Quiz — 14 serie 9 ben saad.pdf

Question 1 sur 10 20:00

[{"id":74005,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 1 ?","option_a":"x = 6","option_b":"x = 4","option_c":"x = 2","option_d":"x = -6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x, on obtient 3x - 2x = 1 + 5, soit x = 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 = 6\", \"b\": \"x = 4\", \"c\": \"x = 2\", \"d\": \"x = -6\"}}","_debug_options_count":4},{"id":74006,"question":"La dérivée de la fonction f(x) = x² + 3x est f'(x) = 2x + 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x et celle de 3x est 3, donc f'(x) = 2x + 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":74007,"question":"Quelle est la valeur de sin(30°) ?","option_a":"0,5","option_b":"√3\/2","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"sin(30°) = 0,5, valeur fondamentale en trigonométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,5\", \"b\": \"√3\/2\", \"c\": \"1\", \"d\": \"0\"}}","_debug_options_count":4},{"id":74008,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant est Δ = (-4)² - 4*1*4 = 0, donc une solution double x = 2.","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":74009,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ x quand x tend vers 0 ?","option_a":"0","option_b":"2","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En simplifiant, f(x) = 2x + 3, donc la limite est 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\": \"0\", \"b\": \"2\", \"c\": \"3\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":74010,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction 1\/x n'est pas définie en x = 0 (division par zéro).","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":74011,"question":"Quelle est la valeur de cos(60°) ?","option_a":"√3\/2","option_b":"0,5","option_c":"1","option_d":"√2\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"cos(60°) = 0,5, valeur fondamentale en trigonométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"√3\/2\", \"b\": \"0,5\", \"c\": \"1\", \"d\": \"√2\/2\"}}","_debug_options_count":4},{"id":74012,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution x \u003E 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant, on obtient x \u003E 2, donc la solution est correcte.","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":74013,"question":"Quelle est la dérivée de la fonction f(x) = 5x³ - 2x² + x ?","option_a":"15x² - 4x + 1","option_b":"15x² - 4x","option_c":"5x² - 2x + 1","option_d":"15x² - 4x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En dérivant terme à terme, on obtient f'(x) = 15x² - 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\": \"15x² - 4x + 1\", \"b\": \"15x² - 4x\", \"c\": \"5x² - 2x + 1\", \"d\": \"1","_debug_options_count":4},{"id":74014,"question":"La fonction f(x) = x³ est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Sa dérivée f'(x) = 3x² est toujours positive (sauf en x=0), donc f est croissante sur ℝ.","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}]