四川省绵阳市高中2022级第二次诊断性考试数学答案

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高中 2022 级第二次诊断性考试

数学参考答案及评分标准

一、选择题：本题共 8小题，每小题 5分，共 40 分．

1．D 2．A 3．C 4．B 5．D 6．B 7．A 8．C

二、选择题：本大题共 3小题，每小题 6分，共 18 分．在每小题给出的四个选项中，有多项符合题目

要求．全部选对的得 6分，选对但不全的得部分分，有选错的得 0分．

9．BCD 10．BC 11．ABD

三、填空题：本题共 3个小题，每小题 5分，共 15 分．

12．3； 13．； 14．

四、解答题：本题共 5小题，第 15 题13 分，第 16、17 小题 15 分，第 18、19 小题 17 分，共 77 分．解

答应写出文字说明、证明过程或演算步骤．

15．解：（1）∵ ，

由正弦定理得：，···························································2 分

又，则，

∴，····················································································4 分

∴，又 B是三角形内角，··········································································5 分

∴；·······································································································6 分

（2）∵ ，且，

∴，·································································································8 分

∴，························································································9 分

∴，························································································11 分

∴．···································································································13 分

16．解：（1）a=0 时，，，且，·····························2 分

∴，·······························································································4 分

故切线方程为：y−(e+1)=e(x−1)，即 ex−y+1=0；························································6 分

（2）∵ ，，········································································7 分

由1<a<e，存在，使得，即，，·······························9 分

当时，，单调递减；·······················································10 分

当时，，单调递增，·························································11 分

故，··············································12 分

令，，···············································13 分

数学参考答案第 1页（共6页）

∴ 在上单调递减，·············································································14 分

易知，所以．········································································15 分

数学参考答案第 2页（共6页）

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摘要：

高中2022级第二次诊断性考试数学参考答案及评分标准一、选择题：本题共8小题，每小题5分，共40分．1．D2．A3．C4．B5．D6．B7．A8．C二、选择题：本大题共3小题，每小题6分，共18分．在每小题给出的四个选项中，有多项符合题目要求．全部选对的得6分，选对但不全的得部分分，有选错的得0分．9．BCD10．BC11．ABD三、填空题：本题共3个小题，每小题5分，共15分．12．3；13．；14．四、解答题：本题共5小题，第15题13分，第16、17小题15分，第18、19小题17分，共77分．解答应写出文字说明、证明过程或演算步骤．15．解：（1）∵，由正弦定理得：，·········...

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四川省绵阳市高中2022级第二次诊断性考试数学答案

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