Quiz — ds10.pdf

Question 1 sur 10 20:00

[{"id":117358,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) quand x tend vers +∞ ?","option_a":"A. 2","option_b":"B. 0","option_c":"C. -∞","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d'un polynôme de même degré au numérateur et au dénominateur est égale au rapport des coefficients dominants. Ici, 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\": \"A. 2\", \"b\": \"B. 0\", \"c\": \"C. -∞\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":117359,"question":"Une suite numérique est convergente si et seulement si elle est bornée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite convergente est nécessairement bornée, mais une suite bornée n'est pas forcément convergente (exemple : la suite (-1)^n).","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":117360,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 2x) ?","option_a":"A. (6x + 2)\/(3x² + 2x)","option_b":"B. (6x + 2)\/(3x² + 2x)²","option_c":"C. (3x² + 2x)\/(6x + 2)","option_d":"D. 6x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x² + 2x, donc u' = 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\": \"A. (6x + 2)\/(3x² + 2x)\", \"b\": \"B. (6x + 2)\/(3x² + 2x)²\", \"c\": ","_debug_options_count":4},{"id":117361,"question":"La probabilité d'un événement A est P(A) = 0,6. Quelle est la probabilité de l'événement contraire A̅ ?","option_a":"A. 0,4","option_b":"B. 0,6","option_c":"C. 0,3","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 1 - 0,6 = 0,4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 0,4\", \"b\": \"B. 0,6\", \"c\": \"C. 0,3\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":117362,"question":"Dans un espace vectoriel, deux vecteurs sont orthogonaux si et seulement si leur produit scalaire est nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs u et v sont orthogonaux si et seulement si u·v = 0.","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":117363,"question":"Quelle est la formule du produit scalaire de deux vecteurs u et v dans l'espace ?","option_a":"A. u·v = x1x2 + y1y2 + z1z2","option_b":"B. u·v = x1x2 - y1y2 + z1z2","option_c":"C. u·v = |u| + |v|","option_d":"D. u·v = (x1 + x2)(y1 + y2)(z1 + z2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit scalaire de deux vecteurs u(x1, y1, z1) et v(x2, y2, z2) est donné par u·v = x1x2 + y1y2 + z1z2.","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. u·v = x1x2 + y1y2 + z1z2\", \"b\": \"B. u·v = x1x2 - y1y2 + z1z2","_debug_options_count":4},{"id":117364,"question":"Combien de mots de 3 lettres peut-on former avec les lettres A, B, C, D sans répétition ?","option_a":"A. 12","option_b":"B. 24","option_c":"C. 6","option_d":"D. 8","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est un arrangement de 4 lettres prises 3 à 3 : A(4,3) = 4 × 3 × 2 = 24.","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. 12\", \"b\": \"B. 24\", \"c\": \"C. 6\", \"d\": \"D. 8\"}}","_debug_options_count":4},{"id":117365,"question":"La fonction f(x) = x³ - 3x est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction n'est pas strictement croissante sur ℝ.","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":117366,"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 × 6 = 36 issues possibles. Une seule issue correspond à un double 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":117367,"question":"Quelle est la limite de la suite u_n = (n² + 1)\/(2n² - n) quand n tend vers +∞ ?","option_a":"A. 0","option_b":"B. 1\/2","option_c":"C. 1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n², on obtient u_n = (1 + 1\/n²)\/(2 - 1\/n), donc la limite est 1\/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\": \"A. 0\", \"b\": \"B. 1\/2\", \"c\": \"C. 1\", \"d\": \"D. +∞\"}}","_debug_options_count":4}]