Quiz — 4_BM_2005-06.pdf

Question 1 sur 10 20:00

[{"id":88408,"question":"Soit la fonction f(x) = x² - 4x + 3. Quelle est la valeur de f(2) ?","option_a":"-1","option_b":"3","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 2 dans l'expression de f(x), on obtient f(2) = (2)² - 4*(2) + 3 = 4 - 8 + 3 = -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\": \"-1\", \"b\": \"3\", \"c\": \"1\", \"d\": \"0\"}}","_debug_options_count":4},{"id":88409,"question":"L'équation x² + 2x + 5 = 0 admet 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 = 4 - 20 = -16 \u003C 0, donc l'équation n'a pas de solutions réelles.","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":88410,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + x - 1 ?","option_a":"9x² - 4x + 1","option_b":"6x² - 4x + 1","option_c":"3x² - 2x + 1","option_d":"x² - x + 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de f(x) = 3x³ - 2x² + x - 1 est f'(x) = 9x² - 4x + 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\": \"9x² - 4x + 1\", \"b\": \"6x² - 4x + 1\", \"c\": \"3x² - 2x + 1\", \"d\": ","_debug_options_count":4},{"id":88411,"question":"Soit une suite géométrique de premier terme u₁ = 2 et de raison q = 3. Quelle est la valeur de u₄ ?","option_a":"18","option_b":"54","option_c":"162","option_d":"81","option_e":"","option_f":"","bonne_reponse":"b","explication":"u₄ = u₁ * q^(4-1) = 2 * 3³ = 2 * 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"18\", \"b\": \"54\", \"c\": \"162\", \"d\": \"81\"}}","_debug_options_count":4},{"id":88412,"question":"La fonction f(x) = 1\/x est définie et continue sur ℝ.","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, donc elle n'est pas continue 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":88413,"question":"Quelle est la solution de l'inéquation 2x - 5 ≤ 3x + 1 ?","option_a":"x ≥ -6","option_b":"x ≤ -6","option_c":"x ≥ 6","option_d":"x ≤ 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 5 ≤ 3x + 1 ⇒ -5 - 1 ≤ 3x - 2x ⇒ -6 ≤ x ⇒ x ≥ -6.","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 ≥ -6\", \"b\": \"x ≤ -6\", \"c\": \"x ≥ 6\", \"d\": \"x ≤ 6\"}}","_debug_options_count":4},{"id":88414,"question":"Soit un triangle ABC rectangle en A avec AB = 3 et AC = 4. Quelle est la longueur de BC ?","option_a":"5","option_b":"7","option_c":"√7","option_d":"√13","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25 ⇒ BC = 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\": \"5\", \"b\": \"7\", \"c\": \"√7\", \"d\": \"√13\"}}","_debug_options_count":4},{"id":88415,"question":"La suite (uₙ) définie par uₙ = 2n + 1 est une suite arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La différence entre deux termes consécutifs est constante : uₙ₊₁ - uₙ = 2(n+1) + 1 - (2n + 1) = 2. Donc c'est une suite arithmétique.","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":88416,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1)\/(x² + 1) lorsque x tend vers +∞ ?","option_a":"0","option_b":"1","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par x², on obtient lim(x→+∞) f(x) = lim(x→+∞) (3 - 2\/x + 1\/x²)\/(1 + 1\/x²) = 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"3\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":88417,"question":"Soit l'équation différentielle y' + 2y = 0. Quelle est la solution générale ?","option_a":"y = Ce^(2x)","option_b":"y = Ce^(-2x)","option_c":"y = Cx²","option_d":"y = C\/x","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"y = Ce^(2x)\", \"b\": \"y = Ce^(-2x)\", \"c\": \"y = Cx²\", \"d\": \"y = C\/x","_debug_options_count":4}]