济源市、平顶山市、许昌市2021-2022学年高三第二次质量检测文科数学试卷（PDF版带答案）

平顶山许昌济源2021-2022学年高三第二次质量检测文科数学参考答案一、选择题：本题共12小题，每小题5分，共60分。1.B2.D3.C4.A5.C6.D7.B8.A9.A10.B11.D12.B二、填空题：本题共4小题，每小题5分，共20分。202213.314.2315.16.(0,2)4045三、解答题：共70分。解答应写出文字说明、证明过程或演算步骤。第17-21题为必考题，每个试题考生都必须作答。第22、23题为选考题，考生根据要求作答。17.（12分）解：（1）因为acosCcsinA由正弦定理得sinAcosCsinCsinA(sinA0)cosCsinC,又0<c<,c···········································4分4（2）因为2sin(b+)=c-23cosa4\2sin(b+c)=4-23cosaabc，\2sina=4-23cosa\sina+3cosa=2\2sin(a+)=23\a+=þa=···········································8分326ac由正弦定理可得，则sinasinc1,14csina2a22···········································10分sinc22117s=acsinb=224sin2+23.········································12分abc221218.（12分）解：（1）由折线图中数据及题中给出的参考数据，72可得t4,tit28，···········································（2分）i17tityiy1267i1所以r0.88，·············（4分）727227273tityiyi1i1即y与t的相关系数近似值为0.88[0.75,1]，所以相关性很强；·············（5分）7259（2）由yi259，得y37，·································（6分）i177tityiyˆ126i1又b74.5，··································（8分）228titi1aˆybˆt374.5419，所以y关于t的回归方程为y4.5t19；·······························（10分）（3）将2022年对应的t8代入回归方程y4.5t19，得y4.581955，所以预测2022年该市某家庭教育支出将达到家庭总支出的5500，因此当某家庭总支出为10万元时，家庭教育支出约为1055005.5万元.......（12分）19.（12分）解：（1）证明：∵dc面abc，bc平面abc∴dcbc∵ab是圆o的直径∴bcac且dcacc∴bc平面acd...........................................................（3分）2,∵四边形dcbe为平行四边形∴bc de="">03x+3&gt;0x+5&gt;0\x&lt;-5或-1</c<,c···········································4分4（2）因为2sin(b+)=c-23cosa4\2sin(b+c)=4-23cosaabc，\2sina=4-23cosa\sina+3cosa=2\2sin(a+)=23\a+=þa=···········································8分326ac由正弦定理可得，则sinasinc1,14csina2a22···········································10分sinc22117s=acsinb=224sin2+23.········································12分abc221218.（12分）解：（1）由折线图中数据及题中给出的参考数据，72可得t4,tit28，···········································（2分）i17tityiy1267i1所以r0.88，·············（4分）727227273tityiyi1i1即y与t的相关系数近似值为0.88[0.75,1]，所以相关性很强；·············（5分）7259（2）由yi259，得y37，·································（6分）i177tityiyˆ126i1又b74.5，··································（8分）228titi1aˆybˆt374.5419，所以y关于t的回归方程为y4.5t19；·······························（10分）（3）将2022年对应的t8代入回归方程y4.5t19，得y4.581955，所以预测2022年该市某家庭教育支出将达到家庭总支出的5500，因此当某家庭总支出为10万元时，家庭教育支出约为1055005.5万元.......（12分）19.（12分）解：（1）证明：∵dc面abc，bc平面abc∴dcbc∵ab是圆o的直径∴bcac且dcacc∴bc平面acd...........................................................（3分）2,∵四边形dcbe为平行四边形∴bc>