高考數(shù)學(xué)（理）二輪專題突破演練（浙江專版）第3部分 專題1 第3講 “4道”保分題專練卷4 Word版含解析

1、“4道”保分題專練卷(四)1在abc中，角a、b、c的對(duì)邊分別為a、b、c，滿足ac2b，且cos(bc).(1)求cos c的值；(2)若a5，求abc的面積解：(1)ac2b，且abc，b.cos(bc)，sin(bc)，cos ccos(bc)bcos(bc)cos bsin(bc)sin b.(2)由(1)可得sin c，sin asin (bc).在abc中，由正弦定理，得c8.sabcacsin b5810.2數(shù)列an的前n項(xiàng)和為sn，a11，an12sn1(nn*)，等差數(shù)列bn滿足b33，b59.(1)分別求數(shù)列an，bn的通項(xiàng)公式；(2)設(shè)cn(nn*)，求證cn1cn.解：

2、(1)由an12sn1，得an2sn11，得an1an2(snsn1)，an13an，an3n1.b5b32d6，d3，bn3n6.(2)證明：an23n1，bn23n，cn，cn1cn0，cn1cnc1，cn1cn.3某社區(qū)為豐富居民的業(yè)余文化生活，準(zhǔn)備舉行一次趣味運(yùn)動(dòng)會(huì)在“射擊氣球”這項(xiàng)比賽中，制定的比賽規(guī)則如下：每人只能參加一場(chǎng)比賽，每場(chǎng)比賽中選手依次射擊編號(hào)為的5個(gè)氣球；在這5次射擊中，若號(hào)氣球都被擊中，且號(hào)氣球至少有1個(gè)被擊中，則此人獲獎(jiǎng)；否則不獲獎(jiǎng)已知甲每次射擊擊中氣球的概率都為，且各次射擊結(jié)果互不影響(1)求甲在比賽中獲獎(jiǎng)的概率；(2)設(shè)甲在5次射擊中擊中氣球的個(gè)數(shù)為隨機(jī)變量，求

3、的分布列及數(shù)學(xué)期望解：(1)記甲在5次射擊中，擊中k次獲獎(jiǎng)的事件為ak，k3,4,5.a3，a4，a5互斥，甲獲獎(jiǎng)的概率pp(a3)p(a4)p(a5)p(a3)c2，p(a4)c2，p(a5)c3，甲在比賽中獲獎(jiǎng)的概率p.(2)隨機(jī)變量的取值可以為0,1,2,3,4,5.p(0)5，p(1)c4，p(2)c23，p(3)c32，p(4)c4，p(5)5.的分布列為012345pe()012345.4.如圖，在四棱錐pabcd中，pd平面abcd，四邊形abcd是菱形，ac2，bd2，e是pb上任意一點(diǎn)(1)求證：acde；(2)已知二面角apbd的余弦值為，若e為pb的中點(diǎn)，求ec與平面pa

4、b所成角的正弦值解：(1)證明：pd平面abcd，ac平面abcd，pdac.四邊形abcd是菱形，bdac.又bdpdd，ac平面pbd.de平面pbd，acde.(2)連接eo，在pdb中，eopd，eo平面abcd.分別以oa，ob，oe所在直線為x，y，z軸建立空間直角坐標(biāo)系，設(shè)pdt(t0)，則a(1,0,0)，b(0，0)，c(1,0,0)，e，p(0，t)由(1)知，平面pbd的一個(gè)法向量為n1(1,0,0)，設(shè)平面pab的一個(gè)法向量為n2(x，y，z)，且(1, ，0)，(1，t)，則根據(jù)得令y1，得平面pab的一個(gè)法向量為n2.二面角apbd的余弦值為，|cosn1，n2|，

5、即，解得t2或t2(舍去)，p(0，2)設(shè)ec與平面pab所成的角為，(1,0，)，n2(，1,1)，sin |cos，n2|，ec與平面pab所成角的正弦值為.高考資源網(wǎng)版權(quán)所有！投稿可聯(lián)系qq：1084591801c29c91afe4ced1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afedd1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af95ad9c91afe4ce

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13、c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad9c91afe4ced15ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29

14、c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad9c91afe4ced195ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced

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16、91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af

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