Quiz — ex 7.pdf

Question 1 sur 10 20:00

[{"id":125438,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. -∞","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d'un polynôme à l'infini est déterminée par le terme de plus haut degré. Ici, (3x²)\/(x²) = 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. 3\", \"b\": \"B. 0\", \"c\": \"C. -∞\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":125439,"question":"La fonction f(x) = x³ - 3x² + 2 est croissante sur l'intervalle [0 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x s'annule en x=0 et x=2. Elle est négative sur ]0 ; 2[, donc la fonction est décroissante sur cet intervalle.","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":125440,"question":"Quel est le résultat de la somme des angles intérieurs d'un polygone convexe à 7 côtés ?","option_a":"A. 540°","option_b":"B. 720°","option_c":"C. 900°","option_d":"D. 1080°","option_e":"","option_f":"","bonne_reponse":"d","explication":"La somme des angles intérieurs d'un polygone à n côtés est (n-2)×180°. Pour n=7, (7-2)×180° = 900°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"A. 540°\", \"b\": \"B. 720°\", \"c\": \"C. 900°\", \"d\": \"D. 1080°\"}}","_debug_options_count":4},{"id":125441,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = -1\/2. Quelle est la valeur de u₃ ?","option_a":"A. -1\/4","option_b":"B. 1\/4","option_c":"C. -1\/2","option_d":"D. 1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"u₃ = u₀ × q³ = 2 × (-1\/2)³ = 2 × (-1\/8) = -1\/4. Attention à la valeur absolue !","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\/4\", \"b\": \"B. 1\/4\", \"c\": \"C. -1\/2\", \"d\": \"D. 1\/2\"}}","_debug_options_count":4},{"id":125442,"question":"L'équation x² + 4x + 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 = 16 - 20 = -4 \u003C 0. Il n'y a donc 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":125443,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 1) ?","option_a":"A. 3\/(3x + 1)","option_b":"B. 1\/(3x + 1)","option_c":"C. 3x\/(3x + 1)","option_d":"D. 1\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x + 1, donc u' = 3. Ainsi, f'(x) = 3\/(3x + 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\": \"A. 3\/(3x + 1)\", \"b\": \"B. 1\/(3x + 1)\", \"c\": \"C. 3x\/(3x + 1)\", \"d\":","_debug_options_count":4},{"id":125444,"question":"Dans un repère orthonormé, quelle est la distance entre les points A(2 ; -3) et B(-1 ; 4) ?","option_a":"A. √74","option_b":"B. √58","option_c":"C. √45","option_d":"D. √37","option_e":"","option_f":"","bonne_reponse":"a","explication":"La distance AB = √[(xB - xA)² + (yB - yA)²] = √[(-1-2)² + (4-(-3))²] = √[9 + 49] = √58.","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. √74\", \"b\": \"B. √58\", \"c\": \"C. √45\", \"d\": \"D. √37\"}}","_debug_options_count":4},{"id":125445,"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, eˣ \u003E 0. C'est une propriété fondamentale de la fonction exponentielle.","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":125446,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² - 4x + 3 au point d'abscisse x = 1 ?","option_a":"A. -2","option_b":"B. 0","option_c":"C. 2","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur de la tangente est f'(1). f'(x) = 2x - 4, donc f'(1) = 2×1 - 4 = -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. 2\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":125447,"question":"Soit un nombre complexe z = 3 + 4i. Quel est son module ?","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. √13","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module de z = a + bi est √(a² + b²). Ici, |z| = √(3² + 4²) = √(9 + 16) = √25 = 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\": \"A. 5\", \"b\": \"B. 7\", \"c\": \"C. √7\", \"d\": \"D. √13\"}}","_debug_options_count":4}]