数学文

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数学（文科）评分标准第 1 页共

7 页

绵阳市高中 2021 级第三次诊断性考试

文科数学参考答案及评分意见

一、选择题：本大题共 12 小题，每小题 5分，共 60 分．

CDACC ACCBD CA

二、填空题：本大题共 4小题，每小题 5分，共 20 分．

13．2 14．

15．

16．

三、解答题：本大题共 6小题，共 70 分．

17．解：（1）①当时，，则．·······························1 分

② 当时，由，得，·····························2 分

两式相减，得，······················································3 分

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

∴数列是以为首项，为公比的等比数列，························5 分

∴．·········································································6 分

（2）由（1）得，·····························8 分

可知数列是以为首项，4为公比的等比数列，···························9 分

∴·····································································10 分

··········································································11 分

．（也可不计算到此步）····································12 分

18．解：（1）调试前，电池的平均放电时间为：

2.5×0.02×5+7.5×0.06×5+12.5×0.08×5+17.5×0.04×5=11 小时，······················4 分

调试后的合格率为：0.1×5+0.06×5=0.8，则，······················5 分

∴a=48；····················································································6 分

数学（文科）评分标准第 2 页共

7 页

（2）由列联表可计算，·················10 分

∴有 95%的把握认为参数调试能够改变产品合格率．··························12 分

19．解：（1）∵E是BP 的中点，AB=AP，

∴AE⊥PB，················································································1 分

又平面 PAB∩平面 PBC=PB，且平面 PAB⊥平面 PBC，

∴AE⊥平面 PBC，·······································································2 分

过D作DF⊥PC 交PC 于F，

∵平面 PCD⊥平面 PBC，且平面 PCD∩平面 PBC=PC，

∴DF⊥平面 PBC，·······································································4 分

∴AE∥DF，················································································5 分

又DF 平面 PCD，AE 平面 PCD，

∴AE∥平面 PCD；·······································································6 分

（2）∵AD∥BC

∴VC-PBD=VD-PBC=VA-PBC=VC-PAB，

∴VC-PBD=VC-PAB=S△ABP·d，······························································8 分

又∵平面 PBC⊥平面 PAB，过 C作CH⊥PB 交PB 于H，

∴CH⊥平面 PAB，········································································9 分

在直角△CHB 中：，····················10 分

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

∴当sin∠BAP=1 时，体积的最大值为．·······································12 分

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摘要：

数学（文科）评分标准第1页共7页绵阳市高中2021级第三次诊断性考试文科数学参考答案及评分意见一、选择题：本大题共12小题，每小题5分，共60分．CDACCACCBDCA二、填空题：本大题共4小题，每小题5分，共20分．13．214．15．16．三、解答题：本大题共6小题，共70分．17．解：（1）①当时，，则．·······························1分②当时，由，得，·····························2分两式相减，得，······················································3分∴，即，····...

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