福建省德化一中、永安一中、漳平一中三校协作2022-2023学年高三上学期12月联考数学试题参考答案(定稿)16k版

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三校联考高三数学试题参考答案 1 共 7 页
“德化一中、永安一中、漳平一中”三校协作
2022—2023 学年第一学期联考
高三数学试题参考答案
一、选择题:本题共 8 小题,每小题 5 分,共 40 分.在每小题给出的四个选项中,只
一项是符合题目要求的.
1.D 2.B 3.C 4.D 5.C 6.B 7.A 8.D
二、选择题:本题共 4 小题,每小题 5 分,共 20 分.在每小题给出的选项中,有多项符
合题目要求。全部选对的得 5 分,有选错的得 0 分,部分选对的得 2 分.
9.ABC 10.AD 11.AD 12.BD
三、填空题:本题共 4 小题,每小题 5 分,共 20 分.
13.
2 1y x 
14.6 15.
2 2
2 6
,0 { }
e e
 
16.
43
5
四、解答题:本题共 6 小题,共 70 分.解答应写出文字说明,证明过程或演算步骤.
17.解:(Ⅰ)∵向量
2acb)与向量
cosCcosB)共线,
∴(2accosBbcosC0········································································2
(2sin sin ) cos sin cosA C B B C 
2sinAcosBsinB+C)=sinA
sinA0,∴cosB
··············································································· 4
B0,∴B
·············································································· 5
(Ⅱ)由已知
1 3 3 3
sin
2 4 4
ABC
S ac B ac
 
,所以
3ac
································6
由余弦定理得
2 2 2 cos 3
3
a c ac
 
,所以
2 2 6a c 
······································7
解得
3a c 
························································································ 9
又因为 B
所以
为正三角形.·························································10
三校联考高三数学试题参考答案 2 共 7 页
18.解:(Ⅰ)当时,,所以··········································1
因为①,所以当时,  ②,······················2
-②得,所以 ········································3
所以 
 
 
 ····························································· 5
所以 是首项为 2,公比为 2的等比数列,
所以,所以······················································· 6
(Ⅱ)由(Ⅰ)知,,所以··················· 7
的公差为,则  ,所以····································8
所以  ····································································· 9
所以  
设数列 的前项和为
所以

-④得
  
   
所以  ······································································ 10
又因为数列 的前项和等于 
································ 11
所以 的前项和为
n
T
 
.···································· 12
19.(Ⅰ)证明:AD // BCBC=
1
2
ADQAD 的中点,
∴四边形 BCDQ 为平行四边形,∴CD // BQ······················································2
∵∠ADC=90° ,∴∠AQB=9,即 QBAD
又∵平面 PAD⊥平面 ABCD,平面 PAD∩平面 ABCD=AD
BQ⊥平PAD
BQ
平面 MQB∴平面 MQB⊥平面 PAD ···············································5
三校联考高三数学试题参考答案 3 共 7 页
(Ⅱ)解:∵PA=PDQAD 的中点,∴PQAD
∵平面 PAD⊥平面 ABCD,且平面 PAD∩平面 ABCD=AD,∴PQ⊥平面 ABCD··· 6
Q
(0, 0, 0)Q
(1,0,0)A
(0,0, 3)P
(0, 3,0)B
( 1, 3,0)C
PM PC
 
,且
0 1
 
,得
( , 3 , 3 3 )M
 
 
所以
( , 3 , 3 3 )QM
 
 
(0, 3, 0)QB
··········································· 7
设平面 MBQ 法向量为
( , , )m x y z
0
0
m QM
m QB
 
 
 
 
,得
3 ( 3 3 ) 0
3 0
x y z
y
 
 
3x
,则
1
( 3, 0, )m
··································································8
由题意知平面 BQC 的一个法向量为
(0, 0,1)n
·············································· 9
∵二面M-BQ-C 60° ,∴
2
1
| |
| | 1
cos 60 2
1
3 ( )
n m
n m
 
 
 
解得
1
2
····························································································· 11
1 3 3
( , , )
2 2 2
QM  
,∴
| |QM
7
2
.·························································· 12
20.解:(Ⅰ)由题意可知
π
3
COE
 
则扇形
COE
的面积为
 
2
1
1 π 2 3 2π 6
2 3
S
 
 
 
 
 
·····································3
//OC AB
,则
AFO FOC
 
,且
2
tan
AF
············································4
∴梯形
OCBF
的面积为
2
1 2 2
4 3 2 4 3
2 tan tan
S
 
   
··································6
1 2
2
4 3 6 tan
S S S
 
3
tan 3
OA
ABO AB
 
,∴
π
6
ABO 
摘要:

三校联考高三数学试题参考答案第1页共7页“德化一中、永安一中、漳平一中”三校协作2022—2023学年第一学期联考高三数学试题参考答案一、选择题:本题共8小题,每小题5分,共40分.在每小题给出的四个选项中,只有一项是符合题目要求的.1.D2.B3.C4.D5.C6.B7.A8.D二、选择题:本题共4小题,每小题5分,共20分.在每小题给出的选项中,有多项符合题目要求。全部选对的得5分,有选错的得0分,部分选对的得2分.9.ABC10.AD11.AD12.BD三、填空题:本题共4小题,每小题5分,共20分.13.21yx14.615.2226,0{}ee16.435四、解答...

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福建省德化一中、永安一中、漳平一中三校协作2022-2023学年高三上学期12月联考数学试题参考答案(定稿)16k版.pdf

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