黑龙江齐齐哈尔市2021-2022学年高二上学期期末考试数学答案
高二数学试卷参考答案及评分标准 第 1页(共 4 页)
高二数学试卷参考答案及评分标准
一.单选题:本大题共 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.
题号
1
2
3
4
5
6
7
8
答案
B
C
D
C
A
A
C
D
二.多选题:本大题共 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,部分选对得 2分.
题号
9
10
11
12
答案
AB
AB
ACD
ABD
三.填空题:本大题共 4小题,每小题 5分,共 20 分.把正确答案写在答题卡相应题的横线上.
13、
2
3
14、
48
15、1 16、
2
x
1
2
n
n
(注:第一空 2分;第二空 3分)
四.解答题:共 70 分,解答应写出文字说明、解答过程或演算步骤.
17.(10 分)
解: (1)【解法一】
直线
l
的斜率为
3
2
l
k
··················································································································································1分
ml //
直线
m
的斜率为
3
2
m
k
·························································································································2分
直线
m
的方程为
)2(
3
2
3 xy
······················································································································3分
即
01332 yx
····························································································································································4分
【解法二】
ml //
直线
m
的方程为
032 Cyx
············································································································1分
直线
m
过点
1303322)3,2( CC
························································································3分
直线
m
的方程为
01332 yx
··························································································································4分
(2)易知圆心
)2,1(C
,半径
1r
······························································································································5分
圆心
C
到直线
l
的距离
13
132
13
2
32
|62312|
22
d
······································································7分
13
136
13
4
122|| 22 drAB
··················································································································9分
线段
AB
的长为
13
136
···············································································································································10分
高二数学试卷参考答案及评分标准 第 2页(共 4 页)
18.(12 分)
解:(1)设等差数列
}{ n
a
的公差为
d
109
1293
1023
122
1
1
14
52
da
da
aa
aa
1
1
1
d
a
·····································3 分
nnan 1)1(1
等差数列
}{ n
a
的通项公式为
nan
···········································································5 分
(2)
n
nnb 2
··································································································································································6 分
nn
nnnS 22)1(232221 1321
①·····················································································7 分
1432 22)1(2322212
nn
nnnS
②·····················································································8 分
①-②得:
132 22222
nn
nnS
·······································································································9 分
1
2
21
)21(2
n
n
nnS
············································································································································10 分
数列
}{ n
b
的前
n
项和
22)1( 1 n
nnS
············································································································12 分
19.(12 分)
解:(1)
)
3
cos(sin3
CbBc
,由正弦定理可得:
)
3
cos(sinsinsin3
CBBC
····················1分
CCCBB sin
2
3
cos
2
1
sin30sin0
·····················································································3分
3
3
tan C
··········································································································································································5分
6
0
CC
角
C
的大小为
6
·····················································································································6分
(2)
Cabbac cos2
222
bbc 612 22
·······························································································7分
22222 8233 bcabc
0236128 222 bbbbb
1b
,或
2b
···················9分
①当
1b
时,
7c
2
3
sin
2
1 CabS ABC
·····························································································10分
②当
2b
时,
2c
3sin
2
1 CabS ABC
································································································11分
ABC
的面积为
3
或
2
3
·········································································································································12 分
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