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重庆市西南大学附属中学
2024届高三年级上学期第二次月考检测
数学试题参考答案
2024年11月
1-8：DDAAC CAD 9. BD 10. ABC 11. BD 12. CD 12解：
设f?x??x?t?x?t 可知f?x?为偶函数 ?x1?x2?x3?0t?t?s ?2t?sf?x?=s,其中必有一解为0，则f?0??
①当0?x?t时,f?x??t?x?t?x?2t?x?t+x?2t,当且仅x?0当时取等2②当x?t时,f?x??t?x?t?x在?t,???递增f?x??s?2t?x?t?x?t?2t?x?t?2又5t4?x?t??x?t??x?t?4t?4x?5t?x?
5564516f?x?在?t,???递增 ?x3?t 即x3=s?t?2t?t?,s?t?4425451664144?s?t??, s?t?52525
13. 12或13 14. 1 15. 22 16.
17. (1) f'?x???3x2?6x?9??3?x?1??x?3?
?f?x?在???,?1?和?3,???上单调递减， 在??1,3?上单调递增
2n?1；
1?(8n?1) 7 1
?f?x?的极大值为f?3???33?3?32?9?3?2?25， f?x?极小值
,
为
f??1??1?3?9?2??7
(2)
f??3?=?33?3?32?3?9?2?25?20 f??2??8?3?4?2?9?2?0?20f?2???8?3?4?9?2?2?20 ?区间①③不符，区间②符合.18. (1) 32?62?AC21在?ABC中,cosB??, ?AC2?32?62?3?6?27 ?AC?332?3?62sin?DACsinDAC3333 (2) ?ACD中,由正弦定理?, ?sinD??sin?DAC??sin30?CDACCD4852?62?BD232?42?BD2在?ABD中,cos?BAD?在?BCD中,cos?BCD?2?5?62?3?4?BAD??BCD?180 ?cos?BAD?cos?BCD?02?25?36?BD2??5?9?16?BD2?52?62?BD232?42?BD2???0??02?5?62?3?4120?2?61?2BD2?5?25?5BD2?0?7BD2?247 则BD?2477??????f?x??sin?x???2?cosx??6?3????1?3??3?sinx?cosx??2?2????2????sin?x???1,33???cos?BAD??35?6?BD?2?5?622225?36?2477?3 19. (1) 607?sinx??cosx?11????2?cosx??sinx??223??33?cosx?sinx22?????3sin?x??3??0?x??,????2?x???,333??3??3??3sin?x???
3?2?
3???f?x?的值域为??3,? (2)
2????sin??acos2??0sin??????acos???2???0关于?有两个不同的解?a?1?2sin???sin??0?2asin2??sin??a?0关于?有两个不同的解
????2设t?sin?,????,??t???1,1??2at?t?a?0在t???1,1?有两个不同的解①当a?0，
?22?不符合题意.②当a?0时，2t2?t?1?0在??1,1?内有两个不同的解令
1a 2
?
?a?R?1?1?1?4a
?0?a??或a?0???a2?8?0?
?4a4???1??1?1?11?1?4a?2???0??a?0或a??a??1或a?1 20. (1) g?t??2t?t?1?4a44aa???
g?1?0????a?1?a??1或a?0
?0??a?a?0或a?1
??g?1??0?
?a?1?0??a
Sn?2an?a1①当
n?2时又
，
a1,a2?1,a3Sn?1?2an?1?a1②①-②:an?2an?2an?1?an?2an?1 ??an?是以公比为2 的等比数列.成等差数列
?2?a2?1??a1?a3?2?2a1?1??a1?4a1 则a1?2 ?an?a1?2n?1?2n(2)
11111Tn?1??3?2?5?3???2n?3??n?1??2n?1??n22222111111Tn?1?2?3?3?5?4???2n?3??n??2n?1??n?1222222111111①-②：Tn??2?2?2?3??2?n??2n?1??n?122222211111??2??n?1??2n?1??n?122222
1?1???1?n?1?12?2?1=???2n?1??n?1
1221?2
111??1?n?1??2n?1??n?122231
??n+1?4?2n?1?22
2n?3
?Tn?3?
2n?
①② 3
2024年11月重庆市西南大学附属中学2024届高三年级上学期第三次月考检测数学参考答案
