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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 ?

?

=

(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

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