Quiz — Correction-Livre-Scolaire-4ème-MATHS-TOME1-1

Question 1 sur 10 20:00

[{"id":21339,"question":"Quel est le PGCD de 48 et 18 ?","option_a":"6","option_b":"8","option_c":"12","option_d":"18","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PGCD (Plus Grand Commun Diviseur) de 48 et 18 se calcule par la méthode des divisions successives : 48 ÷ 18 = 2 reste 12 ; 18 ÷ 12 = 1 reste 6 ; 12 ÷ 6 = 2 reste 0. Le PGCD est donc 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6\", \"b\": \"8\", \"c\": \"12\", \"d\": \"18\"}}","_debug_options_count":4},{"id":21340,"question":"L'équation 3x + 5 = 20 a pour solution x = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Résolvons l'équation : 3x + 5 = 20 → 3x = 15 → x = 5. La solution est bien x = 5, donc l'affirmation est vraie.","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":21341,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Cette propriété s'appelle :","option_a":"Théorème de Pythagore","option_b":"Théorème de Thalès","option_c":"Propriété des angles","option_d":"Formule des aires","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette propriété est connue sous le nom de \u003Cstrong\u003EThéorème de Pythagore\u003C\/strong\u003E, fondamentale en géométrie pour les triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Théorème de Pythagore\", \"b\": \"Théorème de Thalès\", \"c\": \"Pro","_debug_options_count":4},{"id":21342,"question":"Si A = 2x² - 3x + 1 et B = x² + 5x - 4, alors A - B = ?","option_a":"x² - 8x + 5","option_b":"x² - 2x - 3","option_c":"3x² + 2x - 3","option_d":"x² + 2x - 5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Calculons A - B : (2x² - 3x + 1) - (x² + 5x - 4) = 2x² - 3x + 1 - x² - 5x + 4 = x² - 8x + 5. La bonne réponse est donc x² - 8x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x² - 8x + 5\", \"b\": \"x² - 2x - 3\", \"c\": \"3x² + 2x - 3\", \"d\": \"x","_debug_options_count":4},{"id":21343,"question":"Le théorème de Thalès s'applique uniquement aux triangles isocèles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Thalès s'applique à tous les triangles, à condition que les droites soient parallèles. Il n'est pas réservé aux triangles isocèles.","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":21344,"question":"Quelle est la formule de l'aire d'un trapèze de bases b1 et b2 et de hauteur h ?","option_a":"A = (b1 + b2) × h \/ 2","option_b":"A = b1 × b2 × h","option_c":"A = (b1 + b2) × h","option_d":"A = b1 × h \/ 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule de l'aire d'un trapèze est \u003Cstrong\u003EA = (b1 + b2) × h \/ 2\u003C\/strong\u003E, où b1 et b2 sont les longueurs des deux bases parallèles.","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 = (b1 + b2) × h \/ 2\", \"b\": \"A = b1 × b2 × h\", \"c\": \"A = (b1 ","_debug_options_count":4},{"id":21345,"question":"Résolvez l'inéquation : 2x - 7 \u003C 5.","option_a":"x \u003C 6","option_b":"x \u003E 6","option_c":"x \u003C 1","option_d":"x \u003E 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons l'inéquation : 2x - 7 \u003C 5 → 2x \u003C 12 → x \u003C 6. La solution est donc x \u003C 6.","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 \u003C 6\", \"b\": \"x \u003E 6\", \"c\": \"x \u003C 1\", \"d\": \"x \u003E 1\"}}","_debug_options_count":4},{"id":21346,"question":"Dans une série statistique, la moyenne est toujours supérieure à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La moyenne n'est pas toujours supérieure à la médiane. Cela dépend de la distribution des valeurs. Par exemple, dans une série symétrique, moyenne et médiane sont égales.","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":21347,"question":"Quel est le développement de (x + 3)² ?","option_a":"x² + 6x + 9","option_b":"x² + 3x + 9","option_c":"x² + 9","option_d":"x² + 6x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le développement de (x + 3)² est x² + 6x + 9, selon l'identité remarquable (a + b)² = a² + 2ab + b².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + 6x + 9\", \"b\": \"x² + 3x + 9\", \"c\": \"x² + 9\", \"d\": \"x² + 6","_debug_options_count":4},{"id":21348,"question":"Si deux droites sont parallèles, alors leurs coefficients directeurs sont égaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux droites parallèles ont effectivement le même coefficient directeur. C'est une propriété fondamentale de la géométrie analytique.","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}]