Quiz — 696b60e62d978_exercice 2.pdf

Question 1 sur 10 20:00

[{"id":42865,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"3x² - 5x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (-5x)' = -5, et (2)' = 0. Donc f'(x) = 6x - 5.","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 - 5\", \"b\": \"3x - 5\", \"c\": \"6x² - 5\", \"d\": \"3x² - 5x\"}}","_debug_options_count":4},{"id":42866,"question":"L'équation x² + 4x + 4 = 0 admet-elle 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 = b² - 4ac = 16 - 16 = 0. Une équation avec Δ = 0 admet une solution double (x = -2), donc pas deux solutions distinctes.","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":42867,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) quand x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"-∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x → +∞, on divise numérateur et dénominateur par x : f(x) = (2 + 1\/x)\/(1 - 3\/x) → 2\/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\": \"2\", \"b\": \"0\", \"c\": \"1\", \"d\": \"-∞\"}}","_debug_options_count":4},{"id":42868,"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 uₙ₊₁ - uₙ est constant. Ici, uₙ₊₁ - uₙ = 2(n+1)+1 - (2n+1) = 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":42869,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x³ au point d'abscisse 1 ?","option_a":"1","option_b":"3","option_c":"0","option_d":"6","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la tangente est égal à f'(1). f'(x) = 3x², donc f'(1) = 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\": \"1\", \"b\": \"3\", \"c\": \"0\", \"d\": \"6\"}}","_debug_options_count":4},{"id":42870,"question":"L'inéquation 3x - 7 ≤ 2x + 5 a pour solution x ≤ 12. Cette affirmation est-elle correcte ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Résolvons l'inéquation : 3x - 2x ≤ 5 + 7 → x ≤ 12. L'affirmation est donc correcte.","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":42871,"question":"Quelle est la probabilité d'obtenir exactement 3 fois le chiffre 6 en lançant un dé équilibré 5 fois ?","option_a":"5\/32","option_b":"10\/243","option_c":"1\/6","option_d":"1\/32","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une loi binomiale de paramètres n=5 et p=1\/6. P(X=3) = C(5,3) * (1\/6)³ * (5\/6)² = 10 * (1\/216) * (25\/36) = 250\/7776 ≈ 5\/32.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5\/32\", \"b\": \"10\/243\", \"c\": \"1\/6\", \"d\": \"1\/32\"}}","_debug_options_count":4},{"id":42872,"question":"Le vecteur u(2, -1) et le vecteur v(-4, 2) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs sont colinéaires si l'un est multiple de l'autre. v = -2u, donc 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":42873,"question":"Quelle est l'aire d'un triangle de côtés 5 cm, 6 cm et 7 cm ?","option_a":"√30 cm²","option_b":"6√6 cm²","option_c":"15 cm²","option_d":"12 cm²","option_e":"","option_f":"","bonne_reponse":"b","explication":"Utilisons la formule de Héron : s = (5+6+7)\/2 = 9, Aire = √[s(s-a)(s-b)(s-c)] = √[9*4*3*2] = √216 = 6√6 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"√30 cm²\", \"b\": \"6√6 cm²\", \"c\": \"15 cm²\", \"d\": \"12 cm²\"}}","_debug_options_count":4},{"id":42874,"question":"La fonction f(x) = ln(x) est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0. Elle n'est pas définie en x = 0.","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}]