发布时间 : 星期五 文章江苏省南通中学高一数学第一学期期末考试试卷更新完毕开始阅读
江苏省南通中学2008-2009学年度高一数学第一学期期末考
试试卷
一、填空题:本大题共14小题,每小题5分,共计70分.请把答案填写在答题卡相应位置.......上. .
11.cos(?240)= ? .
22.cos13cos17?sin13cos107= 3 . 23.已知tan??3,则2sin2??3sin?cos??4cos2?= 4.已知A(2,1),B(?3,?2),且AM?5.已知直线x?13 . 1024AB,则点M的坐标为 (?,?1 ) . 33πππ是函数y?asin(2x??)?b(|?|?)的一条对称轴,则?= ? . 3266.若向量a?(2,x?1),b?(x?2,6),又a,b的夹角为锐角,则实数x的取值范围 5 为 {x|x??,且x?2} .
47.函数y?log2(2sin2x?3)?9?x2的定义域为 (?5π2π,?)63ππ(,) . 63B中有 1 个元素.
ππ8.若集合A?{(x,y)|y?tanx,x?(?,)},B?{(x,y)|y?x},则A229.国家最近出台的一系列政策已对各地的房地产市场产生了影响,某房地产介绍所对本市一楼群在今年的房价作了统计与预测:发现每个季度的平均单价y(每平方米的价格,单位为元)与第x季度之间近似满足:y?500sin(?x??)?4500(??0),已知第一、二季度平均单价如下表所示,则此楼群在第三季度的平均单价大约是 4000 元.
x y 10.已知?ABC中,sinA?1 5000 2 4500 3 ? 3813,cosB?,则cosC= . 517855π17π ] . )?5sin(x?),其中x?R,则该函数的值域为 [?7,736362π12.若非零向量a,b满足(a?3b)?(2a?b),(a?b)?b,则向量a,b的夹角为 .
311.已知函数y?3sin(x?13.已知f(x)是偶函数,且当0?x?π时f(x)?sinxf(x)? sin .
2x,又f(x?2π)?f(x),则当π?x?2π时,214.下列四个命题:
(1)在四边形ABCD中,若|AB?AC|?|AB?AC|,则四边形ABCD是矩形; (2)已知角?的终边经过点(?3a,4a)(a?0),则sin??4; 5(3)在?ABC中,tanAtanB?1,则?ABC的形状一定为钝角三角形; (4)sin(???)≤sin??sin?.
其中正确的有 (3) (请填写相应的序号).
二、解答题:本大题共6小题,共计90分.请在答题卡指定区域内作答,解答时应写出文字.......说明、证明过程或演算步骤. 15.已知0???π35???π,且cos??,sin(???)??,求sin?,cos?,tan?的值. 2135ππ3π································2分???π∴?????222 35 ∵cos??,sin(???)??13 5解:∵0???
∴sin??412,cos(???)??········································4分513
∴ sin??sin[(???)??]?sin(???)cos??cos(???)sin?··············6分
5312433···································10分????(?)??· 13513565
∴ cos???5633········································14分 ,tan???.
6556注:若先求解cos?可参照上述过程给分. 16.已知函数f(x)?sin2x?3cos2x.求: (1)函数f(x)的单调增区间; (2)函数f(x)的最小正周期;
(3)函数f(x)的图象由函数y?sinx的图象经过怎样的变化可以得到.
解:f(x)?sin2x?3cos2x?2(sin2x(1)2kπ? ∴kπ?13π?cos2x)?2sin(2x?)·············4分 223πππ···········································6分 ?2x??2kπ?,
2325ππ··············································7分 ?x?kπ?·
12125ππ····················8分 ,kπ?](k?Z)·
1212 即函数f(x)的单调增区间为[kπ?(2)函数f(x)的最小正周期为π·········································10分 (3)方法一:将函数y?sinx的图象向左平移
π个单位长度,再将图象上每一个点的横3坐标变为原来的
1倍(纵坐标不变),再将图象上每一个点的纵坐标变为原来的2倍(横2坐标不变);························································14分
方法二:将函数y?sinx的图象上每一个点的横坐标变为原来的再将图象向左平移
1倍(纵坐标不变),2π个单位长度,再将图象上每一个点的纵坐标变为原来的2倍(横坐6标不变).·······················································14分
17.已知向量a?(cos?,sin?)(??R),b?(?3,?1),求|a?2b|的最值及取得最值时?的取值集合.
解:a?(cos?,sin?),b?(?3,?1)
2222····································4分 |a?2b|?(a?2b)?a?4ab?4b
?1?4?(?3cos??sin?)?4?4 ?17?8(sin?13?cos?) 22π ?17?8sin(??)·············································7分
3ππ 当sin(??)?1即??2kπ?,k?Z时,|a?2b|有最大值为25?5········11分
36π5π 当sin(??)??1即??2kπ?,k?Z时,|a?2b|有最小值为9?3·······15分
36C118.在?ABC中,AM?MB,AN?AC,已知BN与CM交于点P, 3设AB?a,AC?b,用向量a,b表示向量AP.
解:AP?AN?NP?AN??NB?AN??(AB?AN) ?(1??)AN??AB?NPAMB1??································4分 AC??AB·
3 又AP?AC?CP?AC??CM?AC??(AM?AC)