Quiz — 6377e2cd42b5f_Exercice type devoir 12.pdf

Question 1 sur 10 20:00

[{"id":64821,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynomiale se calcule terme à terme : f'(x) = 6x + 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\": \"6x + 2\", \"b\": \"6x² + 2\", \"c\": \"3x + 2\", \"d\": \"6x - 5\"}}","_debug_options_count":4},{"id":64822,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique converge uniquement si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc la suite diverge.","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":64823,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"2\/3","option_d":"1\/6","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc P = 3\/6 = 1\/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\": \"1\/2\", \"b\": \"1\/3\", \"c\": \"2\/3\", \"d\": \"1\/6\"}}","_debug_options_count":4},{"id":64824,"question":"Le nombre complexe z = 2 + 2i a pour module :","option_a":"2","option_b":"2√2","option_c":"4","option_d":"√8","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le module de z = a + bi est √(a² + b²) = √(4 + 4) = √8 = 2√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\": \"2√2\", \"c\": \"4\", \"d\": \"√8\"}}","_debug_options_count":4},{"id":64825,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3 est positive sur [-2, -1] et [1, 2], mais négative sur [-1, 1], donc la fonction n'est pas croissante sur tout l'intervalle.","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":64826,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n - 3) quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 - 3\/n) → 2\/1 = 2.","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\", \"b\": \"1\", \"c\": \"2\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":64827,"question":"L'équation x² + 4x + 5 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0, donc l'équation n'a pas de solutions réelles.","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":64828,"question":"Quelle est la probabilité d'obtenir deux fois pile en lançant deux fois une pièce équilibrée ?","option_a":"1\/4","option_b":"1\/2","option_c":"3\/4","option_d":"1\/8","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les lancers sont indépendants. P(pile) = 1\/2, donc P(deux piles) = (1\/2)² = 1\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\/4\", \"b\": \"1\/2\", \"c\": \"3\/4\", \"d\": \"1\/8\"}}","_debug_options_count":4},{"id":64829,"question":"Le plan d'équation x + 2y - z = 4 est parallèle au vecteur directeur (1, 2, -1).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un plan d'équation ax + by + cz = d a pour vecteur normal (a, b, c). Ici, le vecteur (1, 2, -1) est normal au plan, pas parallèle.","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":64830,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (3x² + 2x) dx ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale se calcule comme [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 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\": \"3\", \"d\": \"4\/3\"}}","_debug_options_count":4}]