Quiz — Lycée Pilote Sfax - DC 3 2012 (corrigé).pdf

Question 1 sur 10 20:00

[{"id":27380,"question":"Quelle est la solution de l'équation du second degré 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 x² - 5x + 6 = 0 peut être factorisée en (x - 2)(x - 3) = 0. Les solutions sont donc 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":27381,"question":"Soit f une fonction définie sur ℝ par f(x) = x² - 4x + 3. Quelle est la dérivée de f en x = 2 ?","option_a":"f'(2) = 0","option_b":"f'(2) = -4","option_c":"f'(2) = 4","option_d":"f'(2) = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de f(x) = x² - 4x + 3 est f'(x) = 2x - 4. En x = 2, f'(2) = 2*2 - 4 = 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\": \"f'(2) = 0\", \"b\": \"f'(2) = -4\", \"c\": \"f'(2) = 4\", \"d\": \"f'(2) = 2\"","_debug_options_count":4},{"id":27382,"question":"Vrai ou Faux ? La fonction f(x) = 1\/x est décroissante sur son ensemble de définition.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = 1\/x est décroissante sur chacun des intervalles où elle est définie, c'est-à-dire sur ]-∞, 0[ et sur ]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":27383,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé équilibré a 6 faces numérotées de 1 à 6. Les nombres pairs sont 2, 4 et 6, soit 3 possibilités. La probabilité est donc 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\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":27384,"question":"Soit une sphère de rayon R. Quel est son volume V en fonction de R ?","option_a":"V = 4πR²","option_b":"V = (4\/3)πR³","option_c":"V = πR²","option_d":"V = 2πR","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume d'une sphère de rayon R est donné par la formule V = (4\/3)πR³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"V = 4πR²\", \"b\": \"V = (4\/3)πR³\", \"c\": \"V = πR²\", \"d\": \"V = 2","_debug_options_count":4},{"id":27385,"question":"Vrai ou Faux ? La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle, notée exp(x) ou e^x, est toujours 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":27386,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 1","option_b":"x \u003E 4","option_c":"x \u003C 4","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x \u003E 1\", \"b\": \"x \u003E 4\", \"c\": \"x \u003C 4\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":27387,"question":"Vrai ou Faux ? La probabilité conditionnelle P(A|B) est toujours inférieure ou égale à P(A).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité conditionnelle P(A|B) peut être supérieure à P(A) si l'événement B favorise l'événement A.","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":27388,"question":"Soit f une fonction définie par f(x) = (x² + 1)\/(x - 1). Quelle est l'équation de son asymptote verticale ?","option_a":"x = 1","option_b":"x = -1","option_c":"y = 1","option_d":"y = x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = (x² + 1)\/(x - 1) a une asymptote verticale en x = 1, car le dénominateur s'annule en ce point.","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 = 1\", \"b\": \"x = -1\", \"c\": \"y = 1\", \"d\": \"y = x\"}}","_debug_options_count":4},{"id":27389,"question":"Quelle est la probabilité d'obtenir deux fois le même résultat en lançant deux fois un dé équilibré à 6 faces ?","option_a":"1\/6","option_b":"1\/36","option_c":"1\/12","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'obtenir un résultat donné en lançant un dé est de 1\/6. La probabilité d'obtenir deux fois le même résultat est donc (1\/6) * (1\/6) = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/36\", \"c\": \"1\/12\", \"d\": \"1\/2\"}}","_debug_options_count":4}]