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天津市和平区2017-2018学年高一上学期期末考试数学试卷(WORD版)

2017-2018 学年天津市和平区高一(上)期末数学试卷 一、选择题(每小题 4 分,共 40 分) 1.sin A.﹣ 等于( ) D. ,且|α|< D. ) ,则 tanα 等于( ) B.﹣ C. +α)= 2.已知 cos( A.﹣2 B.﹣ C.2 3.已知 cosα= A.﹣ B. ,则 cos2α 的值为( C.﹣ D. 4.要得到函数 y=cos2x 的图象,只需要把函数 A.向左平移 C.向左平移 个单位长度 B.向右平移 个单位长度 D.向右平移 个单位长度 个单位长度 的图象( ) 5.下列函数中,周期为 π,且在(0, A.y=sin(2x+ 6.已知函数 y= A.x=kπ+ (k∈Z) ) B.y=cos(2x+ )上为增函数的是( ) ) ) C.y=cos(x﹣ ) D.y=sin(2x﹣ ) tan ,x≠(2k+1)π(k∈Z) ,若 y=1,则( B.x=2kπ+ (k∈Z) C.x=kπ+ (k∈Z) (k∈Z) D.x=2kπ+ 7.已知平面向量 =(1,﹣2) , =(﹣2,m) ,且 ∥ ,则 3 +2 等于( A. (﹣2,1) B. (1,﹣2) C. (﹣1,2) D. (2,﹣1) 8.若向量 , 满足| |=| |=2, 与 的夹角为 120°,则 ( + )等于( A.1 B.2 C.3 D.6 ) ) 9. E 为 CD 的中点, 如图, 在边长为 2 的菱形 ABCD 中, ∠BAD=60°, 则 ? 等于 ( ) A.1 B.2 C.3 D.4 ) 10.在△ABC 中,若 cosA= ,cosB=﹣ ,则 cosC 的值为( A. B. C. D.﹣ 二、填空题(本大题共 5 小题,每小题 4 分,共 20 分) 11.已知 =﹣ ,则 = . . 12.已知向量 =(2,1) , =(3,4) ,若向量 与向量 λ + 垂直,则 λ 的值为 13.函数 y=1﹣8cosx﹣2sin2x 的最大值是 14.计算 cos ?cos ?cos = . =2 , =λ ﹣ ,且 ? . 15.如图,在△ABC 中,∠BAC=60°,AB=3,AC=2,若 ﹣4,则 λ 的值为 . = 三、解答题(本大题共 5 小题,共 40 分) 16. (6 分)已知向量 与向量 =(1,﹣2)的方向相反,且| |=3 (1)求向量 的坐标; (2)若 =(2,3) ,求( ﹣ )?( ﹣ )的值. . 17. (8 分)若 (1)求 tanα 的值; (2)求 =1. +sinαcosα 的值. 18. (8 分)已知 α,β∈(0, (1)求 sinβ 的值; (2)求 2α+β 的值. ) ,cosα= ,cos(α+β)= . 19. (8 分)已知 =(1, ) , =(2,m) . (1)当 3 ﹣2 与 垂直时,求 m 的值; (2)当 与 的夹角为 120°时,求 m 的值. 20. (10 分)已知函数 f(x)=4cosxsin(x﹣ (1)求 f(x)的最小正周期; (2)f(x)在区间[ , )+1. ]上的最大值与最小值. 19.解: (1)根据题意, =(1, ) , =(2,m) ,则 3 ﹣2 =(﹣1,3 m=0, ﹣2m) , 若 3 ﹣2 与 垂直时,则有(3 ﹣2 )? =﹣1+9﹣2 解可得 m= (2) =(1, ; ) , =(2,m) , 则| |= =2,| |= ,且 ? =2+ m, 又由 与 的夹角为 120°, 则有 cos120°= 变形可得:2+ 解可得 m=﹣2 故 m=﹣2 . m+ , = =0 =﹣ , 20.解: (1)函数 f(x)=4cosxsin(x﹣ =4cosx(sinxcos ﹣cosxsin )+1 )+1 =2 sinxcosx﹣2cos2x+1 = sin2x﹣cos2x =2( sin2x﹣ cos2x) ) , =π; ∈[ , , ], ]; =2sin(2x﹣ 所以 f(x)的最小正周期为 T= (2)x∈[ 当 x∈[ , , ],则 2x﹣ ]时,2x﹣ ∈[ 函数 f(x)=2sin(2x﹣ 同理,x∈[ , )单调递增; ∈[ , ], ]时,2x﹣ 函数 f(x)=2sin(2x﹣ 又 f( )=2sin )单调递减; )=2sin =2,f( )=2sin =﹣1, =2,f( , f(x)在区间[ ]上的最大值是 2,最小值是﹣1.

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