Quiz — Sol Série DL Partie1.PDF

Question 1 sur 10 20:00

[{"id":105470,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 = 10 → 3x = 15 → x = 5. La solution est donc x = 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\": \"x = 5\", \"b\": \"x = 15\/3\", \"c\": \"x = 5\/3\", \"d\": \"x = 15\"}}","_debug_options_count":4},{"id":105471,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b. Ici, a = 2 et b = 3, donc c'est une fonction affine.","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":105472,"question":"Quel est le résultat de (2x + 3)(x - 4) ?","option_a":"2x² - 5x - 12","option_b":"2x² - 5x + 12","option_c":"2x² + 5x - 12","option_d":"2x² - 8x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant : (2x)(x) + (2x)(-4) + 3(x) + 3(-4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2x² - 5x - 12\", \"b\": \"2x² - 5x + 12\", \"c\": \"2x² + 5x - 12\", \"d","_debug_options_count":4},{"id":105473,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vérifions avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Donc, le triangle est rectangle en B.","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":105474,"question":"Quelle est la dérivée de f(x) = x² + 4x - 1 ?","option_a":"f'(x) = 2x + 4","option_b":"f'(x) = x + 4","option_c":"f'(x) = 2x - 1","option_d":"f'(x) = x² + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 4x est 4, et celle de -1 est 0. Donc f'(x) = 2x + 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 2x + 4\", \"b\": \"f'(x) = x + 4\", \"c\": \"f'(x) = 2x - 1\", \"d\"","_debug_options_count":4},{"id":105475,"question":"L'inéquation 2x + 7 \u003E 3x - 1 a pour solution x \u003C 8 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"2x + 7 \u003E 3x - 1 → 7 + 1 \u003E 3x - 2x → 8 \u003E x → x \u003C 8. La solution est donc x \u003C 8.","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":105476,"question":"Quel est le PGCD de 48 et 60 ?","option_a":"12","option_b":"6","option_c":"24","option_d":"18","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les diviseurs de 48 sont 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Ceux de 60 sont 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Le PGCD est donc 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"12\", \"b\": \"6\", \"c\": \"24\", \"d\": \"18\"}}","_debug_options_count":4},{"id":105477,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = (-x)³ = -x³ ≠ x³ = f(x). Donc, la fonction n'est pas paire.","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":105478,"question":"Résolvez l'inéquation : 5 - 2x ≤ 3x + 7","option_a":"x ≥ -2\/5","option_b":"x ≤ -2\/5","option_c":"x ≥ 2\/5","option_d":"x ≤ 2\/5","option_e":"","option_f":"","bonne_reponse":"d","explication":"5 - 2x ≤ 3x + 7 → 5 - 7 ≤ 3x + 2x → -2 ≤ 5x → x ≥ -2\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"x ≥ -2\/5\", \"b\": \"x ≤ -2\/5\", \"c\": \"x ≥ 2\/5\", \"d\": \"x ≤ 2\/5","_debug_options_count":4},{"id":105479,"question":"Quel est le résultat de √(16) + √(9) ?","option_a":"7","option_b":"5","option_c":"10","option_d":"15","option_e":"","option_f":"","bonne_reponse":"a","explication":"√(16) = 4 et √(9) = 3. Donc √(16) + √(9) = 4 + 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\": \"7\", \"b\": \"5\", \"c\": \"10\", \"d\": \"15\"}}","_debug_options_count":4}]