Quiz — 6348831d39b23_exercice 1 type devoir.pdf

Question 1 sur 10 20:00

[{"id":68266,"question":"Quelle est la solution de l'équation 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 se factorise en (x-2)(x-3)=0, donc les solutions sont 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":68267,"question":"La fonction f(x) = x³ est-elle dérivable en x=0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x)=x³ est dérivable en tout point, y compris x=0, avec f'(x)=3x² et f'(0)=0.","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":68268,"question":"Quel est le résultat de lim(x→∞) (3x² + 2x - 1)\/x² ?","option_a":"3","option_b":"2","option_c":"∞","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant chaque terme par x², on obtient lim(x→∞) (3 + 2\/x - 1\/x²) = 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\": \"3\", \"b\": \"2\", \"c\": \"∞\", \"d\": \"0\"}}","_debug_options_count":4},{"id":68269,"question":"Le théorème de Pythagore s'applique-t-il uniquement aux triangles rectangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de Pythagore est une propriété spécifique aux 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":68270,"question":"Quelle est la dérivée de la fonction f(x) = 2x⁴ - 3x² + 5 ?","option_a":"f'(x) = 8x³ - 6x","option_b":"f'(x) = 6x³ - 3x","option_c":"f'(x) = 8x³ - 3x","option_d":"f'(x) = 2x³ - 6x","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant la règle de dérivation, f'(x) = 2*4x³ - 3*2x + 0 = 8x³ - 6x.","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) = 8x³ - 6x\", \"b\": \"f'(x) = 6x³ - 3x\", \"c\": \"f'(x) = 8x³ ","_debug_options_count":4},{"id":68271,"question":"L'aire d'un cercle de rayon r est donnée par la formule πr². Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule correcte pour l'aire d'un cercle est bien πr².","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":68272,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E -1","option_d":"x \u003C -1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 2x - 5 \u003E 3, on obtient 2x \u003E 8, donc x \u003E 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\": \"x \u003E 4\", \"b\": \"x \u003C 4\", \"c\": \"x \u003E -1\", \"d\": \"x \u003C -1\"}}","_debug_options_count":4},{"id":68273,"question":"La fonction exponentielle f(x) = eˣ est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle eˣ est toujours strictement positive pour tout x réel.","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":68274,"question":"Quel est le volume d'une sphère de rayon r ?","option_a":"(4\/3)πr³","option_b":"πr²","option_c":"4πr²","option_d":"(1\/3)πr³","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du volume d'une sphère est (4\/3)πr³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(4\/3)πr³\", \"b\": \"πr²\", \"c\": \"4πr²\", \"d\": \"(1\/3)πr³\"}}","_debug_options_count":4},{"id":68275,"question":"La dérivée de sin(x) est cos(x). Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de sin(x) est bien cos(x).","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}]