山东省青岛市市南区2021-2022学年八年级上学期期末数学试题（含答案解析）

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14ூᑖ᪆௃(1)᪷Hᙶ᪗«Fᓽ|i(2)᪷H¬®ḄឋDᑮ4ஹB\C,¯°ᓽ|ᑮ9Ci(3)ᑭᵨ☢b²³´ef.পL4᝞ᡠ¶4(3)L4·ABCḄ☢b43x4¸x4x2¸x2xl¸x2x3=12-4-1-3=4,222ᦑ2ᫀ-44.ூ:௃⚪ὃABFᙶ᪗¹¬®efº»Ḅ☢bEF¼½¬®ḄឋDº»☢bḄef¾´L⚪ḄᐵN.16.(1)7(2)8ூᑖ᪆௃(1)᪷HÀ᪷dḄÁᔠef´ᑣKLᓽ|;(2)᪷HÀ᪷dḄÁᔠef´ᑣKLᓽ|i(3)ᵨ²³Ãᐗ´L¾Åᓽ|.(1)L4ᔊÇ2ᫀ57⚓ᐳ18⚓

15573+2>/3=^J3~7ᚖF=7i.2ÊL4.Ë_4Ê.Í+6Ê+”Ï=7-5+>/36=2+6=8i.3ÊÐ-2Ê=-6জL,[2x+y=100ᵨজ+ঝx247x=14,Lx=2,wx=2yᐭᑮজ46-2y=-6,Ly=6,0x=2À¾ÅḄL-.ூ:௃<⚪>⌕ὃABLÀᐗ¾ÅÀ᪷dḄÁᔠefÓÔᐵef´ᑣL⚪ḄᐵN.17..1ÊÕÖ×.10ÊØḄ᝕ÚÛᦪ-20Ûi.2Ê7.6ஹ7.5ஹ7i.3Êᑖᙠ8ᑖ8ᑖmÝḄÛᦪᐳᨵ420Û.ூᑖ᪆௃.1Êᐜ᪷HᩩàeJᵱÚÛᦪ¥ᔠᐰØãÛᦪᓽ|J᝕ÚÛᦪi.2Êᵫᩩàe|«JᵱÚäDåæᡂçḄèᦪé᪷H²ᩗëᙳᦪḄᭆî¥ᔠᡧàe|J᝕ÚäDåæᡂçḄëᙳᦪYðᦪi.3ÊᵨãÛᦪñm᪵<ᵱஹ᝕Úᑖᙠ8ᑖ8ᑖmÝḄÛᦪᓰᐰØÛᦪḄóôᓽ|.ூ}L௃L4.1ÊiÕÖ×.10ÊØᵱÚÛᦪ-2+4+6+5+4+2=23.ÛÊ᝕ÚÛᦪ-43-23=20.ÛÊi.2ÊᵫᩩàeᵱÚäDõæᡂçḄèᦪᱏ7ᑖ2ᫀ58⚓ᐳ18⚓

16᝕ÚäDõæᡂçḄëᙳᦪa=5x5%+6x15%+7x30%+8x25%+9x15%+1Ox10%=7.6.ᑖÊ20÷᝕ÚäDõæᡂçøᑮᜧ᣸ᑡ-5ᑖ1Û6ᑖ3Û7ᑖ6Û8ᑖ5ÛLᑣ᣸ᙠ510.11Ḅp"ᦪ7ஹ8,.ðᦪûü=7.5.ᑖÊ,ᦑ2ᫀ-47.6ஹ7.5ஹ7i
3ᑖᙠ8ᑖ8ᑖmÝḄÛᦪᐳᨵ4860*5+4+2+2஺ýþ.25%+15%+10%=420.ÛÊ.43=:ᑖᙠ8ᑖ8ᑖmÝḄÛᦪᐳᨵ420Û.ூ:௃<⚪ὃABᩩàeஹᡧàem᪵<ÿ
ḄᳮᔜᦪḄᐵ⚪Ḅᐵ.18.ᨵᓻ◅◤⌕ᨚ!"┝ூᑖ᪆௃᝞)⚪◤⌕ᑨ+,CᑮA8Ḅ./ᔲ122503᝞412ᑣᨵᓻ◅ᜧ2ᑣ7ᨵᓻ◅.89:C;2஺ᯠ>᪷@ABᳮᙠDEFEGABCᓽIJKABḄLMᯠ>ᑭᵨFEGḄ☢QRSᓽIJKCC,ᯠ>T2503UVᜧ1ᓽIᑨ+◤⌕ᨚ!"┝.ூW௃X᝞ᡠZ:,C;2,O.XBC=4003AC=3003ZACB=90°,ᙠ[ABCAB2=AC2+BC2AB=>JAC2+BC2=>/3002+4002=5003.VSAABC=JABCD=|BCAC,஺=^/£=24஺3AB♦.•2403V2503.♦•ᙠabᰦẚ!ReABfᨵᓻ◅◤⌕ᨚ!"┝.ூ,g௃)⚪ὃij@ABᳮḄkᵨ⚪Ḅᐵ᪀⌼DEFEGnoᑭᵨ@ABᳮ.pᫀr9⚓ᐳ18⚓

1719.rwxyᫀInz{1500ᐗḄᑭ.ூᑖ᪆௃yᫀX᪷ᑴᡂ᝘ᱏᜩI1ᔴJK4ᜩḄᔴᦪᒕḄD├᝘JKᑭyᫀwX^xᜩ᝘ᱏ(4-x)ᜩ⏚᝘᪷⚪ᑡKyJKyḄ{ᑮxḄaJKᑭUVᓽI{ᑮ4.ூW௃XyᫀXᨬz^4ᔴ᝘ᱏᐸ¢Ḅ᝘D├ᑣᐸᑭ£X4x2000+(9-4)x500=10500(ᐗ)yᫀwX^xᜩ᝘ᱏᑣ^(4-x)ᜩ⏚᝘᪷⚪{Xx+3(4-x)=9,{Xx=1.5,2.5ᜩ^⏚᝘Ḅ᝘3x2.5=7.5ᔴ©IJᑭ£X1.5x2000+3x2.5x1200=3000+9000=12000(ᐗ).•.12000-10500=1500.{ᑮrwxyᫀInz{1500ᐗḄᑭ.ூ,g௃9⚪ὃijᐗ¬yḄkᵨᑖ᪆⚪ᑮᐵ®¯°ᑮᔠ〉Ḅ³´ᐵ⚪Ḅᐵ.20.ZA=ZF,ᳮᵫ¹᪆ூᑖ᪆௃ᐜᵫ/1=/2,{ᑮCE஻9¾I¿NABD=ND,ÀKAC஻஺ÁᑭᵨÂbÃḄឋÅᓽI{K/A=/F.ூW௃Xᳮᵫ᝞XVZ1=Z2,CE//BD,.NABKNC,NC=ND,.ZABD=ZD,.AC//DF,.ZA=ZF.ூ,g௃)⚪Ç⌕ὃijÂbÃḄឋÅÈᑨBÉÊÂbÃḄឋÅÈᑨBᩩÌ⚪Ḅᐵ.21.(l)y=-5x+3(X)0(2)£jÐ{ᨬᜧᑭkÑaA,8ÓxᖪÕᔜ50Ì150ÌIÐ{Ḅᨬᜧᑭ£2750ᐗ.pᫀr10⚓ᐳ18⚓

18ூᑖ᪆௃(1)᪷ᑭ=(Ö-ᡂ))Xᦪ´abJᓽI(2)᪷¬×ᦪḄឋÅJᓽI.(1)Xᵫ⚪{y=(120-110)x+(80—65)(200-x)=-5x+3000(2)X•.•ÚᖪÛÑaAxᖪÕÜ{Ý250Ì504x4100,V-5<0,ßxàᜧá1.•.âx=50!yᨵᨬᜧᨬᜧ£-5x50+3000=2750,200-50=150Ìw£jÐ{ᨬᜧᑭkᑖãÑaA,BÓxᖪÕ50Ì150ÌIÐ{Ḅᨬᜧᑭ£2750ᐗ.ூ,g௃)⚪Ç⌕ὃij¬×ᦪḄå▭kᵨᑡ×ᦪᐵSÉʬ×ᦪḄçᐵÊè⚪Ḅᐵ.22.(1)120,5(2)s=^10/+520(3)1.251!ᡈ2.751!.ூᑖ᪆௃(1)¾ìᵬî31!ᑮï8ðᑣ3x40=120ᓟ3ᓽAஹBÓðḄ./120ᓟ3᪷óîôõḄöM÷£20ᓟ3/!øùóîú!ᡠᵨḄ!£X120+20=61!6+2=8,ᑣ81!>óᑮïᡠnᵬᑮ8ð>51!óᑮï8ð(2)ᑖã⊤Z8ஹ஺Ó,Ḅᙶ᪗ᑭᵨþBᦪÿ
᪆ᑏḄ(3)ᵨᦪEḄ
᪆ᵫḄ!"#$ᐸ
ᓽ'.(1)
*ᵫ⚪,-4)x3=120km,ᵬᑮ8:;<ᑮ=8:◤⌕@120+20-3+2=5D@.ᦑFᫀH*120,5ফFᫀI11⚓ᐳ18⚓

19(2)TABᙢḄP120km,."(3,120),B(10,120),0(13,0),120=10%+஻RST8஺Ḅ
᪆Hs=h+6,ᵫ⚪,-0=13k+Z?%=-40
-:6=520ᵬ^_@Ḅ`$s(ᓟb)c@(D@)ḄdᦪᐵH:s=Y0/+520(10

20ூᑖ᪆௃(1)᝞1ᡠCP,/l+/2=/4C8+/OPEᓽ'-ᑮFᫀ;(2)¡◤⌕Nl+N2=NC+NDPEᓽ'-ᑮFᫀ(3)ᑭᵨ£¤¥᜜¤Ḅឋ¨
ᓽ'(4)ᑭᵨ£¤¥᜜¤Ḅឋ¨
ᓽ'(5)᪷ª⚪,«¥ᑭᵨ£¤¥᜜¤Ḅឋ¨
ᓽ'.(1)
*᝞1ᡠCP,Zl=ZDCP+ZCPD,Z2=ZCPE+ZECP,.\Z1+N2=NDCP+ZCPD+NCPE+NECP=NACB+NDPE,VZACB=70°,ZDPE=60°,.,.Zl+Z2=130°,ᦑFᫀH*130*1(2)
*VZ1+ZCDP=I8O0,Z2+ZC£P=180°,Z1+Z2+ZCDP+ZC£P=360°,VZC=70°,2DPE=Na,NCDP+NCEP+NC+NDPE=360°,.Zl+Z2=NC+NDPE=700+aᦑFᫀH*Zl+Z2=70°+Za;(3)
*RQPc8c¬®VZC+ZCF£)=Z1,ZCFD=Z2+Za,.Zl=Z2+Za+70°,ᦑFᫀH*Zl=Z2+Za+70°*FᫀI13⚓ᐳ18⚓

21c(4)
*᝞ᡠ஺"#Z1=ZDCP+ZCPD,Z2=ZCPE+ZECP,N1+N2=NDCP+ZDPC+ZECP+ZCOD=NACB+360஺-ZDPE,#.Zl+Z2=430°-Za4(5)
*᝞5-1ᡠVZ1=ZC+ZCOD,N2=NP+NP0E,ZCOD^ZPOE,#.Z1-Z2=ZC-NP=70°-Za5-1᝞5-2ᡠ#N1=NP+NPOD,/2=/C+/C0E,NPOD=NCOE,Z2-Zl=ZP-ZC=Za-70°FᫀI14⚓ᐳ18⚓

22ூ௃⚪⌕ὃ£¤¥᜜¤Ḅឋ¨³⚔¤~µµ¶·£¤¥᜜¤Ḅឋ¨P
⚪Ḅᐵ.24.প¹
᪆ফজ(1,0),(3,2)*ঝ(-1,0)ᡈ(2,0)বy=-5x-ioூᑖ᪆௃(1)ᑭᵨA4SACD4º:BECᓽ'(2)জ᪷ªOC=1ᓽ'-ᑮCḄᙶ᪗᪷ªᐰµ£¤¥Ḅឋ¨ᓽ'-ᑮAQ=CE=1,CD=BE=2,w¿-ᑮO£tOC+CQ=3,ᓽ'-ᑮAḄᙶ᪗ঝᑖMᙠÂÃÄÅᙠÂÆÄÇÈÉÊË
ᓽ'(3)᝞ᡠ|8̬4E,|EÌEHLyÍÎ(1)'ÏÐ8Ñ2\8஺4-Ò1Ó8=04EF=OB,AḄᙶ᪗H(-2,0),8Ḅᙶ᪗H(0,3),w¿EḄᙶ᪗H(-3,5),ᓽ'ᑭᵨᦪ
.(1)
*'JADA.DE,BELDE,.ZD=ZE=90°■:ZACB=90°,ZACD=90°-ZBCE=ZCBE,Ô*C4=BC,/O=NE=90஺./\CDA^/\BEC(AAS)*1ফ
*জ•.•:CD4Ö:BEC,OB=2,OC=\,.AD=CE=\,CD=BE=2,CḄᙶ᪗H1,0,.OD=OC+CD=3,FᫀI15⚓ᐳ18⚓

23.♦.AḄᙶ᪗H(3,2)ᦑFᫀH*(1,0),(3,2)ঝ᝞2-1ᡠolᙠÂÃ×@AM,AO,Ø0ஹAஹBஹÙH⚔Ḅº×¥Ḅ☢ÛHS,♦•S-+SMOB^-OBOD+-OMAD22=-x2x3+-OM22=3+-OM2=4,OM=2,MḄᙶ᪗H(2,0)᝞2-2ᡠoMᙠÂÆÄ@BM,OA,••S-S^BOM+=-OBOD+-OMOD22=-x2x3+OM2=3+OM=4,OM=1,FᫀI16⚓ᐳ18⚓

24ÜMḄᙶ᪗H(-1,0)ÞßᡠàMḄᙶ᪗H(-1,0)ᡈ(2,0)(3)
*᝞ᡠ|B̬E,|EÌE£LyÍRᵫ⚪,-/ä8=45°,'#EB±AB,#.ZAEB=45°=ZEAB,.•.ÏABEPµῪ椣¤¥Î(1)TiJiiEAEFB^/XBOA(AAS),#.BF=OA,EF=OB,•AஹBᑖêPæS4*y=^x+3cxÍḄ¬c)Í-ᑮ¬.••AḄᙶ᪗H(-2,0),8Ḅᙶ᪗H(0,3),.•.BF=OA=2,EF=OB=3,#.OF=OB+BF=5,••EḄᙶ᪗H(-3,5),RæS4Ḅ
᪆H>=î+"-3k+b=5-2k+b=0k=-5b=-\0FᫀI17⚓ᐳ18⚓

25/.æS&Ḅ
᪆Hy=-5x-\o3ூ௃⚪⌕ὃpdᦪcðñÞᔠᐰµ£¤¥Ḅឋ¨cᑨᙶ᪗c¥µµ¶·ᐰµ£¤¥Ḅឋ¨cᑨᩩõP
⚪Ḅᐵ.FᫀI18⚓ᐳ18⚓