Quiz — Synt 3 4 M 2011-2012 final.pdf

Question 1 sur 5 10:00

[{"id":1613,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour résoudre 2x² - 5x + 2 = 0, on utilise le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± √9)\/4, soit x = 2 ou x = 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = 1 ou x = 2\", \"b\": \"x = 0,5 ou x = 2\", \"c\": \"x = -1 ou x = 2\",","_debug_options_count":4},{"id":1614,"question":"Quelle est l'image de -3 par la fonction f(x) = 2x + 1 ?","option_a":"-5","option_b":"-6","option_c":"7","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'image de -3 par f(x) = 2x + 1 est calculée en remplaçant x par -3 : f(-3) = 2*(-3) + 1 = -6 + 1 = -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\": \"-5\", \"b\": \"-6\", \"c\": \"7\", \"d\": \"5\"}}","_debug_options_count":4},{"id":1615,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"√136 cm","option_c":"4 cm","option_d":"√8 cm","option_e":"","option_f":"","bonne_reponse":"b","explication":"D'après le théorème de Pythagore, le troisième côté mesure √(10² - 6²) = √(100 - 36) = √64 = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"8 cm\", \"b\": \"√136 cm\", \"c\": \"4 cm\", \"d\": \"√8 cm\"}}","_debug_options_count":4},{"id":1616,"question":"Quelle est la solution du système d'équations { 3x + y = 7 ; 2x - y = 3 } ?","option_a":"x = 2, y = 1","option_b":"x = 1, y = 4","option_c":"x = 3, y = -2","option_d":"x = 0, y = 7","option_e":"","option_f":"","bonne_reponse":"a","explication":"En additionnant les deux équations, on obtient 5x = 10, donc x = 2. En remplaçant x dans la première équation, y = 7 - 6 = 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\": \"x = 2, y = 1\", \"b\": \"x = 1, y = 4\", \"c\": \"x = 3, y = -2\", \"d\": \"x","_debug_options_count":4},{"id":1617,"question":"Quelle est la nature de la fonction f(x) = (x² - 4)\/(x - 2) ?","option_a":"Affine","option_b":"Constante","option_c":"Indéterminée en x=2","option_d":"Polynôme du second degré","option_e":"","option_f":"","bonne_reponse":"d","explication":"La fonction f(x) = (x² - 4)\/(x - 2) se simplifie en f(x) = x + 2 pour x ≠ 2, mais elle reste une fonction rationnelle dont le numérateur est un polynôme du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"Affine\", \"b\": \"Constante\", \"c\": \"Indéterminée en x=2\", \"d\": \"Po","_debug_options_count":4}]