Quiz — correction S20 Mr arrbiii.pdf

Question 1 sur 10 20:00

[{"id":116002,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"x² + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = 3x² + 2x - 5 est f'(x) = 6x + 2, car la dérivée de x² est 2x et celle de x est 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\": \"6x + 2\", \"b\": \"3x² + 2\", \"c\": \"6x - 5\", \"d\": \"x² + 2x - 5\"}}","_debug_options_count":4},{"id":116003,"question":"L'équation x² - 4x + 3 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = 16 - 12 = 4 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","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":116004,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003E 1","option_c":"x \u003C 4","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. La solution est 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 \u003E 1\", \"c\": \"x \u003C 4\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":116005,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur l'intervalle [0, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x + 2. Sur [0, 2], f'(x) change de signe, donc la fonction n'est pas 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":116006,"question":"Quelle est la valeur de la limite lim (x→2) (x² - 4)\/(x - 2) ?","option_a":"0","option_b":"4","option_c":"2","option_d":"indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"lim (x→2) (x² - 4)\/(x - 2) = lim (x→2) (x + 2) = 4 après simplification.","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\": \"4\", \"c\": \"2\", \"d\": \"indéterminée\"}}","_debug_options_count":4},{"id":116007,"question":"Le triangle ABC avec AB = 5, AC = 12 et BC = 13 est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"5² + 12² = 25 + 144 = 169 = 13², donc le triangle est rectangle en A d'après le théorème de Pythagore.","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":116008,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x = 2","option_b":"x = 3","option_c":"x = 1","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"2^(x+1) = 8 ⇒ 2^(x+1) = 2³ ⇒ x + 1 = 3 ⇒ x = 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\": \"x = 2\", \"b\": \"x = 3\", \"c\": \"x = 1\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":116009,"question":"La fonction f(x) = 1\/x est-elle définie en 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 en x = 0 car la division par zéro est interdite.","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":116010,"question":"Quelle est la valeur de l'intégrale ∫(0 à 1) (3x² + 2x) dx ?","option_a":"2","option_b":"3","option_c":"1","option_d":"4","option_e":"","option_f":"","bonne_reponse":"a","explication":"∫(3x² + 2x) dx = x³ + x². Évaluée entre 0 et 1, cela donne (1 + 1) - (0 + 0) = 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\": \"3\", \"c\": \"1\", \"d\": \"4\"}}","_debug_options_count":4},{"id":116011,"question":"Le système d'équations {2x + y = 5; x - y = 1} admet-il une solution unique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le système admet une solution unique car les deux équations sont linéairement indépendantes.","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}]