Quiz — P-EX04-17-CM.pdf

Question 1 sur 10 20:00

[{"id":50913,"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":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : f'(x) = n*a*x^(n-1) pour chaque terme. Ici, 3x² donne 6x, 2x donne 2, et -5 donne 0.","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\": \"6x + 2x - 5\"}}","_debug_options_count":4},{"id":50914,"question":"L'équation x² - 5x + 6 = 0 a pour solutions :","option_a":"x = 2 et x = 3","option_b":"x = -2 et x = -3","option_c":"x = 1 et x = 6","option_d":"x = 0 et x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"On factorise l'équation : (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 et x = 3\", \"b\": \"x = -2 et x = -3\", \"c\": \"x = 1 et x = 6\", ","_debug_options_count":4},{"id":50915,"question":"Vrai ou Faux ? La somme des angles d'un triangle est toujours égale à 180 degrés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est un théorème fondamental de la géométrie euclidienne. Cette propriété est valable pour tous les triangles.","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":50916,"question":"Quelle est l'aire d'un cercle de rayon r = 4 cm ?","option_a":"16π cm²","option_b":"8π cm²","option_c":"4π cm²","option_d":"32π cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un cercle se calcule avec la formule A = πr². Ici, A = π*(4)² = 16π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"16π cm²\", \"b\": \"8π cm²\", \"c\": \"4π cm²\", \"d\": \"32π cm²\"}}","_debug_options_count":4},{"id":50917,"question":"Vrai ou Faux ? La fonction f(x) = x³ est une fonction paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = (-x)³ = -x³ ≠ f(x). Elle est donc impaire.","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":50918,"question":"Résolvez l'inéquation : 2x - 3 \u003E 7.","option_a":"x \u003E 5","option_b":"x \u003C 5","option_c":"x \u003E 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"On isole x : 2x \u003E 10 → x \u003E 5. L'ensemble des solutions est donc x \u003E 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\": \"x \u003E 5\", \"b\": \"x \u003C 5\", \"c\": \"x \u003E 2\", \"d\": \"x \u003C 2\"}}","_debug_options_count":4},{"id":50919,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"b","explication":"On factorise le numérateur : (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1. La limite quand x→1 est donc 1+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\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4},{"id":50920,"question":"Vrai ou Faux ? 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":50921,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e²","option_b":"x = 2e","option_c":"x = 1\/2","option_d":"x = ln(2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, ln(x) = 2 équivaut à x = e² (où e est la base du logarithme népérien).","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 = e²\", \"b\": \"x = 2e\", \"c\": \"x = 1\/2\", \"d\": \"x = ln(2)\"}}","_debug_options_count":4},{"id":50922,"question":"Vrai ou Faux ? La dérivée de sin(x) est cos(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale des fonctions trigonométriques. La dérivée de sin(x) est bien cos(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}]