Quiz — DevoirLibre2.pdf

Question 1 sur 10 20:00

[{"id":34100,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 2x + 7, on soustrait 2x des deux côtés : x - 5 = 7, puis on ajoute 5 : x = 12.","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 = 12\", \"b\": \"x = 2\", \"c\": \"x = -2\", \"d\": \"x = 5\"}}","_debug_options_count":4},{"id":34101,"question":"Dans un repère orthonormé, l'équation d'une droite parallèle à l'axe des abscisses est de la forme y = k.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une droite parallèle à l'axe des abscisses a une équation de la forme y = k, où k est une constante (ordonnée à l'origine).","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":34102,"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":"x² - 9 est une différence de carrés : x² - 3² = (x - 3)(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)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":34103,"question":"La fonction f(x) = 2x + 1 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = 2x + 1 est une fonction affine de coefficient directeur 2 \u003E 0, donc elle est strictement croissante sur ℝ.","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":34104,"question":"Quel est le coefficient directeur de la droite passant par les points A(1; 3) et B(4; 9) ?","option_a":"2","option_b":"3","option_c":"1","option_d":"6","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur m = (yB - yA)\/(xB - xA) = (9 - 3)\/(4 - 1) = 6\/3 = 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\": \"2\", \"b\": \"3\", \"c\": \"1\", \"d\": \"6\"}}","_debug_options_count":4},{"id":34105,"question":"L'inéquation 2x - 4 \u003E 0 a pour solution x \u003E 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 4 \u003E 0 ⇒ 2x \u003E 4 ⇒ x \u003E 2. La solution est bien 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":34106,"question":"Quelle est l'image de 3 par la fonction f(x) = x² - 4x + 5 ?","option_a":"2","option_b":"4","option_c":"5","option_d":"6","option_e":"","option_f":"","bonne_reponse":"a","explication":"f(3) = 3² - 4*3 + 5 = 9 - 12 + 5 = 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\": \"2\", \"b\": \"4\", \"c\": \"5\", \"d\": \"6\"}}","_debug_options_count":4},{"id":34107,"question":"Les vecteurs u(2; -3) et v(-4; 6) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les vecteurs sont colinéaires si leurs coordonnées sont proportionnelles : 2\/-4 = -3\/6 ⇒ -0.5 = -0.5. Donc oui, ils sont colinéaires.","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":34108,"question":"La fonction g(x) = -3x + 2 est-elle décroissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction g(x) = -3x + 2 est une fonction affine de coefficient directeur -3 \u003C 0, donc elle est strictement décroissante sur ℝ.","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":34109,"question":"Quel est le résultat de (x + 2)² - (x - 2)² ?","option_a":"8x","option_b":"4x","option_c":"x²","option_d":"8","option_e":"","option_f":"","bonne_reponse":"a","explication":"(x + 2)² - (x - 2)² = (x² + 4x + 4) - (x² - 4x + 4) = 8x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"8x\", \"b\": \"4x\", \"c\": \"x²\", \"d\": \"8\"}}","_debug_options_count":4}]