内容正文:
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!"#$%&'()*-1
+,-.2020/012312456(
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(
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)
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)
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(
7&8129&,:9&5;,860;.<:9&=>?@ABCD,EFGCHIJ&KLM?.)
! " 1 2 3 4 5 6 7 8 9 10 11 12
# $ A C B C D A C D C B C D
1.A 【-.】NO犕= 狔|狔=
6
狓+3
,狓∈犖,狔∈{ }犖 ,PQR狓=0S,狔=2∈犖;R狓=1S,狔=32犖;R狓=2
S
,狔=
6
5
犖;R狓=3S,狔=1∈犖;R狓≥4S,0<狔<1,∴狔犖.TU 犕= 狔|狔=
6
狓+3
,狓∈犖,狔∈{ }犖 =
1,{ }2 ,VWA#H2A.XBA.
2.C 【-.】狕=i2019(-1-2i)=-i(-1-2i)=-2+i,狕=-2-i,XBC.
3.B 【-.】∵
→
犇犆=
→
犅犇,∴犇 O犅犆 YU?DZ,
→
犃犇=
1
2
(→犃犆+ →犃犅),∴ →犃犇· →犅犆=
1
2
(→犃犆+ →犃犅)·(→犃犆-
→
犃犅)=
1
2
(→犃犆2- →犃犅2)=
1
2
(12-22)=-
3
2
,
XBB.
4.C 【-.】∵
π
3
-( )θ + θ+π( )6 =
π
2
,∴[\]^_`sinθ+
π( )6 =sin
π
2
-
π
3
-( )[ ]θ =cos π3-( )θ =
槡3
3
,
XBC.
5.D 【-.】犪=(槡3)
2
3 =3
1
2
×
2
3 =3
1
3 >3
0=1,a3
1
3 <8
1
3 =23×
1
3 =2.∴1<犪<2.犫=log3e<log33=1,犮=
( )18
-
1
3
=2-3×
-( )13 =2,X犮>犪>犫.BD.
6.A 【-.】[&bc:狓=
12+23+31
3
=22,狔=
15+30+45
3
=30,
defghi7DjZ
(22,30),XF30=22×1.6+^犪,∴^犪=-5.2,
X狔^=1.6狓-5.2,R狓=100S,^狔=154.8≈155.XBA.
7.C 【-.】NOk#:1,3,5,7,9,l#:2,4,6,8,10,PQmk#nl#DopG#F:5×5=25q,rst?
uvwO3?F:(1,4),(3,6),(5,2),(5,8),(7,10),(7,4),(9,6)87q,x犘=
7
25
.XBC.
8.D 【-.】∵犳(狓)=
1+狓4
狓2
+1=
1
狓2
+狓2+1≥2
1
狓2
·狓槡
2 +1=3,RayR
1
狓2
=狓2,z狓=±1S,{|}
~
,∴犪=3.x犵(狓)=sin
1
3
狓+
π( )3 .��#犵(狓)?������
π
2
A����
,
c��#犺(狓)?��,x
犺(狓)=sin
1
3
狓+
π( )2 +
π[ ]3 =sin
1
3
狓+
π( )2 =cos
1
3
狓.
v�ABC,∵犺(-狓)=cos -
1
3( )狓 =cos
1
3
狓=犺(狓),∴�#犺(狓)H��#,ABC��;
v�BBC,∵-π≤狓≤π,∴-
π
3
≤
1
3
狓≤
π
3
,∴�#犺(狓)<[-π,π]U���,BBC��;
!"#$%&'()*-2
v�CBC,∵犺(2π)=cos
2π
3
=-
1
2
≠0,∴�#犺(狓)�����(2π,0)v�,CBC��;
v�DBC,∵犺(3π)=cosπ=-1,∴�#犺(狓)����fg狓=3πv�,DBC��.XBD.
9.C 【-.】�G���:犛=1,�rs��,犻=2;
�����
:犛=3,�rs��,犻=3;
�1���
:犛=6,�rs��,犻=4;
�@���
:犛=10,�rs��,犻=5;
�����
:犛=15,rs��,�>?wO5.
PQ� ¡D?��¢£¤
“犛≥15?”.XBC.
10.B 【-.】¥犉O¦§g狔
2=4狓?¨Z,x犉(1,0),¦§g狔
2=4狓©gª«O狓=-1,N¬犘�®g
犆?U¨Z犉1(0,犮)?¯°±�fg狓=-1?¯°²n{�犘犉1+犘犉,NO犘犉1+犘犉≥犉1犉,PQ犉1犉=
槡22,z 1+犮槡 2 槡=22,∴犮 槡= 7,³
犮
犪
=
槡7
2
,∴犪2=4,犫2=3,z®g?ª«O
狔
2
4
-
狓2
3
=1.XBB.
11.C 【-.】¥狔=犳(狓)=sin狓,狓1=0,狓2=
π
2
,狓3=π,xF狔1=0,狔2=1,狔3=0,
x犽1=
1-0
π
2
-0
=
2
π
,犽=
0-1
π-
π
2
=-
2
π
,犽2=-
4
π
2
,
[犳(狓)≈狔1+