Quiz — Devoir_synthese_2_4m_2023_blue_final (1).pdf

Question 1 sur 10 20:00

[{"id":37590,"question":"Quelle est la solution de l'équation du second degré x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et 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 = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":37591,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle une fonction polynôme de degré 3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x³ - 3x² + 2x est bien une fonction polynôme de degré 3, car le terme de plus haut degré est x³.","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":37592,"question":"Quelle est la dérivée de la fonction f(x) = 4x² - 3x + 1 ?","option_a":"f'(x) = 8x - 3","option_b":"f'(x) = 4x - 3","option_c":"f'(x) = 8x + 1","option_d":"f'(x) = 4x² - 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 8x - 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\": \"f'(x) = 8x - 3\", \"b\": \"f'(x) = 4x - 3\", \"c\": \"f'(x) = 8x + 1\", \"d","_debug_options_count":4},{"id":37593,"question":"Une suite arithmétique a pour premier terme u₀ = 5 et pour raison r = 3. Quel est le terme u₅ ?","option_a":"u₅ = 20","option_b":"u₅ = 17","option_c":"u₅ = 23","option_d":"u₅ = 14","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans une suite arithmétique, uₙ = u₀ + n*r. Donc u₅ = 5 + 5*3 = 20.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"u₅ = 20\", \"b\": \"u₅ = 17\", \"c\": \"u₅ = 23\", \"d\": \"u₅ = 14\"}","_debug_options_count":4},{"id":37594,"question":"La probabilité d'un événement impossible est-elle égale à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est égale à 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":37595,"question":"Quelle est la forme factorisée de l'expression 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":"L'expression x² - 9 est une différence de carrés, donc elle se factorise en (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":37596,"question":"Soit une fonction f définie par f(x) = (2x + 1)\/(x - 3). Quel est son ensemble de définition ?","option_a":"x ≠ 3","option_b":"x ≠ -1\/2","option_c":"x ≠ 0","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = (2x + 1)\/(x - 3) est définie pour tout x sauf x = 3, car le dénominateur ne doit pas être 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\": \"x ≠ 3\", \"b\": \"x ≠ -1\/2\", \"c\": \"x ≠ 0\", \"d\": \"x ∈ ℝ\"}}","_debug_options_count":4},{"id":37597,"question":"La somme des angles d'un triangle est-elle toujours égale à 180° ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans un triangle, la somme des angles est toujours égale à 180°, c'est une propriété fondamentale de la géométrie euclidienne.","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":37598,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x tendant vers l'infini, les termes de plus haut degré dominent. Donc f(x) ≈ 3x²\/x² = 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\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":37599,"question":"Un événement et son contraire sont-ils incompatibles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un événement et son contraire sont incompatibles (ils ne peuvent pas se produire simultanément) et leur union forme l'univers des possibles.","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}]