一、選擇:
1―5AADBA 6―10DCBCB 11―12DA
二、填空
13.2 14.(1)(3) 15.年高三第三次模擬考試%20數(shù)學(xué)理科.files/image119.gif)
16.4 17.14 18.年高三第三次模擬考試%20數(shù)學(xué)理科.files/image121.gif)
三、解答:
19.解:(1)年高三第三次模擬考試%20數(shù)學(xué)理科.files/image123.gif)
年高三第三次模擬考試%20數(shù)學(xué)理科.files/image125.gif)
(2)年高三第三次模擬考試%20數(shù)學(xué)理科.files/image127.gif)
年高三第三次模擬考試%20數(shù)學(xué)理科.files/image129.gif)
年高三第三次模擬考試%20數(shù)學(xué)理科.files/image131.gif)
20.證明:(1)由三視圖可知,平面
平面ABCD,
設(shè)BC中點(diǎn)為E,連結(jié)AE、PE
年高三第三次模擬考試%20數(shù)學(xué)理科.files/image135.gif)
年高三第三次模擬考試%20數(shù)學(xué)理科.files/image137.gif)
,PB=PC
年高三第三次模擬考試%20數(shù)學(xué)理科.files/image141.gif)
年高三第三次模擬考試%20數(shù)學(xué)理科.files/image143.gif)
年高三第三次模擬考試%20數(shù)學(xué)理科.files/image145.gif)
// //
// 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image149.gif) 四邊形CHFD為平行四邊形,CH//DF 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image153.gif) 又年高三第三次模擬考試%20數(shù)學(xué)理科.files/image155.gif) 平面PBC 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image159.gif) ,DF 平面PAD 平面PAB 21.解:設(shè)年高三第三次模擬考試%20數(shù)學(xué)理科.files/image167.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image169.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image171.gif) 對 成立, 依題有 成立 由于 成立 ① 由于 成立 恒成立 ② 綜上由①、②得年高三第三次模擬考試%20數(shù)學(xué)理科.files/image189.gif) 22.解:設(shè)列車從各站出發(fā)時郵政車廂內(nèi)的郵袋數(shù)構(gòu)成數(shù)列年高三第三次模擬考試%20數(shù)學(xué)理科.files/image191.gif) (1)年高三第三次模擬考試%20數(shù)學(xué)理科.files/image193.gif) 在第k站出發(fā)時,前面放上的郵袋 個 而從第二站起,每站放下的郵袋 個 故年高三第三次模擬考試%20數(shù)學(xué)理科.files/image199.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image201.gif) 即從第k站出發(fā)時,共有郵袋年高三第三次模擬考試%20數(shù)學(xué)理科.files/image203.gif) (2)年高三第三次模擬考試%20數(shù)學(xué)理科.files/image205.gif) 當(dāng)n為偶數(shù)時,年高三第三次模擬考試%20數(shù)學(xué)理科.files/image207.gif) 當(dāng)n為奇數(shù)時,年高三第三次模擬考試%20數(shù)學(xué)理科.files/image209.gif) 23.解:①年高三第三次模擬考試%20數(shù)學(xué)理科.files/image211.gif) 上為增函數(shù) ② 增函數(shù) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image217.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image219.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image221.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image223.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image225.gif) 同理可證年高三第三次模擬考試%20數(shù)學(xué)理科.files/image227.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image229.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image231.gif) 24.解:(1)假設(shè)存在 滿足題意 則年高三第三次模擬考試%20數(shù)學(xué)理科.files/image234.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image236.gif) 均成立 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image240.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image242.gif) 成立 滿足題意 (2)年高三第三次模擬考試%20數(shù)學(xué)理科.files/image248.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image250.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image252.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image254.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image256.gif) 當(dāng)n=1時, 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image258.gif) 成立 假設(shè) 成立 成立 則年高三第三次模擬考試%20數(shù)學(xué)理科.files/image266.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image268.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image270.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image272.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image274.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image276.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image278.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image280.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image282.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image284.gif) 年高三第三次模擬考試%20數(shù)學(xué)理科.files/image286.gif) 即得 成立 綜上,由數(shù)學(xué)歸納法可知年高三第三次模擬考試%20數(shù)學(xué)理科.files/image290.gif)
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