Quiz — ct3 4M 20122013.pdf

Question 1 sur 10 20:00

[{"id":31430,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la formule des racines d'une équation du second degré, on trouve x = [5 ± √(25 - 16)] \/ 4 = [5 ± 3]\/4. Les solutions sont donc x = 2 et x = 1\/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\": \"x = 1 ou x = 2\", \"b\": \"x = 2 ou x = 1\/2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":31431,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-1, 1] (car 3x² ≤ 3), donc la fonction est décroissante 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":31432,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x est x² et celle de 1 est x. On ajoute la constante d'intégration C pour obtenir x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + x + C\", \"b\": \"x² + C\", \"c\": \"2x² + x + C\", \"d\": \"x² + 2x","_debug_options_count":4},{"id":31433,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 5 cm et un côté mesure 3 cm, quelle est la longueur du troisième côté ?","option_a":"4 cm","option_b":"2 cm","option_c":"√34 cm","option_d":"√16 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant le théorème de Pythagore : 5² = 3² + x² → 25 = 9 + x² → x² = 16 → x = 4 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\": \"4 cm\", \"b\": \"2 cm\", \"c\": \"√34 cm\", \"d\": \"√16 cm\"}}","_debug_options_count":4},{"id":31434,"question":"La dérivée de la fonction f(x) = sin(2x) est f'(x) = 2cos(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la règle de dérivation des fonctions composées, la dérivée de sin(2x) est 2cos(2x). L'affirmation est donc vraie.","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":31435,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 1 ?","option_a":"x \u003E 8","option_b":"x \u003C 8","option_c":"x \u003E -8","option_d":"x \u003C -8","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant l'inéquation : 3x - 2x \u003E 1 + 7 → x \u003E 8. La solution est donc x \u003E 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 \u003E 8\", \"b\": \"x \u003C 8\", \"c\": \"x \u003E -8\", \"d\": \"x \u003C -8\"}}","_debug_options_count":4},{"id":31436,"question":"Dans un repère orthonormé, quel est le coefficient directeur de la droite passant par les points A(1, 2) et B(3, 6) ?","option_a":"2","option_b":"1","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur m est donné par m = (yB - yA)\/(xB - xA) = (6 - 2)\/(3 - 1) = 4\/2 = 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\": \"1\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":31437,"question":"La fonction f(x) = e^x est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel, car e^x \u003E 0 quel que soit x.","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":31438,"question":"Quelle est la valeur de la limite lim (x→2) (x² - 4)\/(x - 2) ?","option_a":"0","option_b":"2","option_c":"4","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"b","explication":"En factorisant le numérateur : (x² - 4)\/(x - 2) = (x - 2)(x + 2)\/(x - 2) = x + 2 pour x ≠ 2. La limite quand x→2 est donc 4.","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\": \"4\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4},{"id":31439,"question":"Le théorème de Thalès s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Thalès s'applique à tous les triangles, pas seulement aux triangles rectangles. Il nécessite simplement que les droites soient parallèles.","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}]