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高中数学必修一第一章集合题型总结

2015 年暑假必修一集合

2015-7-19

第一章 第一节 集合题型总结

题型一 集合的表示(列举法、描述法)

1. 下列说法:①集合{x∈N|x3=x}用列举法表示为{-1,0,1};

②实数集可以表示为{x|x 为所有实数}或{R};

③方程组?????xx+ -yy= =-3 1 的解集为{x=1,y=2}.
其中正确的有( ). A.3 个 B.2 个 C.1 个 D.0 个 题型二 集合与集合的关系(子集) 1、已知集合 A={x| x2-x-2<0},B={x|-1<x<1},则

A.A?? B

B. B??A

C. A=B

D.A∩B=?

2.设集合 P ? {x | x ? 1}, Q ? {x | x2 ? x ? 0} ,则下列结论正确的是

A. P ? Q

B. P Q ? R

C. P ? Q

D. Q ? P

3.若全集U ? ?0,1, 2,3?且CU A ? ?2? ,则集合 A 的真子集共有( )个,非空子集有
( )个 题型三 集合的运算 ※有限集:直接算
1、已知集合 A ? {?2, 0, 2}, B ? {x | x2 ? x ? 2 ? 0} ,则 A B ? ( )

?

B. ?2?

C. {0}

D. {?2}

2 . 已 知 全 集 U ? {1,2,3,4,5,6} , 集 合 A ? {1, 2}, B ? {x | 2 ? x ? 4, x ? Z} 则 集 合

CU ( A ? B) 中元素的个数为( )

A1

B2

A.

※ 无限集:借助数轴算

C3

D4

4.已知集合 A ? {x | ?2 ? x ? 3}, B ? {x | x ? ?1或x ? 4}, 那么集合 A ? (CRB) ? ( )
A.{x︱-2≤x<4} B.{x︱x≤3 或 x≥4} C.{x︱-2≤x<-1} D.{-1︱-1≤x≤3}

-1-

2015 年暑假必修一集合
5.已知集合 A ? {x x ? 4 ? 0}, B ? {x ? x2 ? 4x ? 3 ? 0} x?4
(1)求 A∪B,
(2)求 A ? Cu B

2015-7-19

※ .有限集与无限集的混合运算:
1、设集合 M={0,1,2},N=?x | x2 ?3x ? 2≤0?,则 M ? N =( )

A.{1}

B.{2}

C.{0,1}

D.{1,2}

2.(2015 汕头高一统考)已知全集 U=R,A={1,2,3,4,5,6,7},B={x|x≤ 2 },则 A∩CuB=( )

A.{2,3,4,5,6,7}

B.{3,4,5,6,7}

题型四 Venn 图在解题中的应用 例:用集合表示下列阴影

C.{x ? Z | x ? 2}

D.{x | x ? 2}

练习:

2.设全集U ? ?1, 2, 3, 4, 5, 6, 7, 8?,集合 A ? ?1, 2 , 3, 5?, B ? ?2 , 4,6?,则图中的阴影部

分表示的集合为 ( ) A. {2} B.{4,6} C.{1,3,5}

D.{4,6,7,8}

-2-

2015 年暑假必修一集合

2015-7-19

3、设全集 U={1,2,3,4,5},A∩B={2},(?UA)∩B={4},?U(A∪B)={1,5},下列结论正确

的是( )

A.3∈A,3?B

B.3?A,3∈B C.3∈A,3∈B

D.3?A,3?B

4. 全集 U={1,2,3,4,5,6},M={2,3},N={1,4},则集合{5,6}等于( ).

A.M∪N

B.M∩N

C.(?UM)∪(?UN)

题型五 含参问题

※ 有限集(注意检验满不满足互异性)

D.(?UM)∩(?UN)

? ? ? ? 1、已知集合 M ? x | x2 ? 3x ? 2 ? 0 , N ? ?x ? Z | ?1? x ?1? 2?,Q ? 1, a2 ?1, a ?1

(1)求 M N (2) 若 M ? Q ,求实数 a 的值

2.若集合 A={x|x2-2x-3=0},B={x|ax-1=0},且 B A,求实数 a 的值.

※ 无限集(画数轴计算)
1. 设关于 x 的不等式 x(x ? a ?1) ? 0(a ? R) 的解集为 M ,不等式 x2 ? 2x ? 3 ? 0 的解集 为 N .(Ⅰ)当 a ?1时,求集合 M ;(Ⅱ)若 M ? N ,求实数 a 的取值范围.

2、设 A={x|y= x ?1 },B={x|1≤x≤3}, C={x|x>a}

(1)求集合 A∪B,A∩(CRB).

(2) 若B ? C ? B,求a的取值范围

(3) 若B ? C ? ? ,求 a 的取值范围

-3-


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