高考数学（理）二轮专题突破演练（浙江专版）第3部分 专题1 第3讲 “4道”保分题专练卷4 Word版含解析.doc

《高考数学（理）二轮专题突破演练（浙江专版）第3部分 专题1 第3讲 “4道”保分题专练卷4 Word版含解析.doc》由会员分享，可在线阅读，更多相关《高考数学（理）二轮专题突破演练（浙江专版）第3部分 专题1 第3讲 “4道”保分题专练卷4 Word版含解析.doc（4页珍藏版）》请在三一办公上搜索。

1、“4道”保分题专练卷(四)1在ABC中，角A、B、C的对边分别为a、b、c，满足AC2B，且cos(BC).(1)求cos C的值；(2)若a5，求ABC的面积解：(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数列an的前n项和为Sn，a11，an12Sn1(nN*)，等差数列bn满足b33，b59.(1)分别求数列an，bn的通项公式；(2)设cn(nN*)，求证cn1cn.解：

2、(1)由an12Sn1，得an2Sn11，得an1an2(SnSn1)，an13an，an3n1.b5b32d6，d3，bn3n6.(2)证明：an23n1，bn23n，cn，cn1cn0，cn1cnc1，cn1cn.3某社区为丰富居民的业余文化生活，准备举行一次趣味运动会在“射击气球”这项比赛中，制定的比赛规则如下：每人只能参加一场比赛，每场比赛中选手依次射击编号为的5个气球；在这5次射击中，若号气球都被击中，且号气球至少有1个被击中，则此人获奖；否则不获奖已知甲每次射击击中气球的概率都为，且各次射击结果互不影响(1)求甲在比赛中获奖的概率；(2)设甲在5次射击中击中气球的个数为随机变量，求

3、的分布列及数学期望解：(1)记甲在5次射击中，击中k次获奖的事件为Ak，k3,4,5.A3，A4，A5互斥，甲获奖的概率PP(A3)P(A4)P(A5)P(A3)C2，P(A4)C2，P(A5)C3，甲在比赛中获奖的概率P.(2)随机变量的取值可以为0,1,2,3,4,5.P(0)5，P(1)C4，P(2)C23，P(3)C32，P(4)C4，P(5)5.的分布列为012345P.E()012345.4.如图，在四棱锥PABCD中，PD平面ABCD，四边形ABCD是菱形，AC2，BD2，E是PB上任意一点(1)求证：ACDE；(2)已知二面角APBD的余弦值为，若E为PB的中点，求EC与平面P

4、AB所成角的正弦值解：(1)证明：PD平面ABCD，AC平面ABCD，PDAC.四边形ABCD是菱形，BDAC.又BDPDD，AC平面PBD.DE平面PBD，ACDE.(2)连接EO，在PDB中，EOPD，EO平面ABCD.分别以OA，OB，OE所在直线为x，y，z轴建立空间直角坐标系，设PDt(t0)，则A(1,0,0)，B(0，0)，C(1,0,0)，E，P(0，t)由(1)知，平面PBD的一个法向量为n1(1,0,0)，设平面PAB的一个法向量为n2(x，y，z)，且(1, ，0)，(1，t)，则根据得令y1，得平面PAB的一个法向量为n2.二面角APBD的余弦值为，|cosn1，n2|

5、，即，解得t2或t2(舍去)，P(0，2)设EC与平面PAB所成的角为，(1,0，)，n2(，1,1)，sin |cos，n2|，EC与平面PAB所成角的正弦值为.高考资源网版权所有！投稿可联系QQ：108459180129C91AFE4CED1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFEDD1B6C87D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF95AD9C91AFE4CE

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