Quiz — Exercice 5.pdf

Question 1 sur 10 20:00

[{"id":33030,"question":"Quelle est la solution de l'équation 2x - 5 = 3 ?","option_a":"x = 1","option_b":"x = 4","option_c":"x = -1","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour résoudre 2x - 5 = 3, on ajoute 5 des deux côtés : 2x = 8, puis on divise par 2 : x = 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 = 1\", \"b\": \"x = 4\", \"c\": \"x = -1\", \"d\": \"x = 2\"}}","_debug_options_count":4},{"id":33031,"question":"La fonction f(x) = 3x + 2 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b, ce qui est le cas ici avec a = 3 et b = 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":33032,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 1 ?","option_a":"1","option_b":"-2","option_c":"2","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans l'équation y = ax + b, a représente le coefficient directeur. Ici, a = -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\": \"1\", \"b\": \"-2\", \"c\": \"2\", \"d\": \"-1\"}}","_debug_options_count":4},{"id":33033,"question":"L'inéquation 3x + 4 \u003E 10 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"On soustrait 4 : 3x \u003E 6, puis on divise par 3 : x \u003E 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 \u003E 2\", \"b\": \"x \u003C 2\", \"c\": \"x \u003E -2\", \"d\": \"x \u003C -2\"}}","_debug_options_count":4},{"id":33034,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"On vérifie avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est rectangle en 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":33035,"question":"Quelle est la forme développée de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² - x - 6","option_c":"x² + x + 6","option_d":"x² - 6x + 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant : x*x + x*(-2) + 3*x + 3*(-2) = x² - 2x + 3x - 6 = x² + 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\": \"x² + x - 6\", \"b\": \"x² - x - 6\", \"c\": \"x² + x + 6\", \"d\": \"x² -","_debug_options_count":4},{"id":33036,"question":"La droite d'équation y = 4x - 1 passe-t-elle par le point (0, -1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 0 : y = 4*0 - 1 = -1. Le point (0, -1) appartient bien à la droite.","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":33037,"question":"Quel est le résultat de l'expression 2(3x - 5) - 4x ?","option_a":"2x - 10","option_b":"6x - 10 - 4x","option_c":"2x + 10","option_d":"6x - 14","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant : 6x - 10 - 4x = 2x - 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2x - 10\", \"b\": \"6x - 10 - 4x\", \"c\": \"2x + 10\", \"d\": \"6x - 14\"}}","_debug_options_count":4},{"id":33038,"question":"L'équation x² - 9 = 0 a pour solutions :","option_a":"x = 3 et x = -3","option_b":"x = 9 et x = -9","option_c":"x = 0","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² = 9 ⇒ x = 3 ou 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 = 3 et x = -3\", \"b\": \"x = 9 et x = -9\", \"c\": \"x = 0\", \"d\": \"x =","_debug_options_count":4},{"id":33039,"question":"La fonction f(x) = x² - 4x + 4 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"On peut écrire f(x) = (x - 2)², qui est un carré donc toujours positif ou nul.","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}]