全国高考2008-2017年文科数学历年试题分类汇编
省固镇县第二中学
The second middle school in anhui province guzhen 2015全国高考文科数学历年试题
分类汇编
年级组:高一年级
学科: 数学
姓名:徐严
时间:2017年4月10日
全国高考文科数学历年试题分类汇编
(一)小题分类
1.集合
(2015卷1)已知集合{32,},{6,8,10,12,14}A x x n n N B ==+∈=,则集合A B 中的元素个数为( )
(A ) 5 (B )4 (C )3 (D )2
(2015卷2)已知集合A={}{}=<<=<<-B A x x B x x 则,30,21
A.(-1,3)
B.(-1,0 )
C.(0,2)
D.(2,3)
(2014卷1)已知集合{}{}12|,31|≤≤-=≤≤-=x x B x x M ,则M
B =( )
A. )1,2(-
B. )1,1(-
C. )3,1(
D. )3,2(-
(2014卷2)已知集合A=﹛-2,0,2﹜,B=﹛x |2x -x -20=﹜,则A B ?=( ) (A) ? (B ){}2 (C ){}0 (D) {}2-
(2013卷1)已知集合{1,2,3,4}A =,2{|,}B x x n n A ==∈,则A B =( )
(A ){0} (B ){-1,,0} (C ){0,1} (D ){-1,,0,1} (2013卷2)已知集合M ={x |-3<x <1},N ={-3,-2,-1,0,1},则M ∩N =( ).
A .{-2,-1,0,1}
B .{-3,-2,-1,0}
C .{-2,-1,0}
D .{-3,-2,-1}
(2012卷1)已知集合A={x |x 2-x -2<0},B={x |-1 (A )A B (B )B A (C )A=B (D )A ∩B= (2012卷2)☆已知集合{|A x x =是平行四边形},{|B x x =是矩形}, {|C x x =是正方形},{|D x x =是菱形},则 (A )A B ? (B )C B ? (C )D C ? (D )A D ? (2011卷1)已知集合M={0,1,2,3,4},N={1,3,5},P=M N ,则P 的子集共有 A .2个 B .4个 C .6个 D .8个 (2010卷1)已知集合A ={x ||x |≤2,x ∈R},B ={x |x ≤4,x ∈Z},则A ∩B =( ) A .(0,2) B .[0,2] C .{0,2} D .{0,1,2} (2009卷1)已知集合}{{}1,3,5,7,9,0,3,6,9,12A B ==,则A B = A .{3,5} B .{3,6} C .{3,7} D .{3,9} (2008卷1)已知集合M ={ x|(x + 2)(x -1) < 0 },N ={ x| x + 1 < 0 },则M ∩N =( ) A. (-1,1) B. (-2,1) C. (-2,-1) D. (1,2) (2016卷1)设集合{1,3,5,7}A =,{|25}B x x =≤≤,则A B = (A ){1,3}(B ){3,5}(C ){5,7}(D ){1,7} (2016卷2)已知集合{1 23}A =,,,2{|9}B x x =<,则A B = (A ){210123}--,,,,, (B ){21012}--,,,, (C ){123},, (D ){12}, (2017卷1)已知集合A ={}|2x x <,B ={}|320x x ->,则 A .A ∩ B =3|2x x ????? B .A ∩B =? C .A B 3|2x x ? ? =??? D .A B=R (2017II 卷1).设集合{}{}123234A B ==,,, ,,, 则=A B A. {}123,4,, B. {}123,, C. {}234,, D. {}134,, 2.复数 (2015卷1)已知复数z 满足(1)1z i i -=+,则z =( ) (A ) 2i -- (B )2i -+ (C )2i - (D )2i + (2015卷2)若a 实数,且=+=++a i i ai 则,312( ) A.-4 B. -3 C. 3 D. 4 (2014卷1)设i i z ++=11,则=||z ( ) A. 2 1 B. 2 2 C. 2 3 D. 2 (2014卷2) 131i i +=-( ) (A )12i + (B )12i -+ (C )1-2i (D) 1-2i - (2013卷1)212(1) i i +=-( ) (A )112i -- (B )112i -+ (C )112i + (D )112 i - (2013卷2)21i +=( ). A . B .2 C D ..1 (2012卷1)复数z =-3+i 2+i 的共轭复数是 (A )2+i (B )2-i (C )-1+i (D )-1-i (2011卷1)复数512i i =-( ) A .2i - B .12i - C . 2i -+ D .12i -+ (2010卷1)已知复数z =3+i 1-3i 2,z 是z 的共轭复数,则z ·z =( ) A.1 4 B.1 2 C .1 D .2 (2009卷1)复数3223i i +=- A .1 B .1- C .i (D)i - (2008卷1)已知复数1z i =-,则2 1z z =-( ) A. 2 B. -2 C. 2i D. -2i (2016卷1)设(12i)(i)a ++的实部与虚部相等,其中a 为实数,则a= (A )-3(B )-2(C )2(D )3 (2016卷2)设复数z 满足i 3i z +=-,则z = (A )12i -+(B )12i -(C )32i +(D )32i - (2017II 卷2)(1+i )(2+i )= A.1-i B. 1+3i C. 3+i D.3+3i (2017卷3)下列各式的运算结果为纯虚数的是 A .i(1+i)2 B .i 2(1-i) C .(1+i)2 D .i(1+i) 3.向量 (2015卷1)已知点(0,1),(3,2)A B ,向量(4,3)AC =--,则向量BC = ( ) (A ) (7,4)-- (B )(7,4) (C )(1,4)- (D )(1,4) (2015卷2)已知向量=?+-=-=a b a b a )则(2),2,1(),1,0(( ) A. -1 B. 0 C. 1 D. 2 (2014卷1)设F E D ,,分别为ABC ?的三边AB CA BC ,,的中点,则=+FC EB ( ) A. B. 21 C. 21 D. (2014卷2)设向量a ,b 满足106a b ( ) (A )1 (B ) 2 (C )3 (D) 5 (2017卷2)设非零向量a ,b 满足+=-b b a a 则 A a ⊥b B. =b a C. a ∥ b D. >b a (2013卷1)已知两个单位向量a ,b 的夹角为60,(1)=+-c ta t b ,若0?=b c ,则t =_____。 (2013卷2)已知正方形ABCD 的边长为2,E 为CD 的中点,则AE BD ?=__________. (2012卷1)已知向量a ,b 夹角为45° ,且|a |=1,|2a -b |=10,则|b |= (2012卷2)☆ABC ?中,AB 边的高为CD ,若CB a =,CA b =,0a b ?=,||1a =,||2b =,则AD = (A )113 3a b - (B )2233a b - (C )3355a b - (D )4455a b - (2011卷1)已知a 与b 为两个不共线的单位向量,k 为实数,若向量a+b 与向量ka-b 垂直,则k=_____________. (2009卷1)已知()()3,2,1,0=-=-a b ,向量λ+a b 与2-a b 垂直,则实数λ的值为( ) A .17- B .17 C .16 - D .16 (2008卷1)已知平面向量a =(1,-3),b =(4,-2),a b λ+与a 垂直,则λ是( ) A. -1 B. 1 C. -2 D. 2 (2016卷1)设向量a =(x ,x +1),b =(1,2),且a ⊥b ,则x =. (2016卷2)已知向量a =(m ,4),b =(3,-2),且a ∥b ,则m =___________. (2017卷1)已知向量a =(–1,2),b =(m ,1).若向量a +b 与a 垂直,则m =______________. 4.框图 (2015卷1)执行右面的程序框图,如果输入的0.01t =,则输出的n =( ) (A ) 5 (B )6 (C )7 (D )8 (2015卷2)右边程序框图的算法思路来源于我国古代数学名著《九章算术》中的“更相减损术”。执行该程序框图,若输入的a,b分别为14,18,则输出的a为 A. 0 B. 2 C. 4 D.14 (2014卷1)执行右面的程序框图,若输入的,, a b k分别为1,2,3,则输出的M=( ) A.20 3 B. 7 2 C. 16 5 D. 15 8