Quiz — 6509c021a47ab_Corrigé_Série d'exercices n 4.pdf

Question 1 sur 10 20:00

[{"id":18299,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 6x² + 2","option_c":"C. 3x + 2","option_d":"D. 6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ainsi, 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\": \"A. 6x + 2\", \"b\": \"B. 6x² + 2\", \"c\": \"C. 3x + 2\", \"d\": \"D. 6x - 5","_debug_options_count":4},{"id":18300,"question":"L'équation x² - 4x + 3 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = 16 - 12 = 4 \u003E 0, donc l'équation admet 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":18301,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"A. x \u003E 4","option_b":"B. x \u003C 4","option_c":"C. x \u003E 1","option_d":"D. x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 2x - 3 \u003E 5, on obtient 2x \u003E 8, puis x \u003E 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. x \u003E 4\", \"b\": \"B. x \u003C 4\", \"c\": \"C. x \u003E 1\", \"d\": \"D. x \u003C 1\"}}","_debug_options_count":4},{"id":18302,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","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":18303,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"A. 1\/2","option_b":"B. √2\/2","option_c":"C. √3\/2","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"sin(π\/6) = sin(30°) = 1\/2, une valeur fondamentale à connaître.","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. 1\/2\", \"b\": \"B. √2\/2\", \"c\": \"C. √3\/2\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":18304,"question":"L'équation 3^(x+1) = 9 admet pour solution x = 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"3^(x+1) = 9 ⇒ 3^(x+1) = 3² ⇒ x+1 = 2 ⇒ x = 1.","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":18305,"question":"Quelle est la primitive de la fonction f(x) = 4x³ ?","option_a":"A. x⁴ + C","option_b":"B. 12x² + C","option_c":"C. x³ + C","option_d":"D. 4x⁴ + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 4x³ est x⁴ + C, car (x⁴)' = 4x³.","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. x⁴ + C\", \"b\": \"B. 12x² + C\", \"c\": \"C. x³ + C\", \"d\": \"D. 4x","_debug_options_count":4},{"id":18306,"question":"Le vecteur u(2, -3) et v(-1, 4) sont orthogonaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux vecteurs sont orthogonaux si leur produit scalaire est nul. u·v = (2)(-1) + (-3)(4) = -2 -12 = -14 ≠ 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":18307,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 1) quand x tend vers l'infini ?","option_a":"A. 2","option_b":"B. 0","option_c":"C. 1","option_d":"D. ∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 1\/x²), dont la limite est 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. 1\", \"d\": \"D. ∞\"}}","_debug_options_count":4},{"id":18308,"question":"L'équation de la droite passant par les points A(1, 2) et B(3, 4) est y = x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. La droite a pour équation y = x + 1 (car 2 = 1*1 + 1).","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}]