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2016-2017学年贵州省遵义四中高一(上)期末数学试卷(解析版)

2016-2017 学年贵州省遵义四中高一(上)期末数学试卷 一.选择题(本大题共 12 小题,每小题 5 分,在每题给的四个选项中,只有一项 是符合题目要求的) 1. (5.00 分)设全集 I={0,2,4,6,8,10},集合 M={4,8},则?IM=( A.{4,8} B.{0,2,4,10} C.{0,2,10} D.{0,2,6,10} 2. (5.00 分)sin750°=( A. B.﹣ C.﹣ ) D. ) 3. (5.00 分)设 f(x)=3x+3x﹣8,用二分法求方程 3x+3x﹣8=0 在 x∈(1,2) 内近似解的过程中得 f(1)<0,f(1.5)>0,f(1.25)<0,f(2)>0 则方程 的根应落在区间( ) C. (1.5,2) D.不能确定 ) A. (1,1.25) B. (1.25,1.5) 4. (5.00 分)设 a=0.7 ,b=0.8 ,c=log30.7,则( A.c<b<a B.c<a<b C.a<b<c D.b<a<c 5. (5.00 分)已知 f(x)为奇函数,当 x>0,f(x)=x(1+x) ,那么 x<0,f(x) 等于( ) C.﹣x(1+x) D.x(1+x) ) A.﹣x(1﹣x) B.x(1﹣x) 6. (5.00 分)已知向量 =(﹣2,1) , =(1,x) ,若 ⊥ ,则 x=( A.1 B.2 C.3 D.4 且 7. (5.00 分)已知角 ( A.﹣ ) B. C. ,则 cosθ﹣sinθ 的值为 D.± )的图象 8. (5.00 分)要得到函数 y=sin2x 的图象,只需将函数 y=sin(2x﹣ ( ) 个单位长度 B.向左平移 个单位长度 D.向左平移 个单位长度 个单位长度 A.向右平移 C.向右平移 9. (5.00 分)已知函数 y=Asin(ωx+φ) (A>0,ω>0,|φ|<π)的一段图象如 图所示,则函数的解析式为( ) A.y=2sin(2x﹣ B.y=2sin(2x﹣ C.y=2sin(2x+ D.y=2sin(2x﹣ ) )或 y=2sin(2x+ ) ) 内的图象是 ) 10 . ( 5.00 分)函数 y=tanx+sinx﹣|tanx﹣ sinx|在区间 ( ) A. B. C . D. 11. (5.00 分)若 f(sinθ)=3﹣cos2θ,则 f(cos2θ)等于( A.3﹣sin2θ B.3﹣cos4θ C.3+cos4θ D.3+cos2θ 且 m≠1)在(0, )内恒成立, ) C. ( ,1) D.[ ,1) ) 12. (5.00 分)若不等式 求实数 m 的取值范围( A. (0, ) B.[ ,1) 二.填空题(本题共 4 道小题,每小题 5 分,共 20 分) 13. (5.00 分) 已知向量 = (﹣1, 2) ,= (1, ﹣2y) , 若 ∥ , 则 y 的值是 14. (5.00 分)设函数 f(x)=cos +f(2017)= . . ,则 f(1)+f(2)+f(3)+…+f(2016) 15. (5.00 分)设 f(x)=asin(πx+α)+bcos(πx+β)+3,其中 a,b,α,β 均为 非零实数,若 f(2016)=6,则 f (2017)= . 16. (5.00 分)欲使函数 y=Asinωx(A>0,ω>0)在闭区间[0,1]上至少出现 25 个最小值,则 ω 的最小值为 . 三.解答题(共 70 分,要求要有必要的文字说明和解题过程) 17. (10.00 分)已知 tanθ=3,求 2sin2θ﹣3sinθcosθ﹣4cos2θ 的值. 18. (12.00 分)已知 (1)求 与 的夹角 θ; (2)求 . 19. (12.00 分)已知向量 =(cosα,sinα) , =(cosβ,sinβ) ,0<α<β<π. (Ⅰ)若| ﹣ |= ,求证 ⊥ ; (Ⅱ)设 =(0,1) ,若 + = ,求 α,β 的值. 20. (12.00 分)已知函数 f(x)=4cosxsin(x+ (1)求 f(x)的最小正周期; (2)求 f(x)在区间[﹣ , ]上的最大值和最小值. )﹣1. 21. (12.00 分)已知常数 a、b 满足 a>1>b>0,若 f(x)=lg(ax﹣bx) ,x∈ (0,+∞) (1)证明 y=f(x)在(0,+∞)内是增函数; (2)若 f(x)恰在(1,+∞)内取正值,且 f(2)=lg2,求 a、b 的值. 22. (12.00 分)是否存在实数 a,使函数 f(x)=cos2x+2asinx+3a﹣1 在闭区间上 的最大值为 4,若存在,则求出对应的 a 值;若不存在,请说明理由. 2016-2017 学年贵州省遵义四中高一(上)期末数学试卷 参考答案与试题解析 一.选择题(本大题共 12 小题,每小题 5 分,在每题给的四个选项中,只有一项 是符合题目要求的) 1. (5.00 分)设全集 I={0,2,4,6,8,10},集合 M={4,8},则?IM=( A.{4,8} B.{0,2,4,10} C.{0,2,10} D.{0,2,6,10} 【解答】解:∵全集 I={0,2,4,6,8,10},集合 M={4,8},则?IM={0,2, 6,10}, 故选:D. ) 2. (5.00 分)sin750°=( A. B.﹣ C.﹣ ) D. 【解答】解:sin750° =sin(2×360°+30°) =sin30° = . 故选:A. 3. (5.00 分)设 f(x)=3x+3x﹣8,用二分法求方程 3x+3x﹣8=0 在 x∈(1,2) 内近似解的过程中得 f(1)<0,f(1.5)>0,f(1.25)<0,f(2)>0 则方程 的根应落在区间( ) C. (1.5,2) D.不能确定 A. (1

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