Quiz — 66d59826f3499_-_Correction Exercice 4.pdf

Question 1 sur 10 20:00

[{"id":33600,"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 résolvant l'équation : 2x - 5 = 3x + 1 → -5 - 1 = 3x - 2x → -6 = x. La solution est donc 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":33601,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction est un polynôme du second degré. Son discriminant Δ = (-4)² - 4×1×3 = 4 \u003E 0, donc elle admet deux racines réelles et change de signe. Elle n'est pas toujours positive.","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":33602,"question":"Quelle est l'aire d'un triangle rectangle dont les côtés de l'angle droit mesurent 3 cm et 4 cm ?","option_a":"6 cm²","option_b":"7 cm²","option_c":"12 cm²","option_d":"24 cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un triangle rectangle est donnée par (base × hauteur) \/ 2. Ici, (3 × 4) \/ 2 = 6 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\": \"6 cm²\", \"b\": \"7 cm²\", \"c\": \"12 cm²\", \"d\": \"24 cm²\"}}","_debug_options_count":4},{"id":33603,"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 dérivant terme à terme : f'(x) = 6x + 2. 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":33604,"question":"Quel est le résultat de √(16) + √(9) ?","option_a":"5","option_b":"7","option_c":"9","option_d":"11","option_e":"","option_f":"","bonne_reponse":"c","explication":"√(16) = 4 et √(9) = 3. Donc √(16) + √(9) = 4 + 3 = 7.","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\": \"9\", \"d\": \"11\"}}","_debug_options_count":4},{"id":33605,"question":"La médiane d'un triangle est toujours perpendiculaire à un côté.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane d'un triangle est une droite reliant un sommet au milieu du côté opposé. Elle n'est pas nécessairement perpendiculaire à ce côté.","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":33606,"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 -6","option_d":"x \u003C -6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant l'inéquation : 3x - 7 \u003E 2x + 1 → 3x - 2x \u003E 1 + 7 → 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 -6\", \"d\": \"x \u003C -6\"}}","_debug_options_count":4},{"id":33607,"question":"Le nombre 0 est-il un nombre premier ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un nombre premier est un nombre naturel supérieur à 1 qui n'a que deux diviseurs : 1 et lui-même. 0 ne vérifie pas cette définition.","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":33608,"question":"Quelle est la valeur de sin(30°) + cos(60°) ?","option_a":"0","option_b":"1","option_c":"√2\/2","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(30°) = 1\/2 et cos(60°) = 1\/2. Donc sin(30°) + cos(60°) = 1\/2 + 1\/2 = 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\": \"0\", \"b\": \"1\", \"c\": \"√2\/2\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":33609,"question":"La somme des angles d'un quadrilatère convexe est toujours égale à 360°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale des quadrilatères convexes : la somme de leurs angles intérieurs est toujours égale à 360°.","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}]