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1、高二数学必修四 第二章 平面向量单元测试题1高二数学必修四 第二章 平面向量单元测试题 一、选择题:(510=50) 1(给出下面四个命题:?;?;?;?AB，BA,0AB，BC,ACAB,AC,BC。其中正确的个数为 ( )(A)1个 (B)2个 (C)3个 0,AB,0(D)4个 2、对于向量，则 ( ) a,(1,2)b,(2,1)(A)? (B)? (C)与的夹角为60? (D)与的夹角为30? abababab,(0,)3、在下面给出的四个函数中，既是区间上的增函数，又是以为周期的偶函数的是 ,2( ) (A) (B) (C) (D) y,cos2xy,sin2xy,|cosx|y,
2、|sinx|、给出向量4=(2,1)，=(3,4)，则向量在向量方向上的投影为 ( ) abab525(A) (B)2 (C) (D)10、 5、函数在一个周期内的图象如右所示，则此函数的解析y,Asin(,x，,)2,y,2sin(2x，)式为( )(A) (B)3,y,2sin(2x，) 3x,y,2sin(,)y,2sin(2x,)(C) (D) 233,abab,1,1,16(向量，且与的夹角为锐角，则的取值范围为 ( ) ，,1,1,1,1A( B( C( D( ,abababab7、当|=|，且与不共线时，+与,的关系为( ) too busy to come over, this
3、 is very responsible. Next to the sanitation department signed removal contracts, in strict accordance with the provisions of the contract. The back street alleys and suburban , to do a good job in environmental health at the same time, do a good job in a timely public facilities maintenance, repair
4、, install, completely solve the piles of garbage, sewage crosscurrent, heidengxiahuo, potholes and other phenomena, do the streets clean, orderly, the convenience of the public life. To some five on the improvement of the urban river construction site. Now our urban river environment really let peop
5、le see not bottom go to, than the works of Lao Shes Longxugou ditch is not strong to where to go. The next step, we should insist on treating the symptoms, the strict implementation of the long river responsibility system, strengthen the river daily cleaning, planting a number of decomposition and g
6、reen vegetation, so that Hanoi no garbage, riverside, no debris, the river no smell. At the same time, it is necessary to focus on the effect a permanent cure, accelerate the rain sewage diversion, to carry out the system of comprehensive remediation, accomplish treat a river, into a piece of landsc
7、ape. The building housing the departments should strengthen the construction site construction supervision, supervise the implementation of construction dust dust measures, the public security traffic police department To A(平行 B(垂直 C(相交但不垂直 D(相等 ,o8、若平面向量与向量,(1，,2)的夹角是180，且,3，则,( ) 5babbA(,3,6) B(3，
8、,6) C(6，,3) D(,6,3) ,9、已知、是夹角为60?的两个单位向量，则=2，与=,3，eabeeee21121,2的夹角是( ) A.30? B.60? C.120? e2D.150? ?2110、如图，点P是?ABC内一点，且AP=AB+AC，则?ABP的面积与?55ABC的面积之比是( ) A、 1:5 B、2:5 C 、1:2 D、 2:1 二.填空题: 11、向量与共线，则, ; ya,(2,3)b,(,4,y),sin，cos1tan,12、已知，则= ; 22sin,3cos,213、函数的值域是 ; y,y,sinx,2sinx?214、已知点A(-2，0)，点B(
9、3，0)，动点P(x,y)满足PA?PB=x,则动点P的轨迹方程为_ ,abc15、设，为任意非0向量，且相互不共线，则下列命题中是真命题的序号为_ ,abccababab(1)(?)?,(?)?=0 (2)|,|,|,|; ,22bcacabcababab (3)( ?)?,(?)?不与垂直 (4)(3+2)(3,2)=9|,4| 三(解答题: bb 16、已知向量=(6，2)，=(,3，k)，问当k为何值时，有:(1)、? ? aabb (2)、? ? (3、与所成角是钝角 , aatoo busy to come over, this is very responsible. Next
10、to the sanitation department signed removal contracts, in strict accordance with the provisions of the contract. The back street alleys and suburban , to do a good job in environmental health at the same time, do a good job in a timely public facilities maintenance, repair, install, completely solve
11、 the piles of garbage, sewage crosscurrent, heidengxiahuo, potholes and other phenomena, do the streets clean, orderly, the convenience of the public life. To some five on the improvement of the urban river construction site. Now our urban river environment really let people see not bottom go to, th
12、an the works of Lao Shes Longxugou ditch is not strong to where to go. The next step, we should insist on treating the symptoms, the strict implementation of the long river responsibility system, strengthen the river daily cleaning, planting a number of decomposition and green vegetation, so that Ha
13、noi no garbage, riverside, no debris, the river no smell. At the same time, it is necessary to focus on the effect a permanent cure, accelerate the rain sewage diversion, to carry out the system of comprehensive remediation, accomplish treat a river, into a piece of landscape. The building housing t
14、he departments should strengthen the construction site construction supervision, supervise the implementation of construction dust dust measures, the public security traffic police department To ,17题、如图，函数y=2sin(x+,),(x?R)(其中0?,?)的图象2与y轴交于点(0，1);?、求,的值;?、设P为图象上的最高点，?M，N是图象与x轴的交点，求PM与PN的夹角。 3,n18(已知向
15、量 (1)求向量; m,(1,1),向量n与向量m的夹角为,且m,n,1.4too busy to come over, this is very responsible. Next to the sanitation department signed removal contracts, in strict accordance with the provisions of the contract. The back street alleys and suburban , to do a good job in environmental health at the same time
16、, do a good job in a timely public facilities maintenance, repair, install, completely solve the piles of garbage, sewage crosscurrent, heidengxiahuo, potholes and other phenomena, do the streets clean, orderly, the convenience of the public life. To some five on the improvement of the urban river c
17、onstruction site. Now our urban river environment really let people see not bottom go to, than the works of Lao Shes Longxugou ditch is not strong to where to go. The next step, we should insist on treating the symptoms, the strict implementation of the long river responsibility system, strengthen t
18、he river daily cleaning, planting a number of decomposition and green vegetation, so that Hanoi no garbage, riverside, no debris, the river no smell. At the same time, it is necessary to focus on the effect a permanent cure, accelerate the rain sewage diversion, to carry out the system of comprehens
19、ive remediation, accomplish treat a river, into a piece of landscape. The building housing the departments should strengthen the construction site construction supervision, supervise the implementation of construction dust dust measures, the public security traffic police department To (2)设向量，其中，若，试
20、求的取x,Rn,a,0|n，b|a,(1,0),向量b,(cosx,sinx)值范围. ,f(x),Asin(x，)(A,0,0,|,)19、已知函数的图象在轴右侧的第一个最大y,2值点和最小值点分别为和( (1)试求的解析式; (2)将(,2),(4,2),y,f(x)f(x)1图象上所有点的横坐标缩短到原来的(纵坐标不变)，然后再将新的图象向轴正方向平x3,移个单位，得到函数的图象(写出函数的解析式，(3)、写出函数y,g(x)y,g(x)y,g(x)3的一个单调递增区间，同时写出它的对称轴方程和对称中心坐标。 too busy to come over, this is very res
21、ponsible. Next to the sanitation department signed removal contracts, in strict accordance with the provisions of the contract. The back street alleys and suburban , to do a good job in environmental health at the same time, do a good job in a timely public facilities maintenance, repair, install, c
22、ompletely solve the piles of garbage, sewage crosscurrent, heidengxiahuo, potholes and other phenomena, do the streets clean, orderly, the convenience of the public life. To some five on the improvement of the urban river construction site. Now our urban river environment really let people see not b
23、ottom go to, than the works of Lao Shes Longxugou ditch is not strong to where to go. The next step, we should insist on treating the symptoms, the strict implementation of the long river responsibility system, strengthen the river daily cleaning, planting a number of decomposition and green vegetat
24、ion, so that Hanoi no garbage, riverside, no debris, the river no smell. At the same time, it is necessary to focus on the effect a permanent cure, accelerate the rain sewage diversion, to carry out the system of comprehensive remediation, accomplish treat a river, into a piece of landscape. The bui
25、lding housing the departments should strengthen the construction site construction supervision, supervise the implementation of construction dust dust measures, the public security traffic police department To 20、(如图，表示电流强度I与时间t的关系式在一个周期内的图象 :?、试I,Asin(,t，,)(A,0,0),根据图象写出的解析式;?、为了使I,Asin(,t，,)1中t在任意
26、一段秒的时内I能同时取最大值|A|和最小值,|A|，那I,Asin(,t，,)100么正整数的最小值为多少, ,ABCDCDMAB21、如图在长方体中，是的中点，是线段上的点，ABaADbN,ab,2,1， ,MABABANCM(1)若是的中点，求证:与共线;(2)在线段上是否,MMCMBD存在点，使得与垂直,若不存在请说明理由，若存在请求出点too busy to come over, this is very responsible. Next to the sanitation department signed removal contracts, in strict accordan
27、ce with the provisions of the contract. The back street alleys and suburban , to do a good job in environmental health at the same time, do a good job in a timely public facilities maintenance, repair, install, completely solve the piles of garbage, sewage crosscurrent, heidengxiahuo, potholes and o
28、ther phenomena, do the streets clean, orderly, the convenience of the public life. To some five on the improvement of the urban river construction site. Now our urban river environment really let people see not bottom go to, than the works of Lao Shes Longxugou ditch is not strong to where to go. Th
29、e next step, we should insist on treating the symptoms, the strict implementation of the long river responsibility system, strengthen the river daily cleaning, planting a number of decomposition and green vegetation, so that Hanoi no garbage, riverside, no debris, the river no smell. At the same tim
30、e, it is necessary to focus on the effect a permanent cure, accelerate the rain sewage diversion, to carry out the system of comprehensive remediation, accomplish treat a river, into a piece of landscape. The building housing the departments should strengthen the construction site construction super
31、vision, supervise the implementation of construction dust dust measures, the public security traffic police department To 的位置; ,ABCD(3)若动点在长方体上运动，试求的最大值及取得最大值时点的位置。 PPAPAB,参考答案: 题次 1 2 3 4 5 6 7 8 9 10 答案 B B D B A D B A C A 2yy,11、, ,6 ;12、 ,3/4 ;13、 ,1,3 ;14、y=x+6 15、(2)(4) 16题解:(1)，k=,1; (2), k=9
32、; (3), k,9, k?,1; ,1517题解:(1)、,=;(2)、夹角的余弦值为 176，,1xy,1,0xx,18(解:(1)令,(,), nxy则或,3,22,0,1yy2,x，ycos,1,4,too busy to come over, this is very responsible. Next to the sanitation department signed removal contracts, in strict accordance with the provisions of the contract. The back street alleys and su
33、burban , to do a good job in environmental health at the same time, do a good job in a timely public facilities maintenance, repair, install, completely solve the piles of garbage, sewage crosscurrent, heidengxiahuo, potholes and other phenomena, do the streets clean, orderly, the convenience of the
34、 public life. To some five on the improvement of the urban river construction site. Now our urban river environment really let people see not bottom go to, than the works of Lao Shes Longxugou ditch is not strong to where to go. The next step, we should insist on treating the symptoms, the strict im
35、plementation of the long river responsibility system, strengthen the river daily cleaning, planting a number of decomposition and green vegetation, so that Hanoi no garbage, riverside, no debris, the river no smell. At the same time, it is necessary to focus on the effect a permanent cure, accelerat
36、e the rain sewage diversion, to carry out the system of comprehensive remediation, accomplish treat a river, into a piece of landscape. The building housing the departments should strengthen the construction site construction supervision, supervise the implementation of construction dust dust measur
37、es, the public security traffic police department To ？a,(1,0),n,a,0？n,(0,1);(2);？n,(,1,0)或n,(0,1)n，b,(cosx,sinx,1)222n，b=cosx，(sinx,1)=;? 1?sinx?1, ?0?2,2sinx2(1,sinx)n，b?2 1T,6,19、(1)由题意可得:? ， A,2，?,，, ;函数图像过(，fxx()2sin(),？3x,2)， ？，,sin()1， ？,，？, ，？f(x),2sin(，);(2)依,26336,g(x),2sin(x,)题意得; 6,120、(1
38、)、图象的解析式为:;(2)、要使t在任意一段秒能取I,300sin(100t，),1003,211得最大值和最小值,必须使得周期T; 即;,200,628.3,100100,由于为正整数,故的最小值为629 ,1121、解:(1)证明:?ANADDNba,，,，CMCBBMba,，, ; ?22,ANCM, ,ABMCMAN ?与共线;(2)解:在线段上存在点，满足条件。设,CMCBBMba,，,，,CMBD; ?与垂直 BMaBDADABba,1,baba,，,0abab,2,1,0BDCM,0? ;即 ? ?;?存在，4,3MPABAM,CMBD满足条件的点，即，使得与垂直。 (3)解:
39、?当在线段上时，2,4PAPABkaak,4APkak,01APAB,设;则:;?的最大值为 ?当在，too busy to come over, this is very responsible. Next to the sanitation department signed removal contracts, in strict accordance with the provisions of the contract. The back street alleys and suburban , to do a good job in environmental health at
40、the same time, do a good job in a timely public facilities maintenance, repair, install, completely solve the piles of garbage, sewage crosscurrent, heidengxiahuo, potholes and other phenomena, do the streets clean, orderly, the convenience of the public life. To some five on the improvement of the
41、urban river construction site. Now our urban river environment really let people see not bottom go to, than the works of Lao Shes Longxugou ditch is not strong to where to go. The next step, we should insist on treating the symptoms, the strict implementation of the long river responsibility system,
42、 strengthen the river daily cleaning, planting a number of decomposition and green vegetation, so that Hanoi no garbage, riverside, no debris, the river no smell. At the same time, it is necessary to focus on the effect a permanent cure, accelerate the rain sewage diversion, to carry out the system
43、of comprehensive remediation, accomplish treat a river, into a piece of landscape. The building housing the departments should strengthen the construction site construction supervision, supervise the implementation of construction dust dust measures, the public security traffic police department To
44、,BC线段上(不含端点)时，设;? ?APakb,，BPkbk,01，,CD?当在线段上时，设 APABakba,，,4PCPkak,01，,; ?的最大值为 ; ?当在线段上APABabkaak,，,414PADAPAB,，,时， 综上得:的最大值是。 4APAB,0APAB,too busy to come over, this is very responsible. Next to the sanitation department signed removal contracts, in strict accordance with the provisions of the con
45、tract. The back street alleys and suburban , to do a good job in environmental health at the same time, do a good job in a timely public facilities maintenance, repair, install, completely solve the piles of garbage, sewage crosscurrent, heidengxiahuo, potholes and other phenomena, do the streets cl
46、ean, orderly, the convenience of the public life. To some five on the improvement of the urban river construction site. Now our urban river environment really let people see not bottom go to, than the works of Lao Shes Longxugou ditch is not strong to where to go. The next step, we should insist on
47、treating the symptoms, the strict implementation of the long river responsibility system, strengthen the river daily cleaning, planting a number of decomposition and green vegetation, so that Hanoi no garbage, riverside, no debris, the river no smell. At the same time, it is necessary to focus on the effect a permanent cure, accelerate the rain sewage diversion, to carry out the system of comprehensive remediation, accomplish treat a river, into a piece of landscape. The building