debug_options_count":4},{"id":34311,"question":"La fonction f(x) = (x² - 1)\/(x - 1) est-elle définie en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"En x=1, le dénominateur s'annule, donc la fonction n'est pas définie en ce point (simplification possible uniquement si x ≠ 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":34312,"question":"Soit la suite définie par uₙ = 2n + 3. Quelle est la valeur de u₅ ?","option_a":"A) 8","option_b":"B) 10","option_c":"C) 13","option_d":"D) 15","option_e":"","option_f":"","bonne_reponse":"c","explication":"En remplaçant n par 5 dans uₙ = 2n + 3, on obtient u₅ = 2×5 + 3 = 13.","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) 8\", \"b\": \"B) 10\", \"c\": \"C) 13\", \"d\": \"D) 15\"}}","_debug_options_count":4},{"id":34313,"question":"L'inéquation 3x - 7 \u003E 5 a pour solution :","option_a":"A) x \u003E 4","option_b":"B) x \u003C 4","option_c":"C) x \u003E -4","option_d":"D) x \u003C -4","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 7 \u003E 5 ⇒ 3x \u003E 12 ⇒ x \u003E 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) x \u003E 4\", \"b\": \"B) x \u003C 4\", \"c\": \"C) x \u003E -4\", \"d\": \"D) x \u003C -4\"}}","_debug_options_count":4},{"id":34314,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant est bien Δ = b² - 4ac, formule fondamentale pour résoudre les équations du second degré.","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":34315,"question":"Soit f(x) = x³ - 3x² + 2x. Le coefficient de x² dans le développement de f(x+1) est :","option_a":"A) -3","option_b":"B) 0","option_c":"C) 3","option_d":"D) 6","option_e":"","option_f":"","bonne_reponse":"b","explication":"En développant f(x+1) = (x+1)³ - 3(x+1)² + 2(x+1), le terme en x² disparaît (coefficient 0).","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) -3\", \"b\": \"B) 0\", \"c\": \"C) 3\", \"d\": \"D) 6\"}}","_debug_options_count":4},{"id":34316,"question":"La suite (uₙ) définie par uₙ = 5 - 2n est :","option_a":"A) Arithmétique de raison -2","option_b":"B) Géométrique de raison 2","option_c":"C) Arithmétique de raison 5","option_d":"D) Constante","option_e":"","option_f":"","bonne_reponse":"a","explication":"uₙ₊₁ - uₙ = (5 - 2(n+1)) - (5 - 2n) = -2, donc la suite est arithmétique de raison -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) Arithmétique de raison -2\", \"b\": \"B) Géométrique de raison ","_debug_options_count":4},{"id":34317,"question":"L'équation |x - 3| = 5 admet pour solutions :","option_a":"A) x = -2 ou x = 8","option_b":"B) x = 2 ou x = -8","option_c":"C) x = 3 ± 5","option_d":"D) x = 8 uniquement","option_e":"","option_f":"","bonne_reponse":"a","explication":"|x - 3| = 5 ⇒ x - 3 = 5 ou x - 3 = -5 ⇒ x = 8 ou x = -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) x = -2 ou x = 8\", \"b\": \"B) x = 2 ou x = -8\", \"c\": \"C) x = 3 ±","_debug_options_count":4},{"id":34318,"question":"Soit f(x) = (x² - 4)\/(x - 2). La limite de f(x) quand x tend vers 2 est :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant f(x) = (x-2)(x+2)\/(x-2) = x+2 (pour x ≠ 2), donc lim(x→2) f(x) = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":34319,"question":"Le produit des racines de l'équation x² - 7x + 12 = 0 est :","option_a":"A) 7","option_b":"B) 12","option_c":"C) -7","option_d":"D) -12","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une équation ax² + bx + c = 0, le produit des racines est c\/a = 12\/1 = 12.","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) 7\", \"b\": \"B) 12\", \"c\": \"C) -7\", \"d\": \"D) -12\"}}","_debug_options_count":4}]