Quiz — Devoir de controle 2 - Lycée pilote sfax.pdf

Question 1 sur 10 20:00

[{"id":44890,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation 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\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":44891,"question":"La fonction f(x) = x² + 3x - 4 est-elle croissante sur l'intervalle [-2, 0] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x)=2x+3 est négative sur [-2,0], donc la fonction est décroissante.","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":44892,"question":"Quel est le discriminant de l'équation 3x² - 2x - 1 = 0 ?","option_a":"Δ = 16","option_b":"Δ = 4","option_c":"Δ = 12","option_d":"Δ = 8","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant se calcule par Δ = b² - 4ac = (-2)² - 4*3*(-1) = 4 + 12 = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Δ = 16\", \"b\": \"Δ = 4\", \"c\": \"Δ = 12\", \"d\": \"Δ = 8\"}}","_debug_options_count":4},{"id":44893,"question":"La fonction f(x) = 1\/x admet-elle une asymptote verticale en x=0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x)=1\/x tend vers l'infini lorsque x tend vers 0, donc elle admet une asymptote verticale en x=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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":44894,"question":"Quelle est la valeur de f(2) pour la fonction f(x) = 2x³ - x² + 5 ?","option_a":"f(2) = 13","option_b":"f(2) = 17","option_c":"f(2) = 19","option_d":"f(2) = 21","option_e":"","option_f":"","bonne_reponse":"b","explication":"En remplaçant x par 2 : f(2) = 2*(8) - 4 + 5 = 16 - 4 + 5 = 17.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"f(2) = 13\", \"b\": \"f(2) = 17\", \"c\": \"f(2) = 19\", \"d\": \"f(2) = 21\"}","_debug_options_count":4},{"id":44895,"question":"L'équation x³ - 3x + 2 = 0 admet-elle trois solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation admet une racine double (x=1) et une racine simple (x=-2), donc seulement deux solutions distinctes.","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":44896,"question":"Quelle est la dérivée de la fonction f(x) = (2x + 1)² ?","option_a":"f'(x) = 4(2x + 1)","option_b":"f'(x) = 2(2x + 1)","option_c":"f'(x) = 4x + 2","option_d":"f'(x) = 8x + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule (u²)' = 2u*u', on obtient f'(x) = 2*(2x+1)*2 = 4(2x+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\": \"f'(x) = 4(2x + 1)\", \"b\": \"f'(x) = 2(2x + 1)\", \"c\": \"f'(x) = 4x + ","_debug_options_count":4},{"id":44897,"question":"La fonction f(x) = x³ - 3x est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction paire vérifie f(-x)=f(x). Ici, f(-x) = -x³ + 3x ≠ f(x), donc elle n'est pas paire.","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":44898,"question":"Quel est le résultat de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant : 2x - 5 \u003E 3x + 1 → -x \u003E 6 → x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003C -6\", \"b\": \"x \u003E -6\", \"c\": \"x \u003C 6\", \"d\": \"x \u003E 6\"}}","_debug_options_count":4},{"id":44899,"question":"La fonction f(x) = √(x² + 1) est-elle définie pour tout x réel ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction √(x² + 1) est définie pour tout x réel car x² + 1 \u003E 0 pour tout x.","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}]