Quiz — Lycée Pilote Ariana - DC 2 2016(1).pdf

Question 1 sur 10 20:00

[{"id":8240,"question":"Quelle est la solution de l'équation 2x² - 5x - 3 = 0 ?","option_a":"x = 3 ou x = -1\/2","option_b":"x = -3 ou x = 1\/2","option_c":"x = 3\/2 ou x = -1","option_d":"x = -1 ou x = 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution s'obtient en utilisant la formule des racines du second degré : x = [5 ± √(25 + 24)] \/ 4 = [5 ± 7] \/ 4. Les solutions sont donc 3 et -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\": \"x = 3 ou x = -1\/2\", \"b\": \"x = -3 ou x = 1\/2\", \"c\": \"x = 3\/2 ou x ","_debug_options_count":4},{"id":8241,"question":"La dérivée de la fonction f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant les règles de dérivation, f'(x) = 6x + 2, donc l'affirmation est 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":8242,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003C 2x + 5 ?","option_a":"x \u003C 12","option_b":"x \u003E 12","option_c":"x \u003C -12","option_d":"x \u003E -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant l'inéquation : 3x - 2x \u003C 5 + 7 → x \u003C 12. La solution est donc x \u003C 12.","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 \u003C 12\", \"b\": \"x \u003E 12\", \"c\": \"x \u003C -12\", \"d\": \"x \u003E -12\"}}","_debug_options_count":4},{"id":8243,"question":"La fonction f(x) = x³ - 3x² + 2x admet un point d'inflexion en x = 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée seconde f''(x) = 6x - 6 s'annule en x = 1, ce qui confirme la présence d'un point d'inflexion en ce point.","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":8244,"question":"Quelle est la valeur de la dérivée de f(x) = √(x) en x = 4 ?","option_a":"1\/4","option_b":"1\/2","option_c":"1\/√4","option_d":"2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de f(x) = √x est f'(x) = 1\/(2√x). En x = 4, f'(4) = 1\/(2*2) = 1\/4. Cependant, la bonne réponse est 1\/2 car la dérivée de √x est 1\/(2√x) et non 1\/√x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/4\", \"b\": \"1\/2\", \"c\": \"1\/√4\", \"d\": \"2\"}}","_debug_options_count":4},{"id":8245,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de Pythagore énonce que dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Il ne s'applique donc qu'aux triangles rectangles.","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":8246,"question":"Quelle est la solution du système d'équations { 2x + y = 5 ; x - y = 1 } ?","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant le système, on trouve x = 2 et y = 1. C'est la seule solution qui satisfait les deux équations.","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 = 3\", \"c\": \"x = 3, y = -1\", \"d\": \"x","_debug_options_count":4},{"id":8247,"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 f(x) = 1\/x est indéfinie en x = 0 car la division par zéro n'est pas autorisée. L'affirmation est donc fausse.","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":8248,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"2e^(2x)","option_b":"e^(2x)","option_c":"2xe^(2x)","option_d":"(2x)e^(2x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la règle de dérivation des fonctions exponentielles, f'(x) = 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2e^(2x)\", \"b\": \"e^(2x)\", \"c\": \"2xe^(2x)\", \"d\": \"(2x)e^(2x)\"}}","_debug_options_count":4},{"id":8249,"question":"L'équation x² + 4x + 5 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = 16 - 20 = -4 est négatif, donc l'équation n'admet pas de solutions réelles. L'affirmation est fausse.","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}]