海南省海口市2019年高三高考调研测试数学（理）试卷PDF版含答案.pdf

书书书 【２０１９!"#$%&'()*+,*-·.&/0　1 １　　　　 2（3４2）45】 ·１９－０１－２３９Ｃ· ２０１９!"#$%&'()* +,*-.&/0（12） １．Ｄ　狕＝１－２ｉ １＋ｉ＝－１－３ｉ ２ ＝－１ ２－３ ２ｉ． ２．Ｂ　∵犃＝｛狓｜－２≤狓≤２，!狓≠０｝，∴犃∩犅＝｛狓｜－１＜狓≤２，!狓≠０｝． ３．Ｄ　"#$%&'(、)(、*(+,%&-./012345678，9:%&;． ４．Ｂ　"犪２＝１，犫２＝８，?犪＝１，犮＝３，@｜犕犉１｜＋｜犉１犉２｜－｜犕犉２｜＝｜犕犉１｜－｜犕犉２｜＋｜犉１犉２｜＝－２犪＋２犮＝４． ５．Ａ　∵狓（狓－５）＝（狓＋１０）２，∴狓＝－４，狓＋１０＝６，AB狇＝－３ ２，∴犪狀＝－４×（－３ ２）狀－１． ６．Ｄ　∵ｓｉｎ４０°＜１＜ｌｏｇ３４，ｌｎ０．４＜０＜ｔａｎ２２６°，ｃｏｓ（－２０°）＝ｃｏｓ２０°＝ｓｉｎ７０°＞ｓｉｎ６５°，∴CD Ａ，Ｂ，Ｃ， ｔａｎ４１０°＝ｔａｎ５０°＞１＞ｓｉｎ８０°＞１ ２＞ｌｏｇ５２，9EＤ． ７．Ｃ　FGHI&J（KL），HMNOP狕＝狓＋２狔QRS ２，（ ）３ T，狕U?VWX，!VWXY８． ８．Ｃ　（３槡２＋狓）５ /Z[\)]^Y4_^/`YＣ２ ５（３槡２）３狓２，狓５，9ab]^cdY２０＋１＝２１． ９．Ａ　efSY（狓０，犽狓０－２），∵狔′＝３ 狓，∴ ３ 狓０ ＝犽①， 犽狓０－２＝１＋３ｌｎ狓０② 烅 烄 烆 ， "①?犽狓０＝３，gh②?１＋３ｌｎ狓０＝１， @狓０＝１，犽＝３． １０．Ｂ　"犪１＝２，犪２ ３＝犪１犪７，b?犱＝１，HM犪狀＝狀＋１，ai １ 犪狀犪狀＋１ ＝ １ 狀＋１－ １ 狀＋２，jkl`mnH?犛２０１９＝（１ ２ －１ ３）＋（１ ３－１ ４）＋（１ ４－１ ５）＋…＋（１ ２０２０－ １ ２０２１）＝１ ２－ １ ２０２１＝２０１９ ４０４２． １１．Ｂ　"o0K、p0KM$qrstuY２!vwxY１ ２×２×（１＋４）＝５/yz{，|sxY１０ ３．}+z~ /sxY８，9sxBY５ １２． １２．Ａ　" 狔＝２狓＋犿 狓２ ５＋狔２烅 烄 烆 ＝１ ，?２１狓２＋２０犿狓＋５犿２－５＝０． e犃（狓１，狔１），犅（狓２，狔２），@狓１＋狓２＝－２０犿 ２１ ，狓１狓２＝５犿２－５ ２１ ， ｜犃犅｜＝ １＋２槡 ２ （狓１＋狓２）２－４狓１狓槡 ２ ＝槡５ ２０（２１－犿２槡 ） ２１ ＝１０ ２１－犿槡 ２ ２１ ． }犗 OP犃犅 /€犱＝｜犿｜ 槡５ ， @△犃犗犅 /wx犛＝１ ２犱·｜犃犅｜＝槡５ 犿２（２１－犿２槡 ） ２１ ≤ 槡５×犿２＋２１－犿２ ２ ２１ ＝槡５ ２， N!‚N犿２＝２１－犿２，ƒ犿２＝２１ ２T，△犃犗犅 /wxU?V6X． „T，｜犃犅｜＝１０ ２１－犿槡 ２ ２１ ＝ 槡５ ４２ ２１ ． １３．８　"６ 犪 ×ｃｏｓ６０°＝２４，? 犪 ＝８． １４．π　…†‡H?犵（狓）＝ｓｉｎ（２狓－π ６），9犜＝２π ２＝π．【２０１９!"#$%&'()*+,*-·.&/0　1 ２　　　　 2（3４2）45】 ·１９－０１－２３９Ｃ· １５．（０，１ ２）　∵犳（狓）＞１＋ｌｏｇ２犪，∴１＋ｌｏｇ２犪＜０，@０＜犪＜１ ２． １６．槡３０ ３０ 　ˆM犗犃，犗犅，犗犆‰‰ŠO，@４π×１２＋１２＋犿４ ４ ＝６π，@犿２＝２，‹Œ →犃犅＝（２，０，－１），@ｃｏｓ〈→犃犅， →犗犇〉＝ １ 槡５×６ ＝ 槡３０ ３０ ． １７．：（１）∵ｔａｎ犆 槡＝ ３５，∴ｃｏｓ犆＝１ ６， ３;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ∴ｃｏｓ２犆＝２×（１ ６）２－１＝－１７ １８． ５;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （２）e△犃犅犆/犃，犅，犆/‘’;“Y犪，犫，犮． ∵３ｓｉｎ犃＝２ｓｉｎ犅，∴３犪＝２犫， ６;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ∵犃犆－犅犆＝犫－犪＝１，∴犪＝２，犫＝３． ８;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ "”•–_H?犮２＝犪２＋犫２－２犪犫ｃｏｓ犆＝１３－２＝１１， １０;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ @犮 槡＝ １１，△犃犅犆/—˜Y 槡５＋ １１． １２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ １８．（１）™š：›K，œ犃犆１，犅犆１． １;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ž+z~犃犅犆－犃１犅１犆１ )，犈 Y犃犆１ /)S． ２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ }ŸY犉 Y犃犅 /)S， ai犈犉∥犅犆１． ３;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ }犈犉 w犅犆犆１犅１，犅犆１ w犅犆犆１犅１， ai犈犉∥ w犅犆犆１犅１． ５;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （２）：i犃１ Y¡S¢£›Ka¤/¥¦O§¨]犃１－狓狔狕， ６;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ !! " #! $! % $ & ' ( ) * @犃（０，０，６），犅１（０，４，０），犈（２，０，３），犉（０，２，６）， ７;ŽŽŽŽŽŽŽ ai犅１→ 犉＝（０，－２，６），→犃犈＝（２，０，－３），→犃犉＝（０，２，０）． ８;ŽŽŽ e w犃犈犉 /©ª«Y狀＝（狓，狔，狕）， @ 狀· →犃犈＝２狓－３狕＝０ 狀· →犃犉＝２狔｛ ＝０ ， ９;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ¬狓＝３，?狀＝（３，０，２）． １０;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ 犅１犉 ®   w 犃犈犉 a ¯  Yθ，@ ｓｉｎθ＝ ｃｏｓ〈犅１→ 犉，狀〉 ＝ 犅１→ 犉·狀 犅１→ 犉 狀 ＝ 槡３ １３０ ６５ ． １２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ １９．：（１）"°±;²O³KHM´µ¶·犡∈［２６，３０）/¸±Y（０．０７５＋０．０２５）×２＝１ ５． ２;ŽŽŽŽŽ “ž¹º４»)，¼½4２»´µ¶·犡∈［２６，３０）”Y¾¿犃， @犘（犃）＝１－犘（珡犃）＝１－［Ｃ１ ４×１ ５×（４ ５）３＋Ｃ０ ４×（４ ５）４］＝１１３ ６２５． ５;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （２）犃 ÀÁ/ÀÂîÄÅÃcdY犢（Æ·：Ç）． ①ÈÉk³ÊË，@犢 /;²ÌY 犢 ０ ５００００ ３０００００ 犘 ０．７８ ０．２ ０．０２ ６;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ 犈犢＝０×０．７８＋５００００×０．２＋３０００００×０．０２＝１６０００（Ç）． ８;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ②ÈÉk³ÊÍ，@犢 /;²ÌY 犢 ８０００ ３０８０００ 犘 ０．９８ ０．０２ ９;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ【２０１９!"#$%&'()*+,*-·.&/0　1 ３　　　　 2（3４2）45】 ·１９－０１－２３９Ｃ· 犈犢＝８０００×０．９８＋３０８０００×０．０２＝１４０００（Ç）． １０;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ③ÈÉk³Ê+：犈犢＝２００００（Ç）． １１;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ŸY１４０００＜１６０００＜２００００，ai犃 ÀÁÎÉk³ÊÍ． １２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ２０．（１）™š：Ï狔＝犽狓＋３gh狓２＝６狔，?狓２－６犽狓－１８＝０． ２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ e 犕（狓１，狔１），犖（狓２，狔２），@狓１狓２＝－１８， ４;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ‹Œ犱１犱２＝｜狓１｜·｜狓２｜＝｜狓１狓２｜＝１８Y–X． ６;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （２）：ОÑ҆‡/S，™š›Ó： e犘（０，犫）YÑ҆‡/S，OP犘犕，犘犖 /Ô±;“Y犽１，犽２． ‹Œ犽１＋犽２＝狔１－犫 狓１ ＋狔２－犫 狓２ ７;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ＝２犽狓１狓２＋（３－犫）（狓１＋狓２） 狓１狓２ ８;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ＝－３６犽＋６犽（３－犫） 狓１狓２ ． ９;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ N犫＝－３T，4犽１＋犽２＝０，@OP犘犕 /ÕԐ®OP犘犖 /ÕԐÖ×， １１;ŽŽŽŽŽŽŽŽŽŽ 9∠犗犘犕＝∠犗犘犖，aiS犘（０，－３）Ñ҆‡． １２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ２１．（１）™š：ŸY狓∈（０，＋∞），犳（狓）＝ｅ狓（ｌｎ狓＋１），ai犳′（狓）＝ｅ狓（ｌｎ狓＋１ 狓＋１）（狓＞０）． １;ŽŽŽŽŽ ¬犵（狓）＝ｌｎ狓＋１ 狓＋１（狓＞０），@犵′（狓）＝１ 狓－１ 狓２ ＝狓－１ 狓２ （狓＞０）． ２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ N０＜狓＜１T，犵′（狓）＜０；N狓＞１T，犵′（狓）＞０， @犵（狓）ž&¦（０，１）ØÆÙÚÛ，ž&¦（１，＋∞）ØÆÙÚÜ． ４;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ 9犵（狓）ｍｉｎ＝犵（１）＝２＞０， ５;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ‹Œ犳′（狓）＞０ž（０，＋∞）Øݯ£， ƒ犳（狓）ž（０，＋∞）ØÆÙÚÜ． ６;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （２）：（©Ë）N狓∈［１，＋∞）T，Þß\犿犳（狓） ｅ３狓 － １ 狓 ≤０ݯ£ßà#N狓∈［１，＋∞）T，Þß\ 犿（ｌｎ狓＋１） ｅ２狓 －１ 狓≤０ݯ£，ƒN狓∈［１，＋∞）T，犿（ｌｎ狓＋１） ｅ狓 －ｅ狓 狓 ≤０ݯ£． ７;ŽŽŽŽŽŽŽŽŽ 犺（狓）＝ｌｎ狓＋１ ｅ狓 ，φ（狓）＝－ｅ狓 狓 ，@犺′（狓）＝ １ 狓－１－ｌｎ狓 ｅ狓 ，φ′（狓）＝ｅ狓（１－狓） 狓２ ． ８;ŽŽŽŽŽŽŽŽŽŽ ŸYN狓≥１T，１ 狓－１－ｌｎ狓≤０，ai犺′（狓）≤０ž［１，＋∞）ݯ£， ƒ犺（狓）ž［１，＋∞）ØÆÙÚÛ． ９;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ŸYN狓≥１T，１－狓≤０，aiφ′（狓）≤０ž［１，＋∞）ݯ£， ƒφ（狓）ž［１，＋∞）ØÆÙÚÛ． １０;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ 犘（狓）＝犿犺（狓）＋φ（狓），ŸY犿＞０，ai犘（狓）ž［１，＋∞）ØÆÙÚÛ，ai犘（狓）ｍａｘ＝犘（１）＝犿 ｅ－ｅ． １１; Ž ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ŸY犿（ｌｎ狓＋１） ｅ狓 －ｅ狓 狓 ≤０ž［１，＋∞）Øݯ£，ai犿 ｅ－ｅ≤０，ƒ犿≤ｅ２． }犿＞０，9犿 /UXáâY（０，ｅ２］． １２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （©Í）"†‡H?犿·狓（１＋ｌｎ狓） ｅ２狓 ≤１‘狓∈［１，＋∞）ݯ£． ７;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ e犺（狓）＝犿·狓（１＋ｌｎ狓） ｅ２狓 （狓≥１），犺′（狓）＝犿·２－２狓＋（１－２狓）ｌｎ狓 ｅ２狓 ， ８;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ŸY狓≥１，ai２－２狓≤０，（１－２狓）ｌｎ狓≤０， ９;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ }犿＞０，ai犺′（狓）≤０‘狓∈［１，＋∞）ݯ£， １０;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ【２０１９!"#$%&'()*+,*-·.&/0　1 ４　　　　 2（3４2）45】 ·１９－０１－２３９Ｃ· @犺（狓）ž［１，＋∞）ØÆÙÚÛ，‹Œ犺（狓）ｍａｘ＝犺（１）＝犿 ｅ２ ≤１， @犿≤ｅ２，}犿＞０， 9犿∈（０，ｅ２］． １２;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ２２．：（１）" 狓＝３＋２ｃｏｓθ， 狔＝２ｓｉｎ｛ θ （θYã^），?（狓－３）２＋狔２＝４，ƒ狓２＋狔２－６狓＋５＝０． ３;ŽŽŽŽŽŽŽŽŽ 9犆/䧨³ÂYρ２－６ρｃｏｓθ＋５＝０． ５;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （２）e犃（ρ１，α），犅（ρ２，α）． ŸYρ２－６ρｃｏｓα＋５＝０，OP犾/䧨³ÂYθ＝α（ρ∈犚）， ６;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ aiρ１＋ρ２＝６ｃｏｓα，ρ１ρ２＝５． ７;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ŸY犽≥０，aiｃｏｓα＞０，@ρ１＞０，ρ２＞０， ８;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ @ １ ｜犗犃｜＋ １ ｜犗犅｜＝１ ρ１ ＋１ ρ２ ＝ρ１＋ρ２ ρ１ρ２ ＝６ｃｏｓα ５ ． ９;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ Nｃｏｓα＝１T， １ ｜犗犃｜＋ １ ｜犗犅｜U?V6X，!V6XY６ ５． １０;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ２３．：（１）犳（狓）＝｜狓＋２｜＋２｜狓－１｜＝ －３狓，狓≤－２ －狓＋４，－２＜狓≤１ ３狓，狓＞ 烅 烄 烆 １ ． ３;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ @犳（狓）ž（－∞，１）ØÆÙÚÛ，ž（１，＋∞）ØÆÙÚÜ， ４;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ai犳（狓）ｍｉｎ＝犳（１）＝３． ５;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （２）（©Ë）犵（狓）＝犳（狓）＋狓－犪＝ －２狓－犪，狓≤－２ ４－犪，－２＜狓≤１ ４狓－犪，狓＞ 烅 烄 烆 １ ． ６;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ¬－２狓－犪＝０，@狓＝－犪 ２；¬４狓－犪＝０，@狓＝犪 ４． ８;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ŸYÞß\犳（狓）＋狓－犪＜０/åY（犿，狀），ai犪 ４－（－犪 ２）＝６， ９;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽ 9犪＝８． １０;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ （©Í）"†‡HM犳（狓）＜－狓＋犪 ‘狓∈（犿，狀）ݯ£， ６;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ¬－狓＋犪＝３狓，?狓＝犪 ４， ７;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ ¬－狓＋犪＝－３狓，?狓＝－犪 ２， ８;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ @犪 ４－（－犪 ２）＝６， ９;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ 9犪＝８． １０;ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ