Quiz — serie 2( énoncé).pdf

Question 1 sur 10 20:00

[{"id":16369,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0.5 ou x = 2","option_c":"x = -1 ou x = 2.5","option_d":"x = 1.5 ou x = 3","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation se résout en utilisant le discriminant Δ = b² - 4ac. Ici, Δ = 25 - 16 = 9, donc les solutions sont x = (5 ± 3)\/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 ou x = 2\", \"b\": \"x = 0.5 ou x = 2\", \"c\": \"x = -1 ou x = 2.5","_debug_options_count":4},{"id":16370,"question":"La fonction f(x) = x³ - 3x est-elle dérivable en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Toute fonction polynôme est dérivable sur ℝ. Sa dérivée f'(x) = 3x² - 3 existe donc en x = 1.","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":16371,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² - 4) quand x tend vers l'infini ?","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 - 4\/x²) → 3\/1 = 3 quand x → ∞.","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":16372,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique de raison 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":16373,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4 et 6, soit 3 cas favorables sur 6 possibles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":16374,"question":"La fonction f(x) = √(x² + 1) est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = √((-x)² + 1) = √(x² + 1) = f(x), donc elle est paire.","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":16375,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 5x + 1 ?","option_a":"x ≥ -4","option_b":"x ≤ -4","option_c":"x ≥ 4","option_d":"x ≤ 4","option_e":"","option_f":"","bonne_reponse":"b","explication":"En isolant x, on obtient -7 - 1 ≤ 5x - 3x → -8 ≤ 2x → x ≥ -4. L'inéquation est donc équivalente à 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 ≥ -4\", \"b\": \"x ≤ -4\", \"c\": \"x ≥ 4\", \"d\": \"x ≤ 4\"}}","_debug_options_count":4},{"id":16376,"question":"La suite géométrique de premier terme u₀ = 3 et de raison q = 2 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite géométrique de raison q \u003E 1 et de premier terme positif est croissante. Ici, uₙ = 3 * 2ⁿ, donc elle est croissante.","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":16377,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"f'(x) = e^(2x)","option_b":"f'(x) = 2e^(2x)","option_c":"f'(x) = e^x","option_d":"f'(x) = 2e^x","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée d'une fonction exponentielle e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 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\": \"f'(x) = e^(2x)\", \"b\": \"f'(x) = 2e^(2x)\", \"c\": \"f'(x) = e^x\", \"d\":","_debug_options_count":4},{"id":16378,"question":"La probabilité de tirer un as dans un jeu de 32 cartes est-elle de 1\/8 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un jeu de 32 cartes contient 4 as. La probabilité est donc 4\/32 = 1\/8. 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}]