Quiz — 1565778522_Exercice 1.pdf

Question 1 sur 10 20:00

[{"id":56517,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = -1 ou x = 2","option_c":"x = 1\/2 ou x = 2","option_d":"x = -1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"c","explication":"Résolvons l'équation : Δ = (-5)² - 4*2*2 = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 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\": \"x = 1 ou x = 2\", \"b\": \"x = -1 ou x = 2\", \"c\": \"x = 1\/2 ou x = 2\",","_debug_options_count":4},{"id":56518,"question":"La dérivée de f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x³ est 3x², celle de -3x² est -6x, et celle de 2x est 2. Donc f'(x) = 3x² - 6x + 2 est correcte.","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":56519,"question":"Quelle est l'image de 2 par la fonction f(x) = ln(x) ?","option_a":"0","option_b":"1","option_c":"ln(2)","option_d":"2","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'image de 2 par la fonction logarithme népérien est ln(2), car f(2) = ln(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\": \"0\", \"b\": \"1\", \"c\": \"ln(2)\", \"d\": \"2\"}}","_debug_options_count":4},{"id":56520,"question":"Le théorème de Pythagore s'applique-t-il dans un triangle rectangle isocèle ?","option_a":"Oui, toujours","option_b":"Non, jamais","option_c":"Seulement si l'angle droit est de 45°","option_d":"Seulement si les côtés sont égaux","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de Pythagore s'applique à tout triangle rectangle, qu'il soit isocèle ou non.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Oui, toujours\", \"b\": \"Non, jamais\", \"c\": \"Seulement si l'angle dr","_debug_options_count":4},{"id":56521,"question":"La moyenne d'une série statistique est toujours égale à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La moyenne et la médiane sont égales uniquement si la distribution est symétrique. Sinon, elles diffèrent.","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":56522,"question":"Quelle est la limite de (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"Indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"Factorisons : (x² - 1)\/(x - 1) = (x - 1)(x + 1)\/(x - 1) = x + 1. Donc la limite est 1 + 1 = 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\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"Indéterminée\"}}","_debug_options_count":4},{"id":56523,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, alors le triangle est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vérifions : 5² + 12² = 25 + 144 = 169 = 13². Donc le triangle est rectangle en B (théorème de Pythagore).","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":56524,"question":"Quelle est la primitive de f(x) = 3x² - 2x + 1 ?","option_a":"x³ - x² + x + C","option_b":"x³ - x² + x","option_c":"3x³ - x² + x + C","option_d":"x³ - x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 3x² est x³, celle de -2x est -x², et celle de 1 est x. Donc F(x) = x³ - x² + x + 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\": \"x³ - x² + x + C\", \"b\": \"x³ - x² + x\", \"c\": \"3x³ - x² + x + ","_debug_options_count":4},{"id":56525,"question":"La fonction f(x) = e^x est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel, car e^x \u003E 0 pour tout x ∈ ℝ.","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":56526,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003C 0 ?","option_a":"x ∈ ]1; 3[","option_b":"x ∈ ]-∞; 1[ ∪ ]3; +∞[","option_c":"x ∈ ]-∞; +∞[","option_d":"x ∈ ∅","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons l'inéquation : x² - 4x + 3 = (x - 1)(x - 3) \u003C 0. Le produit est négatif entre les racines, donc x ∈ ]1; 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 ∈ ]1; 3[\", \"b\": \"x ∈ ]-∞; 1[ ∪ ]3; +∞[\", \"c\": \"x ∈ ","_debug_options_count":4}]