黑龙江省齐齐哈尔市地区学校2022-2023学年联考 高一数学试题答案及评分标

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高 一 数 学 试 卷 答 案
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
D
A
B
D
C
D
A
B
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
答案
AC
ACD
BD
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、
3
32
14、
2
13
15、
]2,1[
16、② ④
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：
cos)tan)(cos(
cos)cos)(sin(
)2cos()tan()cos(
)
2
sin()cos()3sin(
)().1(
f
············································3 分
cos
cos
sin
sin
tan
sin
cos)( f
······················································································································5 分
sin)
2
3
cos().2(
3
1
sin
······················································································································7 分
为第三象限角，
3
22
sin1cos 2
·····························································································9 分
)(
f
的值为
3
22
··························································································································································10 分
18.（12 分）
解：
32 2
)(
mm
xxf
,其中
2 2,m m Z 
当
1m
时
2
)( xxf
···························································································································································1 分
当
0m
时
3
)( xxf
·······························································································································································2 分
当
1m
时
)0(,1)( 0xxxf
·········································································································································3 分
高一数学试卷答案 第 2页（共 4 页）
)(xf
在区间
)0( ，
上单调递增
,1m
或
0m
······························································································4 分
选①时
).1(
)(xf
的解析式为
2
)( xxf
···························································································································6 分
]3,3[,)().2( 2xxxf
易知
2
)( xxf
在
]0,3[
上单调递减，在
]3,0[
上单调递增························································································9 分
当
0x
时，
0)( min xf
······················································································································································10 分
当
3x
时，
9)( max xf
··················································································································································11 分
)(xf
的值域为
]9,0[
···························································································································································12 分
选②时
).1(
)(xf
的解析式为
3
)( xxf
·····························································································································6 分
]3,3[,)().2( 3xxxf
易知
3
)( xxf
在
]3,3[
上是增函数··································································································································9 分
当
3x
时，
27)( min xf
·············································································································································10 分
当
3x
时，
27)( max xf
··················································································································································11 分
)(xf
的值域为
]27,27[
················································································································································12 分
19.（12 分）
解：
b
克糖水中有
a
克糖，则糖的质量与糖水的质量的比为
b
a
···············································································2 分
若再添加
m
克糖，则糖的质量与糖水的质量的比为
mb
ma
·······················································································4 分
根据生活常识可知，加糖后的糖水更甜，所以糖在糖水中占的“比例”就越大，因此
b
a
mb
ma
················5 分
所以这一事实表示为一个不等式是：
)0,0(
mab
b
a
mb
ma
·······································································6 分
证明过程如下：
)(
)(
)(
)()(
mbb
abm
mbb
mbamab
b
a
mb
ma
················································································································8 分
0000 mbmabab
0
)(
)(
mbb
abm
·················································································10 分
0
b
a
mb
ma
b
a
mb
ma
···········································································································································12 分
黑龙江省齐齐哈尔市地区学校2022-2023学年联考 高一数学试题答案及评分标.pdf

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