2023年湖南省张家界市中考数学试卷

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2018
ᓭḕὃᦪᔁஹ⌱⚪ᜧ⚪ᐳ8⚪⚪3ᑖᑖ24ᑖᙠ⚪Ḅ!⌱⚗#ᨵ⚗%&ᔠ⚪(⌕*Ḅ.,1.3.00ᑖ,2018•,2018Ḅ./0%,11A.2018B.-2018C.-------D.-57770201820183.00ᑖ,2018•,2ᐵ4xḄᑖ5678;=1Ḅ:;x=2,ᑣmḄ2.x-10;
A.5B.4C.3D.23.3.00ᑖ,2018•,=ᑡ?@A%B/C?@D%E/C?@Ḅ%,4.3.00ᑖ,2018•,=ᑡXYHIḄ%,A.a2+a=2a3B.5/0^=aC.a+1
2=a2+lD.a3
2=a4565.3.00ᑖ,2018•,2Zᦪ[aia,a3Ḅ\ᙳᦪ;4,6^;3,2_`ᦪ[ai+2,a+2,a?+2Ḅ\ᙳᦪa6^ᑖb%,2A.4,3B.6,3C.3,4D.6,56.3.00ᑖ,2018•,᝞?AB%஺஺ḄLe,gCD1AB4hE,OC=5cm,CD=8cm,ᑣAE=
A.8cmB.5cmC.3cmD.2cm7.3.00ᑖ,2018•,=ᑡFGHIḄ%,A.JᩩLMNOPᩩLMᡠRᑁ┯UVW

1B./UMVWḄ\i!j@%H6@C.VWḄU%/⚔UD.U\ᑖMlḄhᑮUJjḄnoVW8.3.00ᑖ,2018•,pq=ᑡY5r21=2,22=4,23=8,24=16,25=32,26=64,27=128,28=256...,sI2+22+23+24+25+...+2i°i8Ḅtuᦪv%,A.8B.6C.4D.0wஹxy⚪ᜧ⚪ᐳ6⚪⚪3ᑖᑖ18ᑖ,9.3.00ᑖ,2018•,z5ᑖ:ra2+2a+l=.10.3.00ᑖ,2018•,({|l}ᑴ⌼Ḅᱏᨬ\%5ᡃ}ᑴ⌼ᱏḄᨬ\%161=109ᵨᦪG16⊤;.11.3.00ᑖ,2018•,ᙠḄᨵ3⁐ᳫa27⁐ᳫ2¡¢£¤᥎ᳫា§%ᳫḄᭆ᳛;ª,10ᑣᑁᐳᨵᳫḄᦪ;.12.3.00ᑖ,2018•,᝞?AABC«hA⌮┐¯°150஺±ᑮ²ADE,¢hB,C,Dា§ᙠ³LMlᑣNBḄ´ᦪ;.13.3.00ᑖ,2018•,ᐵ4xḄᐗw¶67x2-kx+l=0ᨵJVWḄ·ᦪ᪷ᑣ1<=.14.3.00ᑖ,2018•,᝞?¹@ABCDḄjABºxE\i⚔hAḄ6ᙶ᪗;2,1
,hBºhD½ᙠ¾¿ÀÁᦪy=-x>0
Ḅ?Âlᑣ¹@ABCDxḄᕜÄ;

2Pஹ:Å⚪ᜧ⚪ᐳ9⚪ᐳÆ58ᑖ:ÅÇᑏᦻvFஹÊË7ᡈÍYË7,15.5.00ᑖ,2018•,Î-1
°+-1
2-4sin60°+V12.16.5.00ᑖ,2018•,:W5Zᑏᐸ᦮ᦪ:.1%+2>117.5.00ᑖ,2018•,ᙠ¹@ABCDhEᙠBClAE=AD,DF±AE,ᚖÒ;F.1
*Ê.DF=ABÓ2
2NFDC=30°,ÔAB=4,*AD.18.5.00ᑖ,2018•,ᑡ67:Çᵨ⚪ÕÖ×YØÙᨵ“ÛÒØ"ḄÝ⚪Þᦻ᝞=r"ßᨵᐳàáâãÒ!ᓝãÓâåÒP.Ýâᦪஹáæᔜèéê”⚪ì%r2âᐳ³íîáâ5ᐗᑣ^45ᐗÓâ7ᐗᑣ^3ᐗ.*âᦪaáïᔜ%ðñê19.6.00ᑖ,2018•,▅óᳮ:⚪ᙠ\☢LUᙶ᪗öxOyhPxoyo
ᑮLMAx+By+C=0A2+B2#=0
Ḅno÷ø,\^x+By+C\00ù5;rd=-----f0——>JA2+B2À᝞*hP1,3
ᑮLM4x+3y-3=0Ḅno.:rᵫLM4x+3y-3=0:A=4,B=3,C=-3|441+3*3-3|ᡠüP1,3
ᑮLM4x+3y-3=0Ḅno;:d-V42+32-2᪷[ülᩞᧇ:ÿᑡ⚪:

31
Pl0,0
ᑮ3x-4y-5=0Ḅ.2
P21.0
ᑮx+y+C=0ḄᦪCḄ.20.6,00ᑖ2018•᝞P஺஺Ḅ!AB"#$%&AB=4,M'$%()*+A,B,ᔠ.PM+஺0/0N*+M,ᔠ11Mᙠ34567^MABḄ☢9ᨬᜧ<=>(ᨬᜧ?2
@ABPANs/^PMB.21.8.00ᑖ2018•CDᡃFᐰ☢HIJKL᪥"OPQR᪶TUV"ᦟXD.Y᪥Zᐰ᪥L[I\]J^_`aU_`bcᑖAdeஹBghஹCᔠiஹD*ᔠij(kl.

422.8.00ᑖ2018•2017D9ᨴ8-10¡¢£¤\¥┶᪗¨ᙠᡃFᜩª«¬®◖,°\ᩭ²ᐰᳫ11(´Ḅ16r⌱¶·¸]¹ºḄ»⌲.᝞Y⌱¶½¾¿ᙢ☢1000ÁÂḄA=ÃAB=1000ÁÄÅ»30஺ḄÆᔣ¤\1400ÁᑮDᯠÉᡭËÌÍÎÄÅ»60஺ḄÆᔣÌÍᑮᙢ☢$ḄC⌱¶¤\Ḅ¾¿BC.23.10.00ᑖ2018•᝞ÏÐÑÒᦪy=ax2+laWO,aᦪḄÓÔA-2,2
,%Òᦪy=kx+bkWO,k,bᦪḄÓIÕÔB0,2
.1a<ᑏ=ÑÒᦪ⊤×?2
b?3
ØI+ÑÒᦪÓ/0M,NÙÔMsMCᚖxÛ0C,Ü@ÝAMB=MC?4
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ḄᩩÞᑨàáâMN!Ḅᙊ+xÛḄ56ᐵå<æÝᳮᵫ.

5

62018DèᓭḕFJὃᦪLÜᔁὃᫀ⚪᪆%ஹ⌱í⚪uᜧ⚪ᐳ8(K⚪îK⚪3ᑖïᑖ24ᑖᙠîK⚪ð=Ḅj(⌱⚗Jòᨵ%⚗óᔠ⚪ô⌕Ḅ.1.3.00ᑖ2018•2018ḄöZூὃ௃15AöZ.ூù⚪௃1:úû⚪ü.ூᑖ᪆௃þᑭᵨ
Ḅឋᑖ᪆ᫀ.ூ௃2018Ḅ
2018.ᦑ⌱A.ூ௃⚪⌕ὃ
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Ḅ#$⚪ᐵ&.2.3.00ᑖ'(2018•*+,'-ᐵ.xḄᑖ/01”33=1Ḅ4x=2,ᑣmḄx-14('A.5B.4C.3D.2ூὃ௃B2ᑖ/01Ḅ.ூ7⚪௃1:9:⚪;.ூᑖ᪆௃<=ᑖ/01>?ᫀ.ூ௃•••ᐵ.xḄᑖ/01@=1Ḅ4x=2,x-1x=m-2=2,:m=4.ᦑ⌱:B.ூ௃⚪⌕ὃᑖ/01Ḅ01⚪ᐵ&.3.3.00ᑖ'(2018•*+,'AᑡCDEFEGHCDIJHCDḄ('

7ூὃ௃P3JHCDKR5EGHCD.ூ7⚪௃55LMCD.ூᑖ᪆௃᪷OJHCDPEGHCDḄᭆR>SᑨUᓽW.ூ௃AஹYJHCDEGHCD.ᦑ┯[KBஹJHCDYEGHCD.ᦑ┯[KCஹJHCD\EGHCD.ᦑKDஹJHCDYEGHCD.ᦑ┯[.ᦑ⌱C.ூ௃]⚪ὃḄEGHCDPJHCDḄᭆRJHCDḄᐵ&^_HJCD`aᑖbHJᢚdeWfᔠKEGHCD⌕^_HEGhi180jePkCfᔠ.4.(3.00ᑖ)(2018•*+,)AᑡmnḄ()A.a2+a=2a3B.5/0^=aC.(a+1)2=a2+lD.(a3)2=a6ூὃ௃35ᔠpqr⚗K47tḄu0PvḄu0K4Cwᐰy0z/K733{᪷/ḄឋPᓄ}.ூ7⚪௃1:9:⚪;.ூᑖ᪆௃᪷Oᔠpqr⚗Ḅ~ᑣ!qr⚗Ḅᦪᡠ4ᦪḄᢣᦪYKV^2=a(a20)wᐰy0z/(a±b)2=a2±2ab+b2Ḅu0~ᑣᦪYᢣᦪu>SnᓽW.ூ௃Aஹa?aYqr⚗Yᔠpᦑk⚪n┯[KBஹ=|a],ᦑk⚪n┯[KCஹ(a+1)2=a2+2a+l,ᦑk⚪n┯[;Dஹ(a3)2=a6,ᦑk⚪nKᦑ⌱D.

8ூ௃⚪⌕ὃ3{᪷/Ḅឋஹᔠpqr⚗ஹwᐰy0z/ஹḄu0ᐵ&"ᔜn~ᑣnz/.5.3.00ᑖ'(2018•*+,'-ᦪOaia2,a3Ḅyᙳᦪ44,043,ᦪO+2,a+2,as+2Ḅyᙳᦪ0ᑖ('2A.4,3B.6,3C.3,4D.6,5ூὃ௃W1nyᙳᦪKW70.ூ7⚪௃1:9:⚪;.11ூᑖ᪆௃᪷OᦪOaia,a3Ḅyᙳᦪ44Wai+a+a
=4,OW223ai+2+a+2+a+2
ḄKᵫ043WᦪOai+2,az+2,as+2Ḅ0.23ூ௃•••ᦪOai,a2,a3Ḅyᙳᦪ44,.1ai+a2+a3'=4,311ai+2+a2+2+a3+2
-(81+32+33
+2=4+2=6,33JᦪOai+2,a+2,23+2Ḅyᙳᦪ6K2;ᦪOai,a3Ḅ043,1[ai-4
2+(32-4
2+(33~4'2]=3,Aai+2,a+2,as+2Ḅ0421~|(31+2-6
2+(32+2-6
2+33+2-6'2]1="[ai-4'2+(32-4'2+(33-4'2]=3.ᦑ⌱B.ூ௃⚪⌕ὃ0yᙳᦪ¢£0Ḅ#$⚪Ḅᐵ&.6.3.00ᑖ
2018•*+,'᝞CAB஺0Ḅ<¦§CD1AB.E,OC=5cm,CD=8cm,¨ijAE=('

9A.8cmB.5cmC.3cmD.2cmூὃ௃KQ©ª#ᳮKM2ᚖ¦#ᳮ.ூ7⚪௃55CPᙊᨵᐵḄnK55E<¯°¯D±ᐸ³ᵨ.ூᑖ᪆௃᪷Oᚖ¦#ᳮWCEḄ´jᙠRt^OCEEᑭᵨ©ª#ᳮW0EḄ´jᑭᵨAE=AO+OEᓽWAEḄ´j.ூ௃•.,§CD_LAB.E,CD=8cm,1/.CE=_CD=4cm.2ᙠRtZXOCEE,0C=5cm,CE=4cm,
.OE=JoC2CE2=3cm,AE=AO+OE=5+3=8cm.ᦑ⌱A.ூ௃]⚪ὃᚖ¦#ᳮ·±©ª#ᳮᑭᵨᚖ¦#ᳮᔠ©ª#ᳮ¸0EḄ´j⚪Ḅᐵ&.7.3.00ᑖ'(2018•*+,'Aᑡ¹~EḄ('A.`ᩩ<»¼½°ᩩ<»ᡠ¾ᑁ┯¯ÀB.¯»ÀḄySÁÂD0DC.ÀḄ¯⚔¯D.¯yᑖ»ÄḄᑮ¯`ÂḄÆÇÀூὃ௃J2⚔¯ஹÈ⊡¯KJ6qʯஹᑁ┯¯ஹqËᑁ¯KKF¯yᑖ»ḄឋKL5ySÁÂDḄឋKLG0DḄᑨ#Pឋ.ூ7⚪௃19:⚪;.ூᑖ᪆௃᪷OyS»Ḅឋஹ0DḄᑨ#ஹÌDḄᑨ#ஹ⚔¯Ḅឋஹ¯yᑖ»ឋ⌲ÎᑨUᓽW.ூ௃Aஹ`ᩩyS»¼½°ᩩ<»ᡠ¾ᑁ┯¯ÏÀ┯[ᦑ]⌱

10⚗YÐᔠ⚪ÑKBஹ¯»ÀḄÁÂDÌDY#0D┯[ᦑ]⌱⚗YÐᔠ⚪ÑKCஹÀḄ¯Y#⚔¯┯[ᦑ]⌱⚗YÐᔠ⚪ÑKDஹ¯yᑖ»ÄḄᑮ¯Ḅ`ÂḄÆÇÀᦑ]⌱⚗Ðᔠ⚪ÑKᦑ⌱D.ூ௃]⚪ὃyS»Ḅឋஹ0DḄᑨ#ஹÌDḄᑨ#ஹ⚔¯Ḅឋஹ¯yᑖ»ឋÀÒ¢£yS»Ḅឋஹ0DḄᑨ#ஹÌDḄᑨ#ஹ⚔¯Ḅឋஹ¯yᑖ»ឋḄᑁÓ⚪Ḅᐵ&.8.3.00ᑖ'(2018•*+,'ÔÕAᑡn/:21=2,22=4,23=8,24=16,25=32,26=64,27=128,28=256...,ᑣ2+22+23+24+25+...+21018ḄÖÊᦪ
A.8B.6C.4D.0ூὃ௃1Q×ᦪᱯÙK37:Ú;ᦪḄᓄr.ூ7⚪௃1:9:⚪;.ூᑖ᪆௃ÛÜÔÕÝÞ2nḄÎÊᦪ2,4,8,6ÁÎßàᡠ·᪷O20184=504...2,22஺௃8ḄÎÊᦪP22ḄÎÊᦪq4,>?ᫀ.ூ௃2nḄÎÊᦪ2,4,8,6ÁÎßà2018^4=504...2,22஺18ḄÎÊᦪP22ḄÎÊᦪq4,ᦑ2+22+23+24+25+...+2i°i8ḄÖÊᦪ2+4+8+6+...+2+4Ḅ×ᦪᑣ2+22+23+24+25+...+21018ḄÖÊᦪ2+4=6.ᦑ⌱B.ூ௃]⚪ὃḄ×ᦪᱯÙ᪷O⚪Ñ_ᦪßàḄ:Ú⚪Ḅᐵ&.3ஹáâ⚪(]ᜧ⚪ᐳ6Îå⚪æå⚪3ᑖçᑖ18ᑖ'9.3.00ᑖ'(2018•*+,'è/ᑖa2+2a+l=a+1
2.ூὃ௃54è/ᑖ-mᵨz/~.ூ7⚪௃1:9:⚪;.ூᑖ᪆௃<=ᑭᵨwᐰy0z/ᑖè/ᫀ.

11ூ௃:a2+2a+l=(a+1'2.ᦑᫀ4(a+l'2.ூ௃⚪⌕ὃmᵨz/ᑖè/"wᐰy0z/⚪ᐵ&.10.(3.00ᑖ'(2018•*+,'òóô,Äᑴ⌼Ḅ÷ᱏᨬåúûüy5þÿ
ᡃᑴ⌼ᱏḄᨬ161=109ᵨᦪ!16⊤#$1.6X108.ூὃ*௃1J-ᦪ.⊤#/Ḅᦪ.ூ0⚪௃17-3ᳮ56⚪751-ᦪ9:.ூᑖ᪆௃ᵫ1=10.9>?@16=1.6X108A⚪?B.ூBC௃B-•••1=109A16=1.6X108.ᦑCᫀ$-1.6X108.ூ*H௃I⚪ὃJKLᦪMḄ⊤#/ḄᦪNOLᦪB⚪ḄᐵQ.11.R3.00ᑖTR2018•VWXTᙠ.Z[\]Ḅ^_`aᨵ3Zc⁐efᳫhi7jZk⁐efᳫilmZ^_`no᥎@.ZefᳫាrkᳫḄᭆ᳛$77,ᑣ^_ᑁᐳᨵefᳫḄZᦪ$10.ூὃ*௃X4-ᭆ᳛z:.ூ0⚪௃1-{|⚪}.X7ூᑖ᪆௃~ᨵXZkᳫᑭᵨᭆ᳛z:>?=77,B@XḄ>?kᳫᦪ3+%10ᦪᓽ>.X7ூBC௃B-~ᨵXZkᳫᵫ⚪?-—,3+X10B?-x=7,7+3=10,ᦑCᫀ$-10.ூ*H௃A⚪⌕ὃJKᭆ᳛z:ᐵQNOnoAḄᭆ᳛PRAT=

12A>@Ḅᦪ-ᡠᨵ>@Ḅᦪ.12.3.00ᑖTR2018•VWXT᝞!^ABC*A⌮┐150஺?ᑮADE,m*B,C,Dាrᙠ.¡¢£ᑣNBḄ¤ᦪ$15஺.ூᑖ᪆௃ᐜᑨ§@NBAD=15஺஺AD=AB,ᑨ§@ABAD¨Ὺª«¬ᨬᵨª«¬Ḅᑁ«h®ᳮᓽ>?@¯.ூBC௃B-..•!aABC*A⌮┐150஺?ᑮaADE,.,.ZBAD=150°,AD=AB,•.,*B,C,Dាrᙠ.¡¢£/.BAD⚔«$150஺Ḅ¨Ὺª«¬.•.ZB=ZBDA,1/.ZB=-1800-ZBAD
=15°,2ᦑCᫀ$:15°.ூ*H௃A⚪⌕ὃJKḄឋ³¨Ὺª«¬Ḅᑨ®hឋ³ª«¬Ḅᑁ«h®ᳮᑨ§@ª«¬ABD¨Ὺª«¬BI⚪ḄᐵQ.13.3.00ᑖTR2018•VWXTᐵ´xḄ.ᐗ¶·¸¹x2-kx+l=0ᨵºZ»¨Ḅ¼ᦪ᪷ᑣ1<=±2.ூὃ*௃AA-᪷Ḅᑨ¾:.ூ0⚪௃1:{|⚪}.ூᑖ᪆௃᪷¿⚪>?=RTÀ
>?k2-4=0,Bᓽ>.ூBC௃B-ᵫ⚪?-nkz-d-஺B?-k=±2,ᦑCᫀ$-±2.ூ*H௃A⚪⌕ὃJK᪷Ḅᑨ¾:ᐵQNO.ᐗ¶·¸¹ax2+bx+c=Oa

13NO
Ḅ᪷9442-4acᨵ᝞ÁᐵÂ-জĸ¹ᨵºZ[»¨ḄºZ¼ᦪ᪷;ঝÄ=RT¸¹ᨵºZ»¨ḄºZ¼ᦪ᪷7ঞÄAVO¸¹È¼ᦪ᪷.14.3.00ᑖTR2018•VWXT᝞ɬABCDḄÊAB9xËÌ⚔*AḄᙶ᪗$R2,1
,*B9*DÏᙠÐÑÒÓᦪy2Rx>0
ḄÔ£ᑣɬABCDூὃ*௃G6-ÐÑÒÓᦪÔ£*Ḅᙶ᪗ᱯÖ7LB-ɬḄឋ³.ூ0⚪௃11-L×⚪.ூᑖ᪆௃᪷¿É¬Ḅឋ³ஹᔠ*AḄᙶ᪗?ᑮ*DḄÚᙶ᪗$2,*BḄÛᙶ᪗$1,᪷¿ÐÑÒÓᦪB᪆:@*DḄᙶ᪗*BḄᙶ᪗᪷¿É¬ḄᕜÝz:L×ᓽ>.ூBC௃B-•••ÞʬABCDɬ*AḄᙶ᪗$R2,1
,.•.*DḄÚᙶ᪗$2,*BḄÛᙶ᪗$1,6Äx=2y=-=3,Äy=lx=6,ᑣAD=3-1=2,AB=6-2=4,ᑣɬABCDḄᕜÝ=2X2+4
=12,ᦑCᫀ$-12.ூ*H௃I⚪ὃJḄÐÑÒÓᦪÔ£*Ḅᙶ᪗ᱯÖஹɬḄឋ³NOÐÑÒÓᦪÔ£*Ḅᙶ᪗ᱯÖB⚪ḄᐵQ.ªஹBC⚪RIᜧ⚪ᐳ9Z⚪ᐳL58ᑖBCàᑏ@ᦻãä]ஹå]æ¹

14ᡈè×æ¹T15.5.00ᑖTR2018•VWXTRV5-1
°+-1
2-4sin60°+V12.ூὃ*௃2C-¼ᦪḄé×76E-êᢣᦪì76F-í᦮ᦪᢣᦪì7T5-ᱯï«Ḅª«Óᦪ.ூ0⚪௃1:{|⚪}.ூᑖ᪆௃¡ðᑭᵨíᢣᦪñḄឋ³òóêᢣᦪôḄឋ³òóᱯï«Ḅª«Óᦪஹ¶·᪷:Ḅឋ³ᑖ¾ᓄö?@Cᫀ.ூBC௃B-÷:=1+1-4X^+2ø=2.ூ*H௃A⚪⌕ὃJK¼ᦪé×ùúᓄöᔜᦪB⚪ᐵQ.16.5.00ᑖTR2018•VWXTB[¨:ü12%ᑏ@ᐸ᦮ᦪB.lx4-2>1ூὃ*௃CB-B.ᐗ.·[¨:ü7CC-.ᐗ.·[¨:üḄ᦮ᦪB.ூ0⚪௃1:{|⚪}.ூᑖ᪆௃ᐜ@þZ[¨:ḄBÿ
Ḅᓽ.ூ௃1<•.•জ<3,xঝX-1,Ḅ-1WXV3,Ḅ᦮ᦪ-1,0,1,2.ூ௃⚪ὃ"#ᐗ%&Ḅ᦮ᦪ'᪷)ḄḄ*+⚪Ḅᐵ-.17.5.00ᑖ/02018•123/ᙠ56ABCD8EᙠBC9AE=AD,DF±AE,ᚖ;F.1
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15ூὃ௃KDᐰAB6ḄᑨDEឋG=LB56ḄឋG.ூH⚪௃1:JK⚪L=55656M6NO6.ூᑖ᪆௃(1)ᑭᵨ"AAS”xᐳ

16wx5ᐗᑣ45ᐗ=x7ᐗᑣ3ᐗ.xᦪ&wᔜ*ூὃ௃8Aᐗ%OcḄdᵨ.ூH⚪௃521%Oc0/_dᵨ.ூᑖ᪆௃wxᦪVᦪᐵ5Xwxᦪ+45=7Xwxᦪ+3,ᐵᦪᐭwxᦪᐭOcḄw.ூ௃wxxᑣw05X+45/ᐗ5x+45=7x+3,x=210x/5X21+45=1500ᕒ/wxᦪ21xw150ᐗ.ூ௃⚪ὃ"#ᐗ%OcḄdᵨᐵNᑡᐗ%Oc*⚪Ḅᐵ-.19.6.00ᑖ/2018•123/▅ᳮ⚪ᙠ¡☢`Bᙶ᪗xOy8Pxoyo
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17
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193
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342
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35(3)ÒÿḄ
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362
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381
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39(1)ÎÏÐÑAḄᭆ᳛P(A)=ÐÑAtÓHÔḄ¸¹ᦪᡠᨵtÓHÔḄ¸¹ᦪ.(2)P(ÕᯠÐÑ)=1.(3)P(8tÓÐÑ)=0.