Quiz — Corrigés.pdf

Question 1 sur 10 20:00

[{"id":36440,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2x","option_d":"D. 6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 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. 6x + 2\", \"b\": \"B. 3x + 2\", \"c\": \"C. 6x² + 2x\", \"d\": \"D. 6x - ","_debug_options_count":4},{"id":36441,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction est croissante sur [-2 ; -1] et [1 ; 2], mais décroissante sur [-1 ; 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36442,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A. x = e²","option_b":"B. x = 2","option_c":"C. x = e","option_d":"D. x = 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, ln(x) = 2 équivaut à x = e².","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 = e²\", \"b\": \"B. x = 2\", \"c\": \"C. x = e\", \"d\": \"D. x = 1\"}}","_debug_options_count":4},{"id":36443,"question":"Le nombre complexe z = 3 + 4i a pour module :","option_a":"A. 5","option_b":"B. 7","option_c":"C. 25","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module de z = a + bi est √(a² + b²) = √(9 + 16) = 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. 25\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":36444,"question":"La suite (uₙ) définie par uₙ = 2n + 1 est arithmétique de raison 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs : uₙ₊₁ - uₙ = 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":36445,"question":"Quelle est l'intégrale ∫(3x² + 2x) dx ?","option_a":"A. x³ + x² + C","option_b":"B. 6x + 2 + C","option_c":"C. x³ + x + C","option_d":"D. 3x³ + x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale se calcule terme par terme : ∫3x² dx = x³ et ∫2x dx = x², d'où x³ + x² + C.","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. x³ + x² + C\", \"b\": \"B. 6x + 2 + C\", \"c\": \"C. x³ + x + C\", \"","_debug_options_count":4},{"id":36446,"question":"La probabilité d'un événement impossible est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, la probabilité d'un événement impossible est 0, et celle d'un événement certain est 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36447,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) quand x tend vers +∞ ?","option_a":"A. 2","option_b":"B. 0","option_c":"C. 1","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x, on obtient (2 + 1\/x)\/(1 - 3\/x) → 2 quand 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\": \"A. 2\", \"b\": \"B. 0\", \"c\": \"C. 1\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":36448,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"A. b² - 4ac","option_b":"B. a² - 4bc","option_c":"C. 4b² - ac","option_d":"D. b² + 4ac","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac détermine le nombre de solutions réelles de l'équation.","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. b² - 4ac\", \"b\": \"B. a² - 4bc\", \"c\": \"C. 4b² - ac\", \"d\": \"D.","_debug_options_count":4},{"id":36449,"question":"La fonction exponentielle f(x) = eˣ est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour tout x réel, eˣ \u003E 0, donc la fonction exponentielle est toujours positive.","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}]