Quiz — 6339d45a0051c_Exercice 13 type devoir.pdf

Question 1 sur 10 20:00

[{"id":20789,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 2 ou x = 1\/2","option_b":"x = -2 ou x = -1\/2","option_c":"x = 2 ou x = -1\/2","option_d":"x = -2 ou x = 1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résoudre l'équation du second degré en utilisant le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 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\": \"x = 2 ou x = 1\/2\", \"b\": \"x = -2 ou x = -1\/2\", \"c\": \"x = 2 ou x = ","_debug_options_count":4},{"id":20790,"question":"La fonction f(x) = x³ - 3x est-elle 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 donc pas strictement croissante sur tout 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":20791,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"3","option_b":"0","option_c":"1\/4","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). La limite est donc 3\/1 = 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\": \"3\", \"b\": \"0\", \"c\": \"1\/4\", \"d\": \"+∞\"}}","_debug_options_count":4},{"id":20792,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vérifier si AB² + BC² = AC² : 25 + 144 = 169 = 13². Le triangle est donc rectangle en B.","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":20793,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"f'(x) = 1\/(2x + 1)","option_b":"f'(x) = 2\/(2x + 1)","option_c":"f'(x) = 1\/(x + 1)","option_d":"f'(x) = 2\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 1, donc u' = 2. Ainsi, f'(x) = 2\/(2x + 1).","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) = 1\/(2x + 1)\", \"b\": \"f'(x) = 2\/(2x + 1)\", \"c\": \"f'(x) = 1\/(","_debug_options_count":4},{"id":20794,"question":"L'intégrale ∫(0 à 1) (3x² + 2x) dx vaut :","option_a":"2","option_b":"5\/2","option_c":"3","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Calculer l'intégrale : [x³ + x²] de 0 à 1 = (1 + 1) - (0 + 0) = 2. Cependant, l'intégrale de 3x² + 2x est x³ + x², donc le résultat est 5\/2 (erreur dans l'option, réponse correcte : 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\": \"5\/2\", \"c\": \"3\", \"d\": \"1\"}}","_debug_options_count":4},{"id":20795,"question":"La fonction f(x) = e^(2x) est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = e^(-2x) ≠ e^(2x) = f(x). La fonction n'est donc pas paire.","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":20796,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 ≤ 0 ?","option_a":"x ∈ [1, 3]","option_b":"x ∈ ]-∞, 1] ∪ [3, +∞[","option_c":"x ∈ [0, 4]","option_d":"x ∈ ]-∞, 0] ∪ [4, +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résoudre l'inéquation en trouvant les racines de x² - 4x + 3 = 0 (x = 1 et x = 3). Le polynôme est négatif entre les racines, donc x ∈ [1, 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\": \"x ∈ [1, 3]\", \"b\": \"x ∈ ]-∞, 1] ∪ [3, +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":20797,"question":"Le vecteur u(2, -3) et le vecteur v(-4, 6) 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 un multiple de l'autre. Ici, 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":20798,"question":"Quelle est la primitive de f(x) = 4x³ - 2x + 1 ?","option_a":"F(x) = x⁴ - x² + x + C","option_b":"F(x) = x⁴ - x² + C","option_c":"F(x) = 12x² - 2 + C","option_d":"F(x) = x³ - x + x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 4x³ est x⁴, celle de -2x est -x², et celle de 1 est x. Ainsi, F(x) = x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"F(x) = x⁴ - x² + x + C\", \"b\": \"F(x) = x⁴ - x² + C\", \"c\": \"F","_debug_options_count":4}]