Quiz — Lycée Pilote Ariana+Kairaouan - DS 1 2019.pdf

Question 1 sur 5 10:00

[{"id":370,"question":"Quelle est la solution de l’équation du second degré 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":"Pour résoudre x² - 5x + 6 = 0, on factorise sous la forme (x - 2)(x - 3) = 0. Les solutions sont donc 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":371,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l’infini ?","option_a":"2","option_b":"0","option_c":"1","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x → ∞, on divise chaque terme par x² : f(x) ≈ (2 + 3\/x - 1\/x²)\/(1 - 4\/x²) → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2\", \"b\": \"0\", \"c\": \"1\", \"d\": \"-2\"}}","_debug_options_count":4},{"id":372,"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":"4 cm","option_c":"√64 cm","option_d":"12 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D’après le théorème de Pythagore : 10² = 6² + c² → c² = 100 - 36 = 64 → c = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"8 cm\", \"b\": \"4 cm\", \"c\": \"√64 cm\", \"d\": \"12 cm\"}}","_debug_options_count":4},{"id":373,"question":"Quelle est l’équation de la droite passant par les points A(2, 3) et B(-1, 5) ?","option_a":"y = (-2\/3)x + 13\/3","option_b":"y = (2\/3)x + 5\/3","option_c":"y = -2x + 7","option_d":"y = (3\/2)x + 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur est (5-3)\/(-1-2) = -2\/3. L’équation est y - 3 = (-2\/3)(x - 2) → y = (-2\/3)x + 13\/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\": \"y = (-2\/3)x + 13\/3\", \"b\": \"y = (2\/3)x + 5\/3\", \"c\": \"y = -2x + 7\",","_debug_options_count":4},{"id":374,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + 5x - 1 ?","option_a":"f’(x) = 9x² - 4x + 5","option_b":"f’(x) = 6x² - 4x + 5","option_c":"f’(x) = 9x² - 4x + 1","option_d":"f’(x) = 3x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x³ est 9x², celle de -2x² est -4x, celle de 5x est 5, et celle de -1 est 0. D’où f’(x) = 9x² - 4x + 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\": \"f’(x) = 9x² - 4x + 5\", \"b\": \"f’(x) = 6x² - 4x + 5\", \"c\": \"f","_debug_options_count":4}]