Maybe you could get a part-time job in the evening.
年高考数学（理科）二轮复习专题能力训练 含答案3-2019最新
整理
一、能力突破训练
1.设有下面四个命题
p1:若复数z满足∈R,则z∈R;
p2:若复数z满足z2∈R,则z∈R; p3:若复数z1,z2满足z1z2∈R,则z1=;
p4:若复数z∈R,则∈R.
其中的真命题为( ) A.p1,p3 B.p1,p4 C.p2,p3
D.p2,p4
2.设a,b是两个非零向量,则下列结论一定成立的为( A.若|a+b|=|a|-|b|,则a⊥b B.若a⊥b,则|a+b|=|a|-|b|
C.若|a+b|=|a|-|b|,则存在实数λ,使得b=λa D.若存在实数λ,使得b=λa,则|a+b|=|a|-|b| 3.(2018全国Ⅲ,理2)(1+i)(2-i)=( ) A.-3-i B.-3+i
C.3-i
D.3+i
talk with her4. sleep well 5. good for sleep
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) Maybe you could get a part-time job in the evening.
4.在复平面内,若复数z的对应点与的对应点关于虚轴对称,则z=( )A.2-i C.2+i
B.-2-i D.-2+i
5.已知向量a=(1,-1),b=(-1,2),则(2a+b)·a=( ) A.-1 C.1
B.0 D.2
6.(2018浙江,4)复数(i为虚数单位)的共轭复数是 ( )A.1+i C.-1+i
B.1-i D.-1-i
( )
7.已知菱形ABCD的边长为a,∠ABC=60°,则= A.-a2 C.a2
B.-a2 D.a2
8.已知非零向量m,n满足4|m|=3|n|,cos
B.-4 D.-
9.如图,已知平面四边形ABCD,AB⊥BC,AB=BC=AD=2,CD=3,AC与BD交于点O,记I1=,I2=,I3=,则( ) A.I1 B.I1 talk with her4. sleep well5. good for sleep 2 / 7 Maybe you could get a part-time job in the evening. 10.(2018全国Ⅲ,理13)已知向量a=(1,2),b=(2,-2),c=(1,λ).若c∥(2a+b),则λ= . 11.在△ABC中,∠A=60°,AB=3,AC=2.若=2=λ(λ∈R),且=-4,则λ的值为 . 12.设a∈R,若复数(1+i)(a+i)在复平面内对应的点位于实轴上,则a= . 13.已知a,b∈R,(a+bi)2=3+4i(i是虚数单位),则a2+b2= ,ab= . 14.设D,E分别是△ABC的边AB,BC上的点,|AD|=|AB|,|BE|=|BC|.若=λ1+λ2(λ1,λ2为实数),则λ1+λ2的值为 . 二、思维提升训练 15.在△ABC中,已知D是AB边上一点,+λ,则实数λ=( )A.- B.- C. D. 16.已知,||=,||=t.若点P是△ABC所在平面内的一点,且,则的最大值等于( )A.13 B.15 C.19 D.21 17.已知两点M(-3,0),N(3,0),点P为坐标平面内一动点,且||·||+=0,则动点P(x,y)到点M(-3,0)的距离d的最小值为( ) A.2 C.4 B.3 D.6 18.已知向量a,b满足|a|=1,|b|=2,则|a+b|+|a-b|的最小值是 ,最大值是 . 19.在任意四边形ABCD中,E,F分别是AD,BC的中点,若=λ+μ,则λ+μ= . talk with her4. sleep well5. good for sleep 3 / 7
年高考数学(理科)二轮复习专题能力训练 含答案3-2019最新整理
