Quiz — 63317d7b299e1_Exercice 15.pdf

Question 1 sur 10 20:00

[{"id":127935,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = -4","option_c":"x = 4","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x, on obtient 2x - 3x = 1 + 5 → -x = 6 → x = -6.","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 = -6\", \"b\": \"x = -4\", \"c\": \"x = 4\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":127936,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction du second degré avec un coefficient positif admet un minimum en son sommet.","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":127937,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 2 ?","option_a":"2","option_b":"-3","option_c":"3","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur (pente) est le nombre devant x dans l'équation réduite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"-3\", \"c\": \"3\", \"d\": \"-2\"}}","_debug_options_count":4},{"id":127938,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de Pythagore, une propriété fondamentale en géométrie.","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":127939,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 2x + 1 ?","option_a":"f'(x) = 6x - 2","option_b":"f'(x) = 3x - 2","option_c":"f'(x) = 6x² - 2","option_d":"f'(x) = 3x² - 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n·a·x^(n-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\": \"f'(x) = 6x - 2\", \"b\": \"f'(x) = 3x - 2\", \"c\": \"f'(x) = 6x² - 2\", ","_debug_options_count":4},{"id":127940,"question":"Un angle de 120° est-il aigu ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un angle aigu mesure moins de 90°, un angle obtus mesure entre 90° et 180°.","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":127941,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 5x - 6 ?","option_a":"x \u003C 3","option_b":"x \u003E 3","option_c":"x \u003C -3","option_d":"x \u003E -3","option_e":"","option_f":"","bonne_reponse":"c","explication":"En isolant x, on obtient 2x - 5x \u003E -6 - 3 → -3x \u003E -9 → x \u003C 3 (inversion du sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"x \u003C 3\", \"b\": \"x \u003E 3\", \"c\": \"x \u003C -3\", \"d\": \"x \u003E -3\"}}","_debug_options_count":4},{"id":127942,"question":"Le volume d'une sphère de rayon r est donné par la formule V = (4\/3)πr³. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la formule exacte du volume d'une sphère.","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":127943,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une identité remarquable de la forme a² - b² = (a - b)(a + b).","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)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":127944,"question":"Dans un repère orthonormé, la distance entre les points A(1;2) et B(4;6) est égale à :","option_a":"5","option_b":"√7","option_c":"√25","option_d":"√13","option_e":"","option_f":"","bonne_reponse":"c","explication":"La distance se calcule avec la formule √[(xB - xA)² + (yB - yA)²] = √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"5\", \"b\": \"√7\", \"c\": \"√25\", \"d\": \"√13\"}}","_debug_options_count":4}]