Quiz — DC3.4.13M-c.pdf

Question 1 sur 10 20:00

[{"id":39190,"question":"Quelle est la solution de l'équation 2x + 5 = 11 ?","option_a":"x = 3","option_b":"x = 4","option_c":"x = 5","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 5 des deux côtés, on obtient 2x = 6, puis en divisant par 2, 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 = 3\", \"b\": \"x = 4\", \"c\": \"x = 5\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":39191,"question":"La fonction f(x) = x² - 4x + 3 est-elle croissante sur l'intervalle [2, +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 4 est positive pour x \u003E 2, donc la fonction est croissante sur cet intervalle.","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":39192,"question":"Quel est le résultat de sin(30°) + cos(60°) ?","option_a":"0","option_b":"1","option_c":"√2\/2","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(30°) = 1\/2 et cos(60°) = 1\/2, donc leur somme est égale à 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\/2\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":39193,"question":"L'inéquation 3x - 7 ≤ 2x + 1 a pour solution :","option_a":"x ≤ 8","option_b":"x ≥ 8","option_c":"x ≤ -8","option_d":"x ≥ -8","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 2x des deux côtés, on obtient x - 7 ≤ 1, puis en ajoutant 7, x ≤ 8.","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 ≤ 8\", \"b\": \"x ≥ 8\", \"c\": \"x ≤ -8\", \"d\": \"x ≥ -8\"}}","_debug_options_count":4},{"id":39194,"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. Le triangle est donc 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":39195,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + x - 5 ?","option_a":"f'(x) = 9x² - 4x + 1","option_b":"f'(x) = 6x² - 4x + 1","option_c":"f'(x) = 9x² - 2x + 1","option_d":"f'(x) = 6x² - 2x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée est obtenue en appliquant la règle de puissance : f'(x) = 9x² - 4x + 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\": \"f'(x) = 9x² - 4x + 1\", \"b\": \"f'(x) = 6x² - 4x + 1\", \"c\": \"f'(x)","_debug_options_count":4},{"id":39196,"question":"L'équation x² - 6x + 9 = 0 a pour solution :","option_a":"x = 3 (double)","option_b":"x = -3","option_c":"x = 3 ou x = -3","option_d":"Aucune solution réelle","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant est Δ = 36 - 36 = 0, donc l'équation admet une solution double 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 = 3 (double)\", \"b\": \"x = -3\", \"c\": \"x = 3 ou x = -3\", \"d\": \"Auc","_debug_options_count":4},{"id":39197,"question":"La fonction f(x) = 1\/x est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie pour x = 0 car la division par zéro est impossible.","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":39198,"question":"Quel est le résultat de (2 + √3)² ?","option_a":"4 + 2√3","option_b":"7 + 4√3","option_c":"4 + 4√3","option_d":"7 + 2√3","option_e":"","option_f":"","bonne_reponse":"b","explication":"En développant, on obtient 4 + 4√3 + 3 = 7 + 4√3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"4 + 2√3\", \"b\": \"7 + 4√3\", \"c\": \"4 + 4√3\", \"d\": \"7 + 2√3\"}","_debug_options_count":4},{"id":39199,"question":"L'aire d'un cercle de rayon r est donnée par la formule :","option_a":"A = 2πr","option_b":"A = πr²","option_c":"A = 4πr²","option_d":"A = πr","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule de l'aire d'un cercle est A = πr², où r est le rayon.","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 = 2πr\", \"b\": \"A = πr²\", \"c\": \"A = 4πr²\", \"d\": \"A = πr\"}}","_debug_options_count":4}]