2022-2023学年北京市高二上期末考试数学模拟试卷附答案解析

《2022-2023学年北京市高二上期末考试数学模拟试卷附答案解析》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

2022-2023
ᓅὃᦪᔁ.⌱⚪ᐳ10⚪1.2020•!"#$%ᦪᑡ'()*+ai=-1,“4=8,ᑣ5$6A.32B.-32C.64D.-642.2020•!=>?@AᙢᙳᒴḄFGHIJK”="N@FGO☢Q”,JK8="N@FGR☢Q”Hᑣ4S8ḄᐵUVA.WXB.YWZ[C.YW\[D.Y$3.2020•]^!"#_`/ibax-y-1=0,bax+a+2y+l=0.gᑣhᦪa=A.-1ᡈ1B.0ᡈ1C.-1ᡈ2D.-3ᡈ24.2020•jk!᪥m4#nᦪz=lT1Vqᦪᓫs,ᑣtᑡuviOwḄxA.nᦪzᙠnz☢ᑁZ|Ḅ}~ᙠN▲B.z=-4-2zc.22ḄqViz-4D.=25.2020•!ᙠx-25ḄHḄUᦪVA.5B.-5C.10D.-106.2020•!tᑡ`^=±2V`Ḅx2222A.2_Z_iB.ஹ2__X_=iC.2—=iD.2—=ix=vv4X2427.(2020•jk!᪥m)"#}஻(-2,0),N(2,0),}*+ᩩK|PM|-|PN1=272,ᑣ}PḄ¥¦§¨V()2222A.=1(x>0)B.2__ª=i22222222C.A_-y_=1(x>0)D.^ߟ-^ߟ=14242N1⚓ᐳ26⚓

12218.2015•ᓅ!gᯖ}ᙠx¯Ḅ°ᙊ²_+³´=1Ḅµ¶᳛x³Hᑣ$62m2A.J3B.3C.&D.22339.2020•jk!᪥m᝞½HᙠO§¾HPᙠ`¿8஺ÁHᑣtᑡÂÃOwḄÄᦪᨵI²Ç┵Ḅ¾ÉVÊËÌ2DB\LA\P^3OPS4GᡠᡂḄÑḄÓV[ÕH-].42A.0B.IC.2D.310.2020•jk!᪥mᦪᨵ×ØÙÚÛÜḄ`H`Cbft/3=4x2ßàáV“âãäᴮ`”᝞½ᡠæ.çètᑡ²ÄÂÃbজ`Cᐵ6_`y=xZáÌঝ`CëÚ}ᑮí}ḄîµïðñòIÌঞôᙠÄí}V¶ஹõöVOḄO§÷Hø`CᙠùO§÷!úᑁûõü.ᐸHOwÂÃḄþÿ
A.জঝB.ঝঞC.জঞD.জঝঞ.⚪
ᐳ6⚪II.
2020•ᙠᙶ᪗"Oxyz'()*+4
1,0,0,B
0,2,0,C
0,0,2,D
0,0,1,ᑣ01஺35cᡠᡂḄᜧ.:2⚓ᐳ26⚓

212.
2020•<=“?0᜛=B+33ᙊx2+/-4x-5=0ᨵIJᨵKLMᐳ+”Ḅᐙ⌕ᩩR.2213.
2020•ST᪥V)*W?0CXY-Zl
a>0,b>0Ḅ_ᩩ`a0babzr~22cd(I3eᙊ“=1ᨵMᐳᯖ+.ᑣ?0CḄbcy2123d.14.
2020•ST᪥V?030V=x+6ាᨵ1LMᐳ+(ᑣ6Ḅjkmd.15.
2020•ST᪥Vn᪷pqrᐳᢞᨵ10tuᳫ(pqrḄᳫᦪxyd1,2,3,4,z{t|ᡭẚ_tᳫ(Itᨵᡭẚ☢Ḅᳫ|ᡭr☢Ḅᳫ(ᑣuᳫᡭẚḄᡭᦪ.
ᵨᦪ⊤oooOddAdYO616.
2020•᝞ᦪᑡ23±l=k
dᦪ(ᦪᑡan+lan¢£¤¥¦ᦪᑡ(᝕¢£M¥¦.¨©ᑡnLª«Xজ¬ᦪᑡJ“®=2¯ᑣ°ᦪᑡ¤¥¦ᦪᑡ±anঝᦪᑡ஻•2"¤¥¦ᦪᑡ±ঞᡠᨵḄ¤¥ᦪᑡ¤¥¦ᦪᑡ±টµᙠ¤¦ᦪᑡ¤¥¦ᦪᑡ.ᐸ'ᡠᨵ·¸ª«Ḅ¹Y.K.º»⚪
ᐳ6⚪:3⚓ᐳ26⚓

317.
2020•½¾)*0/¿+
0,3,ÀÁᑡᩩRজஹᩩRঝஹᩩRঞKLᩩR'ÃÄ⌱Æ_LÇd)*(È0/Ḅbc.ᩩRজX0(É¿0AXx+y+l=03g2x-y-4=0ḄË+±ᩩRঝX0/3ᙊ/+f=3Íᑗ±ᩩRঞX0/3ᙶ᪗ÏmᡂḄKÐḄ☢Ñd3.18.
2020•½¾)*+1
1,-2ᙠÓᱥ0f=28
p>0r(¿+/IÖ᳛d2Ḅ03Óᱥ0ḄØ_LË+dB.
IÈpḄkÙÓᱥ0Ḅᯖ+ᙶ᪗±
IIÈÚÛ19.
2020•<=᝞Ý(<☢<☢COE,nßÐN8C஺ßÛd2Ḅ·bÐ(DC=CE,ZDCE=90°,ád஺EḄ'+(+áᙠ0â8Er.
IÈãXDE_L<☢BCF
II¬µᙠ+P,çè<☢CFP3<☢8CFᡠᡂ☢ḄêÚkdë(ÈìḄk.3BE20.
2020•2020íᡃï5GñòóôḄ¯õöí.÷2020íø('ï)óᡂᐰᳫᨬᜧḄ5Gñò.dûᑗüýþÿ
ᓣᦋᗐᵨᡝ▾ᡲᙠᐰᑁ!"#$%ᡠ'
(⚗*+.ᐸ.⚗*+ᑁ/0ᙠ12*34ᢧ⌱.ᩩᐺ9:;<+=>ᙢ5G
B"CD.ᐸ52*34Ḅ5GFᔠHIJ᳛LᓫNOMbpsᦪQ᝞⊤O34:;5GFᔠHIJ᳛ᓫMbpsTUVW:708.92]Uᜧ_3᜜//ᑁb817.13efghi⊙630.34m4⚓ᐳ26⚓

4qUb3r:882.60ᡂtubvw916.02(I){<|5234}~⌱2234ᑖ᪆⌱Ḅ2234“5GFᔠHIJ᳛”tᜧSMMbpsḄᭆ᳛(II)ᵬஹ5G
⃩ᖪᑖ{<|5234}~⌱1234ὃ(ᵬஹḄ⌱)ᵬஹ⃩ᖪាᨵ1⌱Ḅ34“5GFᔠHIJ᳛”ᜧ800MbpsḄᭆ᳛.2221.(2017•3)¡ᙊCOu¤=1(a>b>0)©$/(2,0),¤«¬᳛®.2(I)¡ᙊCḄ¯°(II)±²³y=kx+F¹¡ᙊCºM,N$.½²³x=3|¾ᙠ$P,ÀÁWÂÃ<ÄV0DWÂÃBḄÆ.22.(2020•ÇÈ)ÉÊᦪᑡÌ“"ÎÏÐ"2=4,஺3+஺4=17.(I)ᦪᑡÌÒÎḄ⚗ÓÔ(II)½ᦪᑡÌÕÎÏÐÖ=2,×{জb”+i=2Öঝ2¹+1=ÖঞÖ+1=-6“ÝÞßᩩàá⌱.ßâᦪᑡÌÒ+dÎḄän⚗åT,,,m5⚓ᐳ26⚓

52022-2023_æᓅè4vu|ὃéᦪ_êëéᔁὃᫀ⚪᪆..⌱í⚪Lᐳ10ï⚪ð1.L2020•ÇÈðÉñᦪᑡÌÒÎÏÐai=-1,ò=8,ᑣôÉLðA.32B.-32C.64D.-64ூὃ$௃ÉñᦪᑡḄ⚗ÓÔ.ூ(⚪௃úû⚪¯°üýþᓄ
ᦪᑡᦪᑡ
ᦪ.ூᑖ᪆௃᪷ᦪᑡḄឋᓽ.ூ௃ᦪᑡ஺"!41=-1,04=8,ᑣ0107=042,ᑣ17=-64,ᦑ⌱D.ூ01௃2⚪ὃ56ᦪᑡḄឋ7ὃ56897:;<Ạ⚪.2.>2020?•ABCDEFGHIJᙢᙳᒴḄNO7PQR/="TUJNOV☢XY”,QR8="T[JNO\☢XY”7ᑣX5Ḅᐵ`a>FA.cdB.fcghC.fcjhD.fூὃ0௃cdQRghQR.ூl⚪௃m⚪
nopq
rᓄpq
tᔠ
ᭆ᳛xm
ᦪ.ூᑖ᪆௃᪷⚪y7ᑖ᪆QR/ஹ3Ḅᐵ`7ᓽ|ᫀ.ூ௃᪷⚪y7QR/="TUJNOV☢XY"7QR8="T[JNO\☢XY”7I~QR77AQRᔲgBQRᨵ7fcjhQR7ᦑ⌱C.ூ01௃2⚪ὃ5<2QR7cdஹghQRḄ7:;<Ạ⚪.3.>2020?•CDEFax-y-1=O.bax+>a+2Fy+1-0-/1U27ᑣᦪa=>FA.-1ᡈ1B.0ᡈ1C.-1ᡈ2D.-3ᡈ2ூὃ0௃ḄU¡noḄᚖᐵ`.T6⚓ᐳ26⚓

6ூl⚪௃rᓄpq

ᙊ
ᦪ.ூᑖ᪆௃¦ᑭᵨIᩩᚖ7ᑡᐵ;஺Ḅno7ᓽ.ூ௃ªaᡠa*a+>-1FX>a+2F=0>|a=-1ᡈ2.ᦑ⌱C.ூ01௃2⚪ὃ56Iᩩᚖᐵ`Ḅᵨ7⚪Ḅᐵ®¯°IᩩᚖḄ±ᩩR7ᓽ/”72Ḅnoᑖ²MAix+Biy+Ci=OAi+ᵪa0F,/2A2x+B2y+C2—0>´7ᔊa0F,ᑣ_L/2=4I42+8I82=0.4.>2020?•¶·C᪥¹DEFºᦪ>ia¼ᦪᓫ¾F,ᑣ¿ᑡÀiVÁḄ>FA.ºᦪzᙠºÄ☢ᑁgḄ0ÆᙠT[Ç▲B.z=-4-2ZC.Ê2Ḅ¼Ëa1z-4D,Ì=2ᧇூὃ0௃ºᦪḄ.ூl⚪௃nopqᦪ`Ḅ᡽ᐙкᦪᦪ.ூᑖ᪆௃z=4-2i.ÑÒºᦪzᙠºÄ☢ᑁgḄ0>4,-2FÆᙠTÓÇ▲
ᑖ²Ô[2,Ì7ᵫÖ8×Ø.z-4ூ௃z=>lTF>3i-lF=3i-3i-i+iii=2+4i=2i+4i?=4,2iÜi2g;ºᦪzᙠºÄ☢ᑁgḄ0>4,-2FÆᙠTÓÇ▲7ᦑ4┯Þ
g;8,z=4+2z,ᦑ8┯Þ
g;c,Ê2=2à=á2i_=i-i,ᳮḄ¼Ë1,ᦑcVÁ
z-42i2iz-4g;஺7|zåyj16+4~27^,ᦑ஺┯Þ.ᦑ⌱C.ூ01௃2⚪ὃ5è⚪éᎷḄᑨì7ὃ5ºᦪḄíîyஹᑣ<Ạï7ὃ5T7⚓ᐳ26⚓

7897<Ạ⚪.5.>2020?•ðñCDEFᙠ>x-2F5Ḅóô¡õ7Ḅ`ᦪa>FA.5B.-5C.10D.-10ூὃ0௃[⚗¡ᳮ.ூl⚪௃m⚪
tᔠ
[⚗¡ᳮ
ᦪ.ூᑖ᪆௃ᵫ[⚗óô¡Ḅ÷⚗ø¡7ᓽ|dḄ`ᦪ.ூ௃>X-2F5Ḅóô¡Ḅ÷⚗ag]=c*-r>-2F,,ᡠVḄ`ᦪaCx(-2)=-10.ᦑ⌱D.ூ௃⚪⌕ὃ⚗ᳮḄᵨẠ⚪.6.#2020$•&'()*+,ᑡ./012'=±256780Ḅ9#+222A.;2-<=1B-x2-^-=9xD.y2_^_=iC.y—---=1y4y21ூὃ௃./0ḄឋI.ூJ⚪௃KL⚪MNᓄPQMRᔠTMᙊ┵/0ḄWஹឋIYZ[Mᦪ]^L.ூᑖ᪆௃ᑭᵨ./0ḄZ[bc./0Ḅ780Z[ᑨe⌱⚗Ḅfgᓽi.22ூcj௃c*2-l=1Ḅ780Z[62-^-=0-ᓽm=±Tᡠ2/fp;x44;2_᧡=1Ḅ780Z[6>=tuᡠ28wfpMc21y2zᑶ=]Ḅ780Z[6y^±lx,ᡠ2CwfpMy2_/=1Ḅ780Z[6y=±ᗟXᡠ2஺wfpMᦑ⌱A.ூ௃⚪ὃ./0ḄᓫឋIḄᵨ9Ạ⚪.7.#2020$•(᪥)*+ᦈ#-2,0+,N#2,0+,ᩩ|PM|-|PN|=2M.ᑣḄZ[6#+2222A.=1#x>0+B.2_l=122228⚓ᐳ26⚓

82222c.^ߟ-2—=1(x>0)D.xy1424~Tூὃ௃Z[.ூJ⚪௃NᓄPQMWTMᙊ┵/0ḄWஹឋIYZ[Mᦪ]^L.ூᑖ᪆௃᪷ᩩᔠ./0ḄWiḄ92"N6ᯖḄ./0Ḅ¢£ᓽibc.ூcj௃cᵫ⚪¥iḄ92N6ᯖḄ./0Ḅ¢£•:
M-2,0+,N#2,0+,Pᩩ|PM|-|PN|=2M.c=2,a=V2>**"b=Vc2-a2=72-#V2+2=V2>22PḄZ[6#x>0+.22ᦑ⌱A.ூ௃⚪⌕ὃ./0ḄWẠ⚪.2218.#2015•ᓅ(¯°+±ᯖᙠx³´Ḅµᙊ¶/2_=1Ḅ·¸᳛9ºᑣ»¼#+2m2A.JIB.3C.&D.2233ூὃ௃µᙊḄឋI.ூJ⚪௃KL⚪Mᦪ]^L.ூᑖ᪆௃ᐜ᪷µᙊḄ᪗ÄZ[ba,b,c,ÅᔠµᙊḄ·¸᳛ÆᑡÇᐵÉḄZ[cÊᓽjᫀ.ூcj௃cᵫ⚪¥ᑣa=V2»c=V^,ᓄuᑗ=1.5,ᦑ⌱B.ூ௃⚪ὃµᙊḄឋIYᐸឋIḄᵨÏ¥᪷µᙊḄ᪗ÄZ[ba,b,c,ÐÑ᪷⚪¥ஹᔠᨵᐵឋIᓄஹNᓄஹKLᨬuᑮÕ.9.#2020$•(᪥)*+᝞×ᙠfZØN8CD-m81cg11ᙠ0Ú8஺´^9⚓ᐳ26⚓

9ᑣ,ᑡÕ1fpḄÛᦪᨵ()(1)ÜÝ┵P-4Þ஺1ḄØß6àM(2)DBi±A\P1(3)஺YᡠᡂḄâḄä6[Ü2L].42A.0B.1C.2D.3ூὃ௃ç☢é0êᐸᡠᡂḄâ.ூJ⚪௃NᓄPQMNᓄTMëìâMíîïᳮMéðQñ.ூᑖ᪆௃(1)ᵫV=V_DiÐòᑨeBAA1111(2)óD8i_Lô☢ZiSCi,ᓽiÐòᑨe;(3)ᵫ஺Y8஺ᡠᡂḄâᓽ6ᡠbÅᙠ¼÷øOBCi1Ðòᑖ᪆ᓽi.ூcj௃c(1)ᵫfZØḄឋIBC\//AD\,ô☢441஺,ô☢4415,...8஺஻ô☢441ûüPᙠ0Ú8஺´^•'Vp-,=v_,9àᓽপ
;AADiBAAD/(2)ᵫᚖᳮDB\1.A\B,DB\1.BC\,"A\BC\BC\=B,48ஹ8Ciu☢/iBCi.•.D8i_L☢43Ci,!"#$=☢ᵫ8Ci.DB\LA\P,ᓽ(2)
'(3),BC\//AD\,:.DP(BC\ᡠᡂḄ,ᓽ-DP(AD\ᡠᡂḄ,ᙠ/0103஺4஺#(4஺ᡠᡂḄ,Ḅ568-[:2L],ᓽ(3)┯=.32>10⚓ᐳ26⚓

10.•.
ḄᨵB1DB2D.ᦑ⌱!C.ூHI௃K⚪ὃNOP4(☢ḄQRᐵTஹU☢VḄᜳ,/XYZ[☢\ᡈᚖVḄᑨᳮ(ឋ`ᳮabᑭᵨeḄfghU☢VḄᜳ,ij⚪ḄᐵkὃNlmḄnᓄfgஹOPpqrstuvᳮwxyz4᫏⚪.10.B2020|•}~᪥Dᦪl4ᨵḄC!B/+/D3=4x-“ᴮB᝞ᡠD.ᑡ!জCᐵzVy=x¢'ঝC¤¥¦Hᑮ¨HḄ©ª«¬®1'ঞ°ᙠ¦a¨H-4±ஹ0²-&Ḅ´µ¶Cᙠ·´µ¸ᑁBº0»D.ᐸ4
Ḅ½¾iBDA.জঝB.ঝঞC.জঞD.জঝঞூὃH௃À⚪ḄÁᎷᑨÃ(Äᵨ.ூÅ⚪௃nᓄfg'ᦪµᔠÇ'V(ᙊ'ᦪlÉÊ.ூᑖ᪆௃¢zজᵨবxDÎᣚ´Ð4ḄBx,yD,´ÐµÑ¬ÒᓽÓj¢zঝÔHPBx,yDi¤¥¦HᑣB/+VD3=4x2f,ᑣHPᑮ¨HḄ©ª->11⚓ᐳ26⚓

11ÙᔠÚK¬/ÑḄÛÑᓽÓj¢zঞᵫঝᒹºÝḄa¨H-ᙊ±Ḅᨬ"ḄᙊḄßà-1,ᡠaᨬ"ᙊÄÝiᒹºÝḄᨬ"´µḄᑁᑗᙊᓽÓâ´µḄ0²ᨬã-2,ᓽÓj.ூjä௃j!¢zজᵨ3,x)Îᣚ´Ð4Ḅ(x,y),´ÐµÑ¬ÒᡠaCᐵzVy=x¢ᦑজ
¢zঝÔHP(x,y)i¤¥¦Hå!](x2+j^)3=4x2y2,ᑣHPᑮ¨HḄ©ª-Jx2+y2,2,2,______ᵫ(xZ+y3)3=4ᔬì4><('Jï,jâð2+ñ24],ᦑঝ
¢zঞᵫঝᒹºÝḄa¨H-ᙊ±Ḅᨬ"ḄᙊḄßà-1,ᡠaᨬ"ᙊÄÝiᒹºÝḄᨬ"´µḄᑁᑗᙊᓽ´µḄ0²ᨬã-2,ᦑঞ┯=.ᦑ⌱!A.ூHI௃K⚪ò⌕ὃNÀ⚪ḄÁᎷᑨÃ(Äᵨ◤⌕lmõöḄ÷ᔠwxyz4᫏⚪.ø.ùO⚪(ᐳ6"⚪)11.(2020|•ûü)ᙠOPV,ᙶ᪗TOxyz/(1,0,0),B(0,2,0),C(0,0,2),D(0,0,1),ᑣ4DBCᡠᡂḄᜧ.60°.ூὃ௃!☢#ᐸᡠᡂḄ.ூ%⚪௃'(⚪)*ᓄ,-).ᔠ0)12)ᦪ45(.ூᑖ᪆௃89ᔣ;<BC?8cᡠᡂḄB0,ᵫcose=@ᓽJlADllBCl8N஺Ḅᜧ.ூPQ௃PRSB/(1,0,0),B(0,2,0),C(0,0,2),D(0,0,1),ᡠTU=(-I,0,1),BC=(0,-2,2),?8cᡠᡂḄB஺ᡠTcos஺=τ".BC,}_=2_=A,IAD11BC|&X2[2ᵫ0°<0^90°,ᡠT஺=60°_12⚓ᐳ26⚓

12ᓽ8cᡠᡂḄᜧ60°.ᦑQᫀBR60°.ூd௃e⚪ὃf!☢ᡠᡂḄ80ὃfᔣ;0ḄgᵨijkẠ⚪.12.m2020n•pqrstu“wx=ᬀ|+3ᙊx2+y2-4x-5=0ᨵᨵᐳ”Ḅᐙ⌕ᩩ.5ூὃ௃ᐙᑖᩩஹ⌕ᩩஹᐙ⌕ᩩ.ூ%⚪௃ᦪᔠ)0)᧕)ᳮRᦪ45(.ூᑖ᪆௃᪷wᨵᨵᐳᑣy=>l|x|+3ᙠx<0ḄᑖᙊᑗᙠXx0Ḅᑖᙊᯠὶ¡¢£¤ᑭᵨᑨ§¨©ª8PᓽJ.ூPQ௃PRᙊx2+y2-4x-5=0,ᓽᙊmX-2u2^=9,ᡠTᙊ¬Bm2,0u,®B3,ᵫ¯°J±²ᩩḄ³´j0,µwy=¶x|+3ឤ¸m0,3u,¹¯°ᨵᨵᐳº»=ổ|+3ᙠx<0Ḅᑖᙊᑗᙠx20Ḅᑖᙊ,,fy=-kx+3½x<0¾ὶ¿.x2+y-4x-5=0ᡠTm3+1ux2-6k+4x+4=0,À=m6A+4u2-4X4XmR+lu=20+48Â=0,PN¿=¿ᡈ0mÄÅu5_13⚓ᐳ26⚓

13ᦑ“wÆ=ổ|+3ᙊ/"-4È5=0ᨵᨵᐳ”Ḅᐙ⌕ᩩ⊟=Ê15ூd௃e⚪Ë⌕ὃfÌᙊḄÍÎᐵÐT#ᐙᑖᩩஹ⌕ᩩḄgᵨѾὃfÌ4ÒᳮḄÓÔÕ5(8PḄÓÔij᫏⚪.2213.m2020n•×Ør᪥ÚstuÛwCR^--^lm>0,b>0uḄÞᩩßà¢ar—2222£BVÀgXâᙊ£=1ᨵᐳᯖ.ᑣwcḄ¢£Bå--=1.y212345ூὃ௃ᙊ┵wḄ.ᔠ.ூ%⚪௃¢£,-)çÐᦪ0)ᙊ┵wḄஹឋ颣)ᦪ45(.ூᑖ᪆௃ᵫÛwḄßࢣJNê=ëজ8NâᙊḄᯖJN஺2+/>2=9,a2ঝP¢£JN஺b,©µNᑮÛwḄ¢£.22ூPQ௃PRÛwCR-E=lma>0,b>0uḄßࢣBð=ñòa2*4b2aᵫÞᩩßࢣBþÿ
=
জ2*2a22ᙊ=1Ḅᯖ-3,0,3,0,123஺2+62=9,ঝᵫD2a=2,b=^/$22ᓽ&'(Ḅ)*+-,=1,4522ᦑQᫀBR--=1.45ூd௃e⚪ὃfâᙊÕÛwḄ¢£Õឋéὃf¢£,-Õ5(ÓÔijkẠ⚪.14.m2020n•×Ør᪥Ústuwô=õ1N=X+6ាᨵ1ᐳᑣbḄ÷øúBÈ-2,2u52ª.ூὃ௃w¢£.ூ%⚪௃.ᔠ⚪)ᦪᔠ)ᦪᔠ0).ᔠ0.ூᑖ᪆௃ᵫ⚪ûJNy=x+6ᙊü=4my20uᨵᐳ½¸ᨴm2,-14⚓ᐳ26⚓

1400
16Ḅ2345(67ᙊ8ᑗ:80
᪷<ᙊ=ᑮ5(Ḅ?@A:7B16Ḅ2
ᦪDEᔠGHᑮbḄI2K.ூNO௃NQᵫ⚪S5(T7ᙊX2+/=4
yNOាᨵ1WXᐳ
᝞Zᡠ\Q45(]^
2,00
0=2+6,16=-2.45(67ᙊ8ᑗ:B0
ᵫᙊ=ᑮ5(Ḅ?@A:7B$L=2,16=2ᡃ
ᡈ6=-2&ab
ᦑbḄI2Kd-2,2U{2&},ᦑOᫀQ-2,2U{2&}.ூf௃g⚪⌕ὃj5(6ᙊḄklᐵn
ᑮ5(Ḅ?@XoḄpᵨ
rstuᓄஹᦪDEᔠḄᦪxyz
{:|Ạ⚪.15.
2020~᪥᪷ᐳᢞᨵ10ᳫ
Ḅᳫᦪ1,2,3,4,ᡭẚᳫ
Hᨵᡭẚ☢Ḅᳫᡭ☢Ḅᳫ
ᑣᳫᡭẚḄ¡¢wᡭ£ᦪd12600.ᵨᦪ¤⊤\mdூὃ௃᣸ᑡஹ¨ᔠ©ªᓫ¬ᦪ⚪.ூ®⚪௃¬¯⚪3)*yz3uᓄyz3᣸ᑡ¨ᔠ.-15⚓ᐳ26⚓

15ூᑖ᪆௃᪷<⚪S
10Wᳫ²³´µI-10,ᑖ᪆·⚪¸uᓄ´µ1-10Ḅ10W¹ᳫ᣸ᑡ
ᐸ»2ஹ3µஹ4ஹ5ஹ6µ
7ஹ8ஹ9ஹ10µ¹ᳫÀÁdGÂᑮÃḄÄÅ
ᢥ¹ᳫGÂᑮÃḄ´µÄÅÇẚ¹ᳫᓽ
ᵫÈᑖ£¬¯Oᫀ.ூNO௃NQ᪷<⚪S
᝞Z
10Wᳫ²³´µ170
·⚪¸uᓄ´µ1-10Ḅ10W¹ᳫ᣸ᑡ
ᐸ»2ஹ3µஹ4ஹ5ஹ6µ
7ஹ8ஹ9ஹ10µ¹ᳫÀÁdGÂᑮÃḄÄÅ
ᢥ¹ᳫGÂᑮÃḄ´µÄÅÇẚ¹ᳫᓽ
ioAᑣᨵ.?=12600Í᣸ᑡ)£
AᑴÏᑣᨵ12600Í¡¢ᡭ£
ᦑOᫀQ12600.ூf௃g⚪ὃj᣸ᑡஹ¨ᔠḄÐ▭pᵨ
ᐵÒd·⚪uᓄ
ᑭᵨ᣸ᑡᦪXoᑖ᪆.16.2020~ÔÕ᝞Öᦪᑡ×ØÙÚÛÜ23±l=k%áᦪ
âãᦪᑡ×ØÙan+lanåæAçèᦪᑡ
éåæXçè.êëᑡWEìQজíᦪᑡ×஺“ÙÚÛQ⊈=2n
ᑣðᦪᑡdAçèᦪᑡ3anঝᦪᑡ×"2"ÙdAçèᦪᑡ3ঞᡠᨵḄAçᦪᑡdAçèᦪᑡ3টôᙠAèᦪᑡdAçèᦪᑡ.ᐸ»ᡠᨵö÷EìḄŵdজবভ.ூὃ௃ú⚪ḄûᎷᑨþTpᵨ.ூ®⚪௃ÿᔠ⚪ᓄᦪᑡᦪᑡᳮ.16⚓ᐳ26⚓

16ூᑖ᪆௃ᑭ⚪!ḄᦪᑡḄ#ᓽᦪᑡ%&'()*+,-=k112ᦪ)#an+lan8ᔠᦪᑡ9ᦪᑡḄ:;<⚗>?@ᔜB⌱⚗DE⌲Gᑖ᪆ᑨI#ᓽJKᑮMᫀ.ூOM௃OP᪷R⚪S#ᦪᑡ%“”'()V±=2rvᑣ\⎃3^=211+2-2x2#anan+lanᡠ:ᦪᑡcᦪᑡ#ᦑ⌱⚗জfg@ᦪᑡ%஻-2"',ᑣ=+2_an+l=(n+2A2*2_(+l)«2n+12n+42n+2=n=a.a(+l)-2n+1(nA2“n+1nnn992n+4n-2n-4rr2=-2rc2ᦪ#n(n+l)~n(n+1)ᡠ:ᦪᑡ%ᓝ2"'rcᦪᑡ#ᦑ⌱⚗ঝ┯wᵫᦪᑡḄJy#a^a„.\q,nᡠ:/82._aL=q_q=o,an+lanᡠ:ᡠᨵḄᦪᑡ|cᦪᑡ#ᦑ⌱⚗ঞfgP~ᦪᑡ1>1d,ᡠ:an+2_fn+l=2da+d__d2nan+lanajda(&+d)nnd=o#ᑣ\93±L=o,ᡠ:ᙠᦪᑡcᦪᑡ#ᦑ⌱⚗টfg.an+lanᦑ⌱Pজঞট.ூ௃⚪ὃ⚪#:1ὃᦪᑡyḄᵨ#O⚪ḄᐵcfgᳮO⚪S#8ᔠᡠḄᦪᑡḄᐵᭆஹ>?ஹᳮyDEẆ¢.£.OM⚪(ᐳ6¤⚪)17.(2020§•©ª«¬)®y¯°/(0,3),±²³ᑡᩩµজஹᩩµঝஹᩩµঞ¶£Bᩩµ·S⌱¸GB¹1®y#º¯°/Ḅ»¼.ᩩµজP¯°/½¯°APx+yH=0À2x-y-4=0ḄÁᩩµঝP¯°/ᙊ#+Ã=3ᑗᩩµঞP¯°/ᙶ᪗ÇÈᡂḄ£ÊËḄ☢Í13.17⚓ᐳ26⚓

17ூὃ௃¯°ᙊḄÎÏᐵÐ.ூÑ⚪௃»¼ÒÐᦪ¯°ᙊᦪÓÔ.ூᑖ᪆௃Õ⌱¸ᩩµজ#ὶׯ°»¼ºÁ#±ºØ᳛#ᑭᵨ¯°»¼ḄØÚ?KMᫀÕ⌱¸ᩩµঝ#~!¯°»¼#ᵫᙊÛᑮ¯°ḄÜÝÞߺØ᳛#±ᵫ¯°»¼ḄØÚ?KMᫀÕ⌱¸ᩩµঞ#~!¯°»¼#º!¯°ᙠXÇàḄÚÜ#ᵫ£ÊË☢ͺK¯°ḄØ᳛#±ᵫ¯°»¼ḄØÚ?KMᫀ.ூOM௃OP⌱¸ᩩµজPO»¼áâ4y+1=஺+K#x=l,l2x-y-4=0y=-2ᑣ¯°/ḄØ᳛1k**=-5#¯°/Ḅ»¼1ä=-5x+3,ᓽ5x+y-3=0.⌱¸ᩩµঝP~¯°/Ḅ»¼1y=h+3åæᯠ¯°/ḄØ᳛ᙠè#ᓽfcv-é3=0.ᙊê#2=3ḄᙊÛ10,0,Þß1•.•¯°/ᙊ#+᮱=3ᑗ#3...-^,OKk=±&.=Vk2+1/.¯°/Ḅ»¼1y=±V2x+3,ᓽ±ìx-y+3=0.⌱¸ᩩµঞP~¯°/Ḅ»¼1>=î+3åæᯠ¯°/rᙶ᪗ÇïEè#ðy=0,Kñ=ò.kᑣS=1x3X|-1-|=3-OKk=+3..•.¯°/Ḅ»¼1y=±W>x+3,ᓽóSx-y+3=0ூ௃⚪ὃ¯°»¼Ḅº#ὃ¯°ᙊÎÏᐵÐḄᵨ#ὃÓÔºOôõ#cöẠ⚪.18⚓ᐳ26⚓

1818.(2020§•©ª«¬)®y/(1,-2)ᙠùᱥ°᮱=2px(p>0)à#/üØ᳛12Ḅ¯°ùᱥ°ḄýGBÁ1B.(I)ºpḄÿ
ᱥḄᯖᙶ᪗(II)|/ᓺூὃ௃
ᱥḄឋ
ᱥḄᔠ.ூ⚪௃!⚪"#ᓄ%&"ᔠ'ᙊ┵*Ḅ+,ஹឋ./"ᦪ12!.ூᑖ᪆௃(I)ᵫ6(1,-2)ᙠ
ᱥ<=2/(p>0)ABCp.Dᑮ
ᱥḄ./Bᯖᙶ᪗.(II)ᨴ8Ḅ./Hy=2x-4,ὶM./
ᱥ./BNᙶ᪗BᯠPCQRᓽT.ூCU௃C"(I)ᵫ/(1.-2)ᙠ
ᱥ᮱=2px(p>0)ABDW=2.2ᡠY
ᱥḄ./H᮱=4x,ᯖᙶ᪗H(1,0).....................5(H)Ḅ./H\2=2(x-1),ᓽy=2x-4,...............7C./^_`4x,D,=1,ᡈfx=4).............9,y=2x-4[y=-2.[y=4.ᡠY8Ḅᙶ᪗H(4,4).ᡠY|AB|=7(1-4)2+(-2-4)2=3>/5,....................12ூi௃j⚪ὃk
ᱥḄlmᐵoḄpᵨBὃk#ᓄ%&Yr!s6Btu᫏⚪.19.(2020w•yz{|})᝞By☢y☢COE,6tH2Ḅ.BDC=CE,NDCE=90°,FH஺EḄuB\ᙠ8EA.(1)"y☢BCF1(II)ᙠP,Dy☢CFPy☢8CFᡠᡂ☢ḄHBḄ.3BE19⚓ᐳ26⚓

19Dூὃ௃y☢ᚖ☢Ḅy☢r'.ூ⚪௃!⚪ᦪᔠ#ᓄ%&ᔠ'lmᐵoQR"ᳮᦪ12!.ூᑖ᪆௃(1)¢8C_LC£).N8C_Ly☢CDE.D£U8C_LDE.¢CF_LDE,ᯠP¢஺EJLy☢8b.'"(I)YCH¤BCD=CE,\H஺EḄuBᡠYCµLOE,´8Cnb=C,BCuy☢8CF,CFuy☢8CF,ᡠY஺E_Ly☢8b.................................(5ᑖ)'"³H.N8CD,ᡠYBC_LCD.³Hy☢/8CDJ_y☢CDE,´y☢y☢CDE=CD,ᡠY8C_Ly☢CDE.................................(2ᑖ)ᡠY8C_LCE,³H/£>CE=90°ᡠY8C,CE,CD¶·ᚖ.YCH¤BYC8,CE,CDᑖ¥Hx,y,z¦§Mᙶ᪗oB20⚓ᐳ26⚓

20ᵫ⚪¸C(0,0,0),B(2,0,0),D(0,0,2),E(0,2,0),F(0,1,1).¹4ᑖºᡠY»=¹0,2,-2>CF=¹O,1,1ºBCB=¹2,0,0>³H»•»=0,DECF=0'ᓽ஺E_LC3,DELCF,CBCCF=C,ᡠY஺EJ_y☢8cÂ.................¹6ᑖº¹HºC"³HPᙠ1ABÄ\¹x,n0º.ᡠYᙠᐭÆ0,1º,D»=ᐭÇ.³H»=¹x-2,y,0º>BE=¹-2,2,0>ᡠY1x-2=-2ᐭBᡠY\¹2-2ᐭB2ÈB0º.ly=2ᐭᡠY»=¹2-2ᐭB2ÊB0>.............¹8ᑖºÄy☢CFPḄ«¬'ᔣ®HË=Q,b,c>ᑣÏÐ=°,ᓽf(2-2j+2ᐭb=0{cFn=Olb+c=OᡠYn=(1B-1>1),.............(10ᑖ)1-N³H஺E_Ly☢8CRᡠYy☢2CFḄ«¬'ᔣ®tÕ=9,2,-2ºº....¹11ᑖºÖ³Hy☢CFPy☢8CFᡠᡂ☢ḄH,3—ØÙ----------------@,•…“¹13ᑖº2+¹ÜºX2ÕᡠYÈÞᡈᐭ=2ß0,1àáâ.ᡠY²Þ.¹14ᑖº3BE321⚓ᐳ26⚓

21ூi௃j⚪ὃky☢ᚖḄᑨä+ᳮḄpᵨB☢Ḅy☢Ḅ'Bὃk#ᓄ%&Yr!s6Btu᫏⚪.20.2020w•åæ{|}º2020çtᡃé5Gêë§ÄḄÕìíç.î£2020çïBuéð§ᡂᐰᳫᨬᜧḄ5Gêë.Hõᑗ÷øùøêë®úᓣBüäᦋᗐᵨᡝ
▾ᡲᙠᐰᑁᡠ⚗"#.ᐸ&⚗"#ᑁ'(ᙠ)*"+,ᢧ⌱&ᩩᐺ1234#56ᙢ5G89:.ᐸ5*"+,Ḅ5G<ᔠ>?@᳛BᓫDEMbpsᦪG᝞⊤E+,235G<ᔠ>?@᳛BᓫDEMbpsJKLM2708.92NKᜧP+᜜//ᑁS817.13TUVWX⊙630.34ZKS+[2882.60ᡂ]^S_`916.02BIab4c5*+,de⌱f2*+,ghᑖ᪆k⌱fḄ2*+,“5G<ᔠ>?@᳛”]ᜧmSOOMhpsḄᭆ᳛oII
ᵬஹrst5Gu⃩ᖪᑖxb4c5*+,de⌱f1*+,ὃzBᵬஹrḄ⌱f{|}~akᵬஹrstu⃩ᖪាᨵ1t⌱fḄ+,“5G<ᔠ>?@᳛”ᜧmSOOMbpsḄᭆ᳛.ூὃ௃ᐺᭆ1ᐸᭆ᳛oᑡᦪ8Ḅᭆ᳛.ூ⚪௃ᓄooᓄoᭆ᳛oᦪPu.ூᑖ᪆௃BI
5*+,“5G<ᔠ>?@᳛”ᜧm800MᑗsḄᨵ3*A,222⚓ᐳ26⚓

22¡“5G<ᔠ>?@᳛”|ᜧm800MbpsḄᨵ2*¬ᔊ.de⌱f2*+,ᑭᵨᑡ°k±⌱fḄ2*+,“5G<ᔠ>?@᳛”]ᜧm800MbpsḄᭆ᳛.(II)ᵬ⌱fḄ+,“5G<ᔠ>?@᳛”ᜧm800MbpsC,r⌱fḄ+,“5G<ᔠ>?@᳛”ᜧm800஻¸s஺ាᨵ1tu⃩ᖪ⌱fḄ+,“5G<ᔠ>?@᳛”ᜧm800¸¸5N.»¼±P(C)=P(D)½ᵫPWhPClUÄD)=5P(C)P(D)+P(C)P(D),°k±ᵬஹrstu⃩ᖪាᨵ1t⌱fḄ+,“5G<ᔠ>?@᳛”ᜧmSOOMbpsḄᭆ᳛.ூÈÉ௃ÈE(ூ)5*+,“5G<ᔠ>?@᳛”ᜧm800MᑗsḄᨵ3*Ai,A3,“5G<ᔠ>?@᳛”|ᜧm800/W/wsḄᨵ2*4ᔊ.de⌱f2*+,ᡠᨵÌ°E4Î81,/±2,A2A3,A2B1+A2B2,A3B1,A3B2,B1B2,ᐳ10Ï.ᐸ2*+,“5G<ᔠ>?@᳛”]ᜧm800M᝞sḄᨵÐ2,AIA,A2A3,ᐳ3Ï.3sÑ+,“5G<ᔠ>?@᳛”]ᜧm800஻¸sᡠ4P(H)=Ó(II)ᵬ⌱fḄ+,“5G<ᔠ>?@᳛"ᜧm8W)MbpsC,r⌱fḄ+,“5G<ᔠ>?@᳛”ᜧm800Mbps஺ាᨵ1tu⃩ᖪ⌱fḄ+,“5G<ᔠ>?@᳛”ᜧm800M¸sMÕ⚪Öp(C)=P(D)25ᡠ4P(N)=P(CBUCD)=P(CD)+P(CD)=P(C)P(D)+P(C)P(D)-^-x—•555525ூ#௃⚪ὃÞᭆ᳛ḄkὃÞᐺᭆ1ஹᑡஹß{àáᭆ᳛âஹ{ãᭆ᳛¸ஹäáᭆ᳛åẠçèὃÞukÈ°é(Ạ⚪.2221.(2017ë•ì+íî)ïçðᙊCE&&4=1(a>b>0)õ4(2,0),ö÷ø᳛ù.2(I)kðᙊCḄúû;23⚓ᐳ26⚓

23BIIaýþy=kx+«ᙊCM,N.x=3ᙠP,!"#$᝕Ḅ'.ூὃ௃ᙊḄ᪗,-./ᙊ┵1Ḅ2ᔠ/ᙊḄ2ᔠ.ூ4⚪௃67⚪/-.89/:ᓄ89/2ᔠஹឋA-..ூᑖ᪆௃D1FᑭᵨIJᩩL$Ma,h,ᓽPᑮᙊḄ-..DIIFR1Ḅ-.Ty=஻Dx-2F,ᑮYD3,k,$M|p|=]^_#`aDᑢ#A“F#NDX2,"F.ὶgᙊ-.#ᑭᵨhi=ᳮklmno:ᓄ$pᓽP.ூpq௃Dr]⚪sᑖ14ᑖFpuDIFᵫ⚪w஺=2,@£F,ᡠ<:|.}D2ᑖF_a2~T=+/,}D3ᑖF_ᡠ6=1,}D4ᑖF_2,ᡠᙊCḄ-.T+y2=_.}D5ᑖF_DIIFBMW!"#ᑣPA//MN,%|=|V_.}D6ᑖF_ᡠPAḄ-.Tஹ=Dx-2F,ᡠPD3,4F#|p|=+_.}D7ᑖF_A`A/Cxi,yiF,NDX2#»2F.y=kx+V3-cᵫ,22D4k?+lFx2+Qkx+8=o,}D8ᑖF_X+4y=4ᵫ>0,k2>f+--8}D9ᑖF_A1'AnQAiAnQ*••*4k'+l4k*+l,•=J42+1F¡¢£}D10ᑖF_ᡠ|MN|=/Dk2+lF}Dx+xF2-4_A12X1X2VD4k2lF2+~T¤|=|MN|,ᡠJ@2+1F*K-3'=4k2+LY-1F2᦮ᳮ16k4-56+33=0,}D12ᑖF_©24⚓ᐳ26⚓

24pk=¬ᗟ#ᡈk=±.}D13ᑖF_°±²ᙳ´ᔠµDF,¶k=-·¸¹sº!"#»¼.ᡠ½=¾#ᡈ½=±ᖛ.}D14ᑖF_ூÀ௃r⚪ὃÁᙊ-.Ḅ$<#ᙊḄÂÃᐵÅḄÆᵨ#ὃÁ:ᓄ89k67ÇÈ.22.D2020É•ÊË^ÌÍFIJÎÏᦪᑡÒ““Ósºk=4,43+஺4=17.DIF$ᦪᑡÒÔÓḄÕ⚗no/DIIFᦪᑡÒdÓsº"=2,ØÙজb”+i=2d/ঝ2+1=a/ঞa+1=-6஻ßàáᩩLâã⌱åáæTIJ#$ᦪᑡGa,,+hHḄçn⚗èT,,,nூὃ௃ᦪᑡḄ$è.ூ4⚪௃-.89/:ᓄ89/2ᔠ

25ᵫbi=2,26n+)=hnUJ#0,ߟbn2ᡠᦪᑡ!"#$!q2ᡠ&=1>4-1=20+=8-2,ᡠ77?=(஻i+஻2+................+/)+(2+ᔊ+................+)—n(l3n-2)23n2-n,1^2.++425I-2—67)+4,2⌱ঞbn+lᵫ6=2,ᵫ+1=-9஺W0,=-1>ᡠ;ᦪᑡ!"᜛=-1,ᡠbn=biqnT=2(l)n-l.ᡠ7^=(4]+஻2+...................+/)+(2+ᔊ+................+bn)=n(l+3n-2)2(1-(-1)")=3n2-n+2(«.2+~1-(-1)2I)n-ூAB௃D⚪F⌕ὃIJஹᦪᑡḄLMNODPḄQRஹᑖTUVWᙠᦪᑡUVYḄZᵨ!\]Y᫏⚪.26⚓ᐳ26⚓