Quiz — 6543f417b2ad4_Enoncé-Bac Pratique.pdf

Question 1 sur 10 20:00

[{"id":37020,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A. f'(x) = 2x + 3","option_b":"B. f'(x) = x² + 3","option_c":"C. f'(x) = 2x - 5","option_d":"D. f'(x) = 3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation : (x^n)' = n*x^(n-1). Ici, f'(x) = 2x + 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\": \"A. f'(x) = 2x + 3\", \"b\": \"B. f'(x) = x² + 3\", \"c\": \"C. f'(x) = 2","_debug_options_count":4},{"id":37021,"question":"La limite de la suite u_n = (n² + 1)\/n en +∞ est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n², on obtient u_n = 1 + 1\/n² → 1 en +∞. La limite n'est donc pas 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},{"id":37022,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"A. 1\/6","option_b":"B. 1\/12","option_c":"C. 1\/36","option_d":"D. 1\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 6 faces sur chaque dé, soit 36 combinaisons possibles. Une seule donne un double 6 (6-6), donc P = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 1\/6\", \"b\": \"B. 1\/12\", \"c\": \"C. 1\/36\", \"d\": \"D. 1\/18\"}}","_debug_options_count":4},{"id":37023,"question":"Dans un repère orthonormé, le produit scalaire de deux vecteurs u(2;3) et v(-1;4) est égal à :","option_a":"A. 10","option_b":"B. 5","option_c":"C. -5","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit scalaire u.v = (2)(-1) + (3)(4) = -2 + 12 = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 10\", \"b\": \"B. 5\", \"c\": \"C. -5\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":37024,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour tout x ∈ ℝ, e^x \u003E 0. La fonction exponentielle est strictement positive.","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":37025,"question":"Quelle est la solution générale de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(-2x)","option_b":"B. y = Ce^(2x)","option_c":"C. y = Cx + C","option_d":"D. y = C\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation y' + 2y = 0 est une équation différentielle linéaire du 1er ordre. Sa solution générale est y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. y = Ce^(-2x)\", \"b\": \"B. y = Ce^(2x)\", \"c\": \"C. y = Cx + C\", \"d","_debug_options_count":4},{"id":37026,"question":"Un dé est truqué : la probabilité d'obtenir 6 est de 1\/2, et les autres faces ont une probabilité égale. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"A. 1\/2","option_b":"B. 3\/4","option_c":"C. 2\/3","option_d":"D. 5\/6","option_e":"","option_f":"","bonne_reponse":"b","explication":"P(6) = 1\/2. Les faces 2, 4 ont une probabilité de (1 - 1\/2)\/3 = 1\/6 chacune. P(pair) = P(2) + P(4) + P(6) = 1\/6 + 1\/6 + 1\/2 = 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\": \"A. 1\/2\", \"b\": \"B. 3\/4\", \"c\": \"C. 2\/3\", \"d\": \"D. 5\/6\"}}","_debug_options_count":4},{"id":37027,"question":"La droite d'équation y = 3x + 2 et la parabole y = x² - 4x + 5 se coupent en deux points distincts.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons 3x + 2 = x² - 4x + 5 → x² - 7x + 3 = 0. Le discriminant Δ = 49 - 12 = 37 \u003E 0, donc deux solutions réelles distinctes.","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":37028,"question":"Quelle est la valeur de la somme S = 1 + 2 + 4 + 8 + ... + 2^n (n termes) ?","option_a":"A. 2^(n+1) - 1","option_b":"B. 2^n - 1","option_c":"C. n*2^(n+1)","option_d":"D. 2^(n-1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette somme est une suite géométrique de raison 2. S = 2^(n+1) - 1 (formule de la somme des termes d'une suite géométrique).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 2^(n+1) - 1\", \"b\": \"B. 2^n - 1\", \"c\": \"C. n*2^(n+1)\", \"d\": \"D.","_debug_options_count":4},{"id":37029,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","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 pour 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}]