2019-2020学年天津市七年级（下）期末数学试卷（附答案详解）

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2019-2020
ᜩᓭ᪥
ᦪᔁ1.ᑡ〉ᵨ᪵Ḅ"A.
#$%Ḅ&'()B.*ᙶ,-Ḅ./"ᔲ123Ἥᱥ6C.᪥ᙠ8%9ᑴ᪥;<=>ᜧ@ḄD.#6ABḄCᵨDE2.᝞G41,42"HIJḄ"3.ᑡE⚪LMNE⚪Ḅ"A.O⊡ḄJ"Q⊡JB.ᙠHRS☢ᑁ᝞Va_Lb,b1c,ᑣa1cC.HIJXYD.ᙠHR■S☢ᑁ᝞Va஻b,b//c,ᑣa஻c4.ᙠS☢\Jᙶ᪗^_`4-1,-2
ᔣbSc3dᓫIfghᑮ`5,ᑣ`Bᡠᙠk▲mA.nRk▲B.npk▲C.nqk▲D.nrk▲5.sY4Q-1
W3x-2Ḅt᦮ᦪvḄdᦪ"A.0B.1C.2D.36.Rdwxm80Ḅ᪵yᨬᜧ{m143,ᨬ@{m50,|}~m10,ᑣᑖᡂA.10}B.9}C.8}D.7}7.RdtᦪḄdS᪷"2m-43m-1,ᑣḄ{mA.—3B.—1C.1D.8.qJḄᑡ_qJḄ☢ᑖᡂXYᑖḄ"A.B.JSᑖC.D.s9.᝞GᑡᑨAB஻CDḄᩩḄdᦪ"জ+/BCO=180"ঝ42=43ঞ41=Z4;CEটNB=z5.

1A.IdB.2dC.3dD.4d10.r¨ABC஺ª4«BZC«4஺=2«3«2«5,ᑣ4BḄgᦪ"()A.60°B.90°C.120°D.150°11.᝞GᨵRᙽ\JqJ·xrz»¼ᙠA/IBCqJ·XYZḄᩩ\J¨XKxzᦋÂI¼ÃÄÅÆÇÈÉBஹC`.᝞VËABCª4=52஺ᑣª4BX+/.ACX=()12.ÍÎ`P(x,y)ᙠnpk▲ÑyW2x+6,x,yᙳm᦮ᦪᑣ`PḄdᦪ"()A.3B.6C.10D.ᦪd13.ÍÎqJḄ¨fᑖÔ"46,ᑣnqᩩ¨fxḄ|{Ö".14.9ḄS᪷".15.`Pᙠnpk▲ᑁ×ÑᑮxØḄ~Ùm2,ᑮyØḄ~Ùm3,ᑣ`ÚḄᙶ᪗m16.dJḄ¨ᑖÔSÛÜᐸRdJÞßRdJḄ2àá30஺ᑣâdJḄgᦪᑖÔm.17.᝞G\8CÈÉå`஺`4ᙠxØ,4஺1BCM஺.Ü4(4,0)ஹB(m,3)ஹC(n,—5),ᑣAD-BC=.n2⚓ᐳ15⚓

2r18.ÍÎx=l+2a,y=l-a,ᐸR2WaW3,ᨵᑡrdîï«®-3C#$%&Ḅ"9D.22.᝞F,4஺44BCḄI,AE,BF44BCḄLMᑖOCBF=32஺P4FB=72".(1)/840=°B(2)TZZMEḄWᦪB(3)XYGDO[8C=\-]Y^AGFCD_L`LabᑣT/BFGḄWᦪ.

3BDE23.ᵬஹPfᖪhij᪵lm@nj᪵Ḅᖪo7pqᔜst@#jḄuvwᫀᙠᵬᖪhyzᱥ|}100ᐗ|@100ᐗḄᑖᢥ90%ᦈBᙠPᖪhyzᱥ|}50ᐗ|@50ᐗḄᑖᢥ95%ᦈᙠj]ᖪhyzᱥxᐗᐸx>100.(1)᪷⚪-ᑏ⊤(ᓫᐗ);yzᱥ130290X▭ᙠᵬᖪh127—…—ᙠPᖪh126—•—(2)^xbᙠᵬஹPfᖪhḄ▭j(3)^ᙠj]ᖪhyzᱥ|}100ᐗbᙠᖪhḄ▭24.᝞F1,aABC஺ᔜ⚔YḄᙶ᪗ᑖ¡D(-2,8),(-11,6),(-14,0),(0,0).(1)OC=YAᑮx<Ḅ¤¥D.(2)TaABCOḄ☢§.(3)᝞F2,YPDx<¨©<=Ḅ]ªY,YP«ᔲᙠ]®¯44PABḄ☢§«a4BC0☢§Ḅ]©Xᙠ)T@YPḄᙶ᪗BX#ᙠ)°±ᳮᵫ.´4⚓ᐳ15⚓

42ᫀ·"᪆1.ூ2ᫀ௃Dூ"᪆௃"4»¼½¾¿ÀÁÂÃḄÄÅÆÇ〉ᔠᐰ☢»¼Ê˼Ìᦑ0⌱⚗#ᔠ⚪-BA»¼ÐᙶÑÒḄÓÔ«ᔲÕÖ×Ἥᱥo〉ᔠᐰ☢»¼Ê˼Ìᦑ0⌱⚗#ᔠ⚪-BC.Â᪥ᙠÚÂÃÛᑴ᪥ÝÞßàᜧḄ»¼〉ᔠᐰ☢»¼Ê˼Ìᦑ0⌱⚗#ᔠ⚪-BD»¼ÀoãLEQæḄ¯ᵨèé〉ᔠê᪵»¼ᦑ0⌱⚗ëᔠ⚪-Bᦑ⌱D.ᵫ˼4ᑮḄ»¼*ìíîïðñᡠóÅஹᱥÅ·bôîõöê᪵»¼4ᑮḄ»¼*ìíî÷ø.0⚪ὃ¼úê᪵»¼·ᐰ☢»¼Ḅû¡⌱ü˼ý«ê᪵»¼⌕᪷ᡠ⌕ὃ¼ḄÿḄᱯᮣ⌱ᵨᩭᐹᨵẚឋḄஹஹḄᡈ!ᜧ#$⌱%&᪵()*⌕,-Ḅ.ᐵ0ᜧḄ11⌱ᵨ.2.ூ6ᫀ௃Bூ9᪆௃9;4!=“F”A=ᑁ┯DᦑF⌱⚗!Hᔠ⚪KL=“M’A=OPDᦑF⌱⚗Hᔠ⚪KC.!=“F”A=ORᑁDᦑF⌱⚗!Hᔠ⚪KD!=“F”A!=OPDᦑF⌱⚗!Hᔠ⚪;ᦑ⌱;B.᪷UOPD=V᝞XY“F"᎔\]^ᡈ_\`ᑨbᓽd.OPDḄe;fᩩhijklᩩhiᡠnVᡂḄDpqfrDsᙠfhiḄOuvwᙠklᩩhixniyḄORᑣ{᪵D|}OPD.~⚪ὃOPDᑁ┯DORᑁDᑖḄᱯ=9⚪Ḅᐵ.3.ூ6ᫀ௃Dூ9᪆௃ூᑖ᪆௃~⚪ὃ⚪eᳮ;ᑨb.ᱥḄ|⚪KL)Ḅ⚪⚪┯Ḅ⚪Ꮇ⚪KᳮḄ⚪eᳮ.᪷U⊡DḄeAᑨbK᪷UiḄឋ8ஹCஹ஺ᑨb.ூ
௃9;Aஹ⊡ḄD!e=⊡DᡠA⌱⚗Ꮇ⚪KBஹᙠO☢ᑁ᝞¡aJLb,b1c,ᑣa஻c,ᡠB⌱⚗Ꮇ⚪;CஹfhiOPDª«ᡠC⌱⚗Ꮇ⚪K

5DஹᙠO☢ᑁ᝞¡a஻b,bl/c,ᑣd/c,ᡠ஺⌱⚗⚪.ᦑ⌱;D.4.ூ6ᫀ௃Dூ9᪆௃9;4(-1,-2)ᔣ¯°3rᓫP²*³ᙶ᪗¶-1+3=2,¸ᙶ᪗!¶ᡠᡠ¹Ḅᙶ᪗(2,-2),ᙠkº▲ᦑ⌱;D.᪷UḄ°¼½¾¯°³ᙶ᪗¿À¸!¶Á°¸ᙶ᪗À¿³!¶ᓽd9Ḅ6ᫀ.~⚪ὃᑭᵨ°96ᙶ᪗ÄVḄ¶ᓄ°pḄ¶ᓄ¼½=;³ᙶ᪗¯°À¾°¿K¸ᙶ᪗Á°À°¿.5.ூ6ᫀ௃Cூ9᪆௃9;`Æǹ;4x—4<3x—2,°⚗¹;4x-3x<4-2,ᔠvOÈ⚗¹;x<2,ᑣL᦮ᦪ9=;1,2.ᦑ⌱;C.`ÆÇஹ°⚗ஹᔠvOÈ⚗ᯠÌÍᦪᓄᡂ1ᓽd,¹!«ÎÏḄ9ÐᯠÌ)eL᦮ᦪ9ᓽd.~⚪ὃᐗÒ!«ÎḄ᦮ᦪ9L)9!«Î,Ó9Ð=96~⚪Ḅᐵ.9!«Î$᪷U!«ÎḄÔ~ឋ.6.ூ6ᫀ௃Aூ9᪆௃9;ᙠ᪵~ᦪUpᨬᜧ143,ᨬÖ50,Ḅ×=143-50=93,ØÙÏÚ10,ÛÜᵫÞ=9஺ᦑdᑖᡂ10Ï.1010ᦑ⌱;A.᪷UÏᦪ=(ᨬᜧ-ᨬÖ)+ÏÚãäåÖᦪæᑖ⌕P.~⚪ὃḄ=ÏᦪḄãäçÔẠ⚪é⌕᪷UÏᦪḄe“ᦪUᑖᡂḄÏḄrᦪÏᦪ”ᩭ9ᓽd.7.ூ6ᫀ௃Cூ9᪆௃9;ᵫ⚪d¹;2m-4+3m-1=0,9¹;m=1,ᦑ⌱;C.᪷UrLᦪᨵfrê᪷ª_ᦪᑡÓêì,ÓíḄ.k6⚓ᐳ15⚓

6~⚪ὃḄ=ê᪷ḄᭆñòórLᦪᨵfrê᪷ª_ᦪK0Ḅê᪷=0;ôᦪõᨵê᪷=9⚪Ḅᐵ.8.ூ6ᫀ௃Cூ9᪆௃9;•••lDVḄpi÷lDVᑖᡂfr«øO-ḄlDV•••lDVḄpiùlDVḄ☢úᑖᡂª«fæᑖ.ᦑ⌱;C.᪷U«ø«-ḄlDVḄ☢úª«96.~⚪ὃlDVḄ☢úû⌕ᑭᵨ“lDVḄpi÷lDVᑖᡂfr«øO-ḄlDV”ḄÙü~Ùü=pý▤ÿ
Ḅ☢ᵨ⌕ᮣᵨ.9.ூᫀ௃Aூ᪆௃জND+NBCC=180஺ᵫ"#ᑁ%⊡'()*+,4D஻BC,ᦑজ/0ᔠ⚪34ঝ42=43,N264378"#ᑁᦑ/9ᑨ;4B஻CD,ᦑঝ/0ᔠ⚪34ঞ41=44,4164478"#ᑁᦑ/9ᑨ;4B஻CD,ᦑঞ/0ᔠ⚪34টNB=N5,N164578">ᵫ">?@'()*+,AB஻CD,ᦑট0ᔠ⚪34ᦑAᨵ1C9ᑨ4B஻CD,ᦑ⌱A.᪷F*+)ḄᑨᩩHI+ᑖ᪆ᓽL.M⚪N⌕ὃP*+)ḄᑨḄᐵRST*+)ḄᑨᩩHᮣUᵨ.10.ூᫀ௃Bூ᪆௃VN4=2X஺
ᑣNB=3X஺
ZC=2x°,zD=5x°,᪷FXYḄᑁZ[360஺,\4+48+NC+4஺=360°,ᓽ2x+3x+2%+5x=360,•x—30»Z.B=3x°=90°.ᦑ⌱B.ᐜV\4=2x஺ᑣzB=3x஺zC=2x°,Z.D=5x\_᪷FXYḄᑁZ[360஺ᑡabcdeᦪᑣL,NBḄg.M⚪ὃPhiYᑁ6᜜M⚪klV〉nḄoᦪ᪷FXYḄᑁZ[360஺pqabcrxḄgs_c48Ḅg.

711.ூᫀ௃4ூ᪆௃tuAX,•••BXC=90°,♦AXB+Z.AXC=360°-Z.BXC=270°,•44=52°,:.BAX+4C4X=52°,vZ-ABX+(BAX+AXB=180°,Z.ACX+^CAX+Z-AXC=180°,•••^ABX+Z.ACX=360°-270°-52°=38°,ᦑ⌱A.᪷F⚪3vrᔠ〉Ḅwx)_᪷F
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Yᐵ§TឋºS⚪ḄᐵR.14.ூᫀ௃±3ூ᪆௃¿±3Ḅ*aS9,9Ḅ*a᪷S±3.ᦑᫀ[±3.(uᑭᵨ*a᪷ḄÁÂÃᓽL.Ä⚪N⌕ὃPh*a᪷ḄÁ⌕Å3CÆÇᦪḄ*a᪷ᨵ'C%[?ÈᦪÉg[ÃÊ*a᪷.15.ூᫀ௃(3,2)ூ᪆௃•••Pᙠ▲ᑁ•••ḄÑᙶ᪗¶80,Óᙶ᪗ᜧ80,•••ᑮxÖḄ×Ø[2,ᑮyÖḄ×Ø[3,•••ḄÑᙶ᪗S-3,Óᙶ᪗S2.ᑣPḄᙶ᪗[(-3,2).ᦑᫀÛ(-3,2).ᐜᑨ;rPḄÑÓᙶ᪗Ḅ0ÜI£᪷Fᑮᙶ᪗ÖḄ×Øᑨ;ᐸᐹßᙶ᪗.M⚪N⌕ὃPh*☢(ᙶ᪗§à▲ḄḄᙶ᪗Ḅ0Üᱯ¦Ḅᙶ᪗Ḅáâ3ÁᑮxÖḄ×Ø[ḄÓᙶ᪗ḄãägᑮyÖḄ×Ø[ḄÑᙶ᪗Ḅãäg.16.ூᫀ௃70஺110°ூ᪆௃ூᑖ᪆௃Ä⚪ὃPh*+)Ḅឋº.Ä⚪è{〉à⚪ḄᐵRSÅ3ᵫ'CḄ'Yᑖé*+,L,ê'C?@ᡈ%⊡ᵫ'CḄ'Yᑖé*+L,ê'C?@ᡈ%⊡LVᐸàC[ᵫᐸàCëìCḄ2íî30,ᓽLᑡababᓽLc,ê'CḄ{ᦪ.ூ௃•••'CḄ'Yᑖé*+••.ê'C?@ᡈ%⊡VᐸàC[£••ᐸàCëìCḄ2íî30,•••ê'C%⊡ᑣ2(180-x)-x=30,,x=110,

9•.ê'CḄ{ᦪᑖé[110஺70°4ê'CḄ{ᦪᑖé[70஺110°.ᦑᫀ[70°,110°17.ூᫀ௃32ூ᪆௃lBvBE1Ö8£,lCvCFJLyÖ8÷,•,B(m,3),•BE=3,•••4(4,0),•AO=4,vC(n,—5),•OF=5,iiS&AOB=~A0-BE=-x4x3=6,S-oc=%஺.OF=x4x5=10,S^AOB+S^AOC=6+10=16,VS&ABC=SAAOB+sAAOC.-BC-AD=16,2:.BC-AD=32,ᦑᫀ32Ḅ᪷ᙶ᪗BEஹOA.஺$Ḅ%ᑭᵨ☢)*+,-4).0⚪ὃ34ᙶ᪗56ឋ8᪷9Ḅᙶ᪗⊤;<=>Ḅ%☢)*ᙠ@AB⚪CDEFᵨ⌕HIJKL0⚪᪷☢)*>Ḅ).18.ூᫀ௃জঞூR᪆௃Rx=1+2a,y=1-a,ᐸCV2

10v%=1+2Q,y=1—a,,%+y=2+a,v-2

11ூR᪆௃wᑭᵨ᪷ஹ᪷ᓽ+¡.¢⚪ὃ34£ᦪḄFHIJKF*ᑣrR0⚪Ḅᐵ{.21.ூᫀ௃x>-lx<4-l1জூR᪆௃R¦_,/+2x§Rwজ-xN—1LRwঝ-xீ4L©ªwজঝR«ᙠᦪ¬⊤;ᩭ;-7-6-5-4-3-24012356>w¯ḄR«V1

12(2)(3)Éᫀ஺(1)᪷ÊËᑖ᪆ḄN4BCᓽ+RÎB⚪.(2)᪷=BAE-ABAD,NB4Eᓽ+RÎB⚪.(3)ᑖ¹º»জ¼"GC=90஺¾.ঝ¼4GFC=90஺¾ᑖÒRᓽ+.0⚪ὃ3ᑁÓᳮḄ᜜Ḅឋ8ᑖḄÖR⚪Ḅᐵ{rHIJK×0ÖØÙCὃEὃ⚪Ú.23.ூᫀ௃R(1)271L0.9x4-10L278L0.95x4-2.5L(2)᪷⚪}-0.9x+10=0.95x+2.5,R-x=150.¼x150¾oÛᙠᵬஹÇᖪÞḄ£▭àáL(3)ᵫ0.9x+10<0.95x+2.5,R-:x>150,ᵫ0.9x+10>0.95x+2.5,R-x<150,§¼oÛäåᱥᜧÙ150¾⌱éᵬᖪÞ£▭àáêL¼äåᱥ_ë150ᐗ¾ᖪÞàáL¼oÛäåᱥìí100ᐗuᑮ150ᐗ¾ᙠÇᖪÞ£▭àáê.ூR᪆௃ூᑖ᪆௃¢⚪⌕ὃ34VᐗV·wḄ=ᵨÓVᐗV·îḄ=ᵨïðᫀ⌱é¾=5îᡈwὶòóᩭ.প᪷¹ôõᫀᓽ+L(2)᪷⚪C(1)CḄpq-ᑮ0.95x+2.5=0.9%+10,Rî-_`pqL(3)᪷0.95%+2.550.9%+10÷øtu-_`pq.ூR௃R(1)ᙠᵬᖪÞ100+(290-100)X0.9=271,100+(%-100)x0.9=0.9%+10LᙠÇᖪÞ50+(290-50)x0.95=278,50+(X—50)x0.95=0.95%+2.5L(2)(3)Éᫀ.24.ூᫀ௃148ூR᪆௃R(1)ᵫ⚪}OC=14,9Aᑮx¬Ḅúû8.ᦑᫀ14,8L(2)᝞6í944F1X¬ÙF,í9BBE_Lx¬ÙE.

13••A(—2,8),•OF=2,AF=8,.OE=11,BE=6,EF=0E-0F=9,(CE=0C-0E=3,••S&BCE=2CE,BE=~X3X6=9,S&AOF=\OF-AF=ix2x8=8,SÿᷨEFA="BE+”)-EF=X(6+8)X9=63,,1,S)*+ABCO=Sf0F+S,+BEFA+5AFCE=8+63+9=80,ABC஺Ḅ☢80.(3)ᙠ.ᳮᵫA/x8BH11"-.P/PN110N.P(m,0).•AN=m4-2,PN=8,AH=9,BH=2,HN=11+m,•••S-BH=.4H=x2x9=9,14⚓ᐳ15⚓

14S^APN=\AN,PN=gx(m+2)x8=4(m+2),S,+BHNP="B"+PN)•HN=X(2+8)x(11+m)=5(m+11),APB=S,+BHNP~~ABH-S^ANP=5(m+11)-9-4(m+2)=m+38,,S&ABP=)*+ABCO=3*8஺=4G,:.m+38=40,m=2,.•.ᙠ$%^P48Ḅ☢'4BC஺☢Ḅ()P(2,0).(1)ᑭᵨᙶ᪗ᱯ/012⚪ᓽ56(2)᝞8A9F1xF,8BE1%E.᪷Ḅ?0=S“OF+S,+BEFA+SABCE1A0ᓽ56(3)ᙠ.A/X-.B/BH1I0H,PPN12N.᪀CDEA0ᓽ5.F⚪GHᔠ⚪ὃKLḄ☢☢Mᙶ᪗NOPQ0⚪ḄᐵS'TUᑭᵨᒘ⊡XA☢TUᑭᵨYᦪ᪀CDE012⚪.