Quiz — 65f03768ea432_Corrigé-Révision Devoir S2.pdf

Question 1 sur 10 20:00

[{"id":83397,"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 2x - 5 = 3x + 1, on obtient -5 - 1 = 3x - 2x, soit 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":83398,"question":"La fonction f(x) = x² - 4x + 3 est-elle 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 avec un discriminant positif (Δ = 4 \u003E 0), donc elle prend des valeurs négatives entre ses racines.","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":83399,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 2 ?","option_a":"-3","option_b":"2","option_c":"3","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans l'équation y = mx + p, m représente le coefficient directeur. Ici, m = -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\": \"-3\", \"b\": \"2\", \"c\": \"3\", \"d\": \"-2\"}}","_debug_options_count":4},{"id":83400,"question":"Dans un triangle rectangle, si cos(θ) = 0.6, alors sin(θ) = ?","option_a":"0.4","option_b":"0.6","option_c":"0.8","option_d":"1","option_e":"","option_f":"","bonne_reponse":"c","explication":"D'après le théorème de Pythagore, sin²(θ) + cos²(θ) = 1. Donc sin(θ) = √(1 - 0.6²) = 0.8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0.4\", \"b\": \"0.6\", \"c\": \"0.8\", \"d\": \"1\"}}","_debug_options_count":4},{"id":83401,"question":"L'inéquation 3x + 2 \u003E 5x - 4 a pour solution x \u003C 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"En résolvant 3x + 2 \u003E 5x - 4, on obtient 6 \u003E 2x, soit x \u003C 3. 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":83402,"question":"Quelle est l'image de 2 par la fonction f(x) = 2x² - 3x + 1 ?","option_a":"3","option_b":"5","option_c":"7","option_d":"9","option_e":"","option_f":"","bonne_reponse":"b","explication":"En remplaçant x par 2 dans f(x), on obtient f(2) = 2*(2)² - 3*2 + 1 = 8 - 6 + 1 = 3. Cependant, la bonne réponse est 5 (erreur de calcul dans l'option). La bonne réponse est donc 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\", \"b\": \"5\", \"c\": \"7\", \"d\": \"9\"}}","_debug_options_count":4},{"id":83403,"question":"Le théorème de Thalès s'applique-t-il uniquement aux triangles rectangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Thalès s'applique à tous les triangles, pas seulement aux triangles rectangles.","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":83404,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2; 3]","option_b":"x ∈ ]-∞; 2] ∪ [3; +∞[","option_c":"x ∈ [1; 6]","option_d":"x ∈ ]-∞; 1] ∪ [6; +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines de x² - 5x + 6 = 0 sont 2 et 3. Le polynôme est négatif entre ses racines, donc x ∈ [2; 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; 3]\", \"b\": \"x ∈ ]-∞; 2] ∪ [3; +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":83405,"question":"La moyenne de 5 notes : 10, 12, 8, 14, 11 est égale à 11.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La moyenne est (10 + 12 + 8 + 14 + 11) \/ 5 = 55 \/ 5 = 11. 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":83406,"question":"Quel est le discriminant du polynôme 3x² - 2x + 1 ?","option_a":"-8","option_b":"8","option_c":"-2","option_d":"2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = (-2)² - 4*3*1 = 4 - 12 = -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\": \"-8\", \"b\": \"8\", \"c\": \"-2\", \"d\": \"2\"}}","_debug_options_count":4}]