Quiz — serie_25__correct_partielle.pdf

Question 1 sur 5 10:00

[{"id":2832,"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 se factorise 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":2833,"question":"Quelle est l'expression d'une fonction affine dont la représentation graphique passe par les points A(1 ; 3) et B(2 ; 5) ?","option_a":"f(x) = 2x + 1","option_b":"f(x) = x + 2","option_c":"f(x) = 3x - 2","option_d":"f(x) = -x + 4","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur est (5-3)\/(2-1) = 2. En utilisant le point A(1 ; 3), on obtient f(x) = 2(x - 1) + 3 = 2x + 1. Cependant, en vérifiant avec B(2 ; 5), on trouve f(2) = 5, ce qui correspond à f(x) = 2x + 1. L'option correcte est donc f(x) = 2x + 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\": \"f(x) = 2x + 1\", \"b\": \"f(x) = x + 2\", \"c\": \"f(x) = 3x - 2\", \"d\": \"","_debug_options_count":4},{"id":2834,"question":"Dans un cube d'arête 4 cm, quel est le volume d'une pyramide dont la base est une face du cube et le sommet est le centre du cube ?","option_a":"16\/3 cm³","option_b":"32\/3 cm³","option_c":"64\/3 cm³","option_d":"8 cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume de la pyramide est V = (1\/3) × aire de la base × hauteur. L'aire de la base (face du cube) est 4×4 = 16 cm². La hauteur est la moitié de l'arête du cube, soit 2 cm. Donc V = (1\/3)×16×2 = 32\/3 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"16\/3 cm³\", \"b\": \"32\/3 cm³\", \"c\": \"64\/3 cm³\", \"d\": \"8 cm³\"}}","_debug_options_count":4},{"id":2835,"question":"On lance un dé équilibré à 6 faces. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Les nombres pairs sur un dé sont 2, 4 et 6. Il y a donc 3 issues favorables sur 6 possibles. 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":2836,"question":"Si f(x) = 3x + 2, quelle est l'image de -1 par f ?","option_a":"-1","option_b":"1","option_c":"-5","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'image de -1 par f est f(-1) = 3×(-1) + 2 = -3 + 2 = -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\": \"-1\", \"b\": \"1\", \"c\": \"-5\", \"d\": \"5\"}}","_debug_options_count":4}]