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qifa950com:【新课标-精品卷】2018年最新北师大版高中数学必修五模块检测试题及答案解析

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(新课标)2017-2018 学年北师大版高中数学必修五 模块检测 (时间:120 分钟 满分:150 分) 一、选择题(本大题共 10 小题,每小题 5 分,共 50 分) 1 . 已 知 数 列 {an} 的 前 ( ). B.152 C.218 D.279 n 项 和 Sn = n3 , 则 a5 + a6 的 值 为 A.91 解析 a5+a6=S6-S4=63-43=152. 答案 B 2. 在△ABC 中, sin A∶ sin B∶ sin C=4∶ 3∶ 2, 则 cos A 的值是 1 A.- 4 1 B. 4 C.- 2 3 2 D. 3 ( ). 解析 由正弦定理得 a∶ b∶ c=4∶ 3∶ 2,设 a=4k,b=3k,c=2k,则 cos A= 9k2+4k2-16k2 1 =- . 2×3k×2k 4 答案 A 3.在正项等比数列{an}中,a1 和 a19 为方程 x2-10x+16=0 的两根,则 a8·a10·a12 等于 ( ). B.32 C.64 D.256 A.16 解析 ∵{an}是等比数列且由题意得 a1·a19=16=a102(an>0), ∴a8·a10·a12=a103=64. 答案 C 4 . 等 差 数 列 {an} 满 足 a42 + a72 + 2a4a7 = 9 , 则 其 前 10 项 之 和 为 ( ). B.-15 C.15 D.±15 A.-9 解析 a42+a72+2a4a7=(a4+a7)2=9.∴a4+a7=±3, 10?a1+a10? ∴a1+a10=±3,∴S10= =±15. 2 答案 D 5.在坐标平面上,不等式组? ( ). A. 2 3 B. 2 3 2 C. 2 D.2 ? ?y≥x-1, ?y≤-3|x|+1 ? 所表示的平面区域的面积为 解析 |CD|=1+1=2, ?y=x-1, 1 ?y=-3x+1, ∴xA= . 2 ? ?y=x-1, ? ? ?y=3x+1, ? ∴xB=-1, 1 1 1 ∴S△CDA= ×2× = , 2 2 2 S△CDB= ×2×1=1. 3 故所求区域面积为 . 2 答案 B 6 . 如果不 等式 ( ). B.(-∞,3) D.(-∞,+∞) 2x2+2mx+m < 1 对 一 切 实数 x 均成 立, 则实数 m 的 取 值 范 围 是 4x2+6x+3 1 2 A.(1,3) C.(-∞,1)∪(2,+∞) 解析 ?2x2+ 3? 3 ? ∵4x2+6x+3=?2x+ ?2+ >0,∴原不等式?2x2+2mx+m<4x2+6x+3 2? 4 ? (6-2m)x+(3-m)>0,x∈R 恒成立?Δ=(6-2m)2-8(3-m)<0,∴1<m<3. 答案 A 7.△ABC 中,a,b,c 分别是内角 A,B,C 的对边,且 cos 2B+3cos(A+C)+2=0, b ( = ). 3 , 则 c ∶ sin C 等 于 A.3∶ 1 C. 2∶ 1 B. 3∶ 1 D.2∶ 1 解析 cos 2B+3cos(A+C)+2=2cos2B-3cos B+1=0, 1 π ∴cos B= 或 cos B=1(舍).∴B= . 2 3 c b 3 ∴ = = =2. sin C sin B 3 2 答案 D 8.已知各项都为正数的等比数列{an}的公比不为 1,则 an+an+3 与 an+1+an+2 的大小关 系 ( A.an+an+3<an+1+an+2 C.an+an+3>an+1+an+2 解析 因为 an+an+3=an(1+q ), 3 是 ). B.an+an+3=an+1+an+2 D.不确定的,与公比有关 an+1+an+2=an(q+q2), an+an+3-(an+1+an+2)=an(1+q3-q-q2)= an(1-q)(1-q2)=an(1-q)2(1+q)>0. 答案 C 9. 已知公差不为 0 的等差数列的第 4,7,16 项恰好分别是某等比数列的第 4,6,8 项, 则该等 比 ( ). B. 2 C.± 3 D.± 2 数 列 的 公 比 是 A. 3 解析 等差数列记作{an},等比数列记作{bn}, 则 q2= = = 答案 C b8 b6 b8-b6 a16-a7 9d = = =3,∴q=± 3. b6 b4 b6-b4 a7-a4 3d x+3y-3≥0, ? ? 10.若实数 x,y 满足不等式组?2x-y-3≤0, ? ?x-my+1≥0, 于( A.-2 ). B.-1 且 x+y 的最大值为 9,则实数 m 等 C.1 D.2 解析 如图,作出可行域, ?x-my+1=0, ? ? 1+3m , 5 ?, 由? 得 A? ? ?-1+2m -1+2m? ? ?2x-y-3=0, 1+3m 5 平移 y=-x,当其经过点 A 时,x+y 取得最大值,即 + =9,解得 -1+2m -1+2m m= 1. 答案 C 二、填空题(本大题共 5 小题,每小题 5 分,共 25 分) 11.正项等比数列{an}满足 a2a4=1,S3=13,bn=log3an,则数列{bn}的前 10 项和是 ________. 解析 ∵{an}成等比数列,an>0,∴a2a4=a32=1. ∴a3=1,∴a1q2=1.① ∵S3=a1+a2+1=13,∴a1(1+q)+1=13.② 1 由①②得,a1=9,q= ,an=33-n. 3 ∴bn=3-n.∴S10=-25. 答案 -25 12.如图所示,为测一树的高度,在地面上选取 A、B 两 点,从 A、B 两点分别测得树尖的仰角为 30°,45°, 且 A、B 两点之间的距离为 60 m,则树高的高度为 ________. AB PA 60 解析 ∵∠A=30°,∠ABP=45°,∴∠AP

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