Quiz — 63399ddc1a422_Exercice 5 type devoir.pdf

Question 1 sur 10 20:00

[{"id":33380,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2x","option_c":"6x² + 2","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2 et (-5)' = 0. Donc f'(x) = 6x + 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\": \"6x + 2\", \"b\": \"3x² + 2x\", \"c\": \"6x² + 2\", \"d\": \"3x + 2\"}}","_debug_options_count":4},{"id":33381,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle ]-∞; -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 positive lorsque x² \u003E 1, soit x \u003C -1 ou x \u003E 1. La fonction est donc croissante sur ]-∞; -1[ et ]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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":33382,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quelle est la valeur de u₃ ?","option_a":"18","option_b":"54","option_c":"162","option_d":"6","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le terme général d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 2 × 3³ = 2 × 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"18\", \"b\": \"54\", \"c\": \"162\", \"d\": \"6\"}}","_debug_options_count":4},{"id":33383,"question":"Dans un repère orthonormé, l'équation de la droite passant par les points A(1; 2) et B(3; 4) est :","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x + 2","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. L'équation est y = x + b. En remplaçant A(1;2), on obtient 2 = 1 + b ⇒ b = 1. Donc y = x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"y = x + 1\", \"b\": \"y = 2x - 1\", \"c\": \"y = x + 2\", \"d\": \"y = 2x + 1","_debug_options_count":4},{"id":33384,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé a 6 faces : 3 nombres pairs (2, 4, 6) et 3 nombres impairs. La probabilité est donc 3\/6 = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":33385,"question":"Soit f(x) = ln(x). Quelle est la limite de f(x) lorsque x tend vers 0+ ?","option_a":"0","option_b":"+∞","option_c":"-∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln(x) tend vers -∞ lorsque x tend vers 0+. Donc f(x) = ln(x) tend vers -∞.","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\": \"+∞\", \"c\": \"-∞\", \"d\": \"1\"}}","_debug_options_count":4},{"id":33386,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est l'énoncé du théorème de Pythagore, valable uniquement pour les 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":33387,"question":"Résoudre l'inéquation 2x - 3 \u003E 5.","option_a":"x \u003E 1","option_b":"x \u003E 4","option_c":"x \u003C 4","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. L'ensemble des solutions 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\": \"b\", \"options\": {\"a\": \"x \u003E 1\", \"b\": \"x \u003E 4\", \"c\": \"x \u003C 4\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":33388,"question":"Soit une fonction f définie par f(x) = e^x. Quelle est sa fonction dérivée ?","option_a":"e^x","option_b":"x e^(x-1)","option_c":"e^(x-1)","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction exponentielle e^x est elle-même : f'(x) = e^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\": \"e^x\", \"b\": \"x e^(x-1)\", \"c\": \"e^(x-1)\", \"d\": \"1\"}}","_debug_options_count":4},{"id":33389,"question":"La moyenne d'une série statistique est toujours supérieure ou égale à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Ce n'est pas toujours vrai. Par exemple, pour la série {1, 2, 100}, la moyenne est 34,33 et la médiane est 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]