Quiz — 67910913489ee_série de révision n°20_arith_les enregistrements.pdf

Question 1 sur 10 20:00

[{"id":29520,"question":"Quel est le PGCD de 56 et 98 ?","option_a":"12","option_b":"14","option_c":"16","option_d":"18","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le PGCD de 56 et 98 est 14, car 56 = 2³ × 7 et 98 = 2 × 7², donc le PGCD est 2 × 7 = 14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"12\", \"b\": \"14\", \"c\": \"16\", \"d\": \"18\"}}","_debug_options_count":4},{"id":29521,"question":"Le nombre 97 est-il un nombre premier ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"97 est un nombre premier car il n'a pas d'autres diviseurs que 1 et lui-même.","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":29522,"question":"Quel est le PPCM de 12 et 18 ?","option_a":"36","option_b":"24","option_c":"48","option_d":"72","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PPCM de 12 (2² × 3) et 18 (2 × 3²) est 2² × 3² = 36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"36\", \"b\": \"24\", \"c\": \"48\", \"d\": \"72\"}}","_debug_options_count":4},{"id":29523,"question":"L'algorithme d'Euclide permet de calculer :","option_a":"Le PGCD de deux nombres","option_b":"Le PPCM de deux nombres","option_c":"La somme de deux nombres","option_d":"Le carré d'un nombre","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'algorithme d'Euclide est une méthode efficace pour déterminer le PGCD de deux nombres entiers.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Le PGCD de deux nombres\", \"b\": \"Le PPCM de deux nombres\", \"c\": \"L","_debug_options_count":4},{"id":29524,"question":"Si a ≡ b [n], alors n divise :","option_a":"a + b","option_b":"a - b","option_c":"a × b","option_d":"a² + b²","option_e":"","option_f":"","bonne_reponse":"b","explication":"La congruence a ≡ b [n] signifie que n divise (a - b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"a + b\", \"b\": \"a - b\", \"c\": \"a × b\", \"d\": \"a² + b²\"}}","_debug_options_count":4},{"id":29525,"question":"Le théorème de Bézout s'applique uniquement aux nombres premiers.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Bézout s'applique à tous les entiers, pas seulement aux nombres premiers.","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":29526,"question":"Quel est le reste de la division de 1234 par 7 ?","option_a":"2","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"d","explication":"1234 ÷ 7 = 176 avec un reste de 2, car 7 × 176 = 1232 et 1234 - 1232 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"2\", \"b\": \"3\", \"c\": \"4\", \"d\": \"5\"}}","_debug_options_count":4},{"id":29527,"question":"La décomposition en facteurs premiers de 84 est :","option_a":"2² × 3 × 7","option_b":"2³ × 3 × 7","option_c":"2 × 3² × 7","option_d":"2 × 3 × 7²","option_e":"","option_f":"","bonne_reponse":"a","explication":"84 = 2² × 3 × 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2² × 3 × 7\", \"b\": \"2³ × 3 × 7\", \"c\": \"2 × 3² × 7\", \"d\": ","_debug_options_count":4},{"id":29528,"question":"Si deux nombres sont premiers entre eux, leur PGCD est égal à :","option_a":"0","option_b":"1","option_c":"2","option_d":"leur produit","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux nombres premiers entre eux ont un PGCD de 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\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"leur produit\"}}","_debug_options_count":4},{"id":29529,"question":"L'équation 15x + 20y = 5 a-t-elle des solutions entières ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PGCD de 15 et 20 est 5, qui divise 5, donc l'équation a des solutions entières (par exemple x = 1, y = -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}]