2021-2022学年河北省秦皇岛市青龙县七年级（下）期末数学试卷（附答案详解）

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2021-2022
ᓅḕḇ☘
ᦪᔁ1.ᑡᐗḄ()A.x+2y=3B.x2+y=1C.y+!=2D.2&1=52.ᓄ#a3-a2Ḅ$%()A.aB.a6C.a5D.a93.ᙠ)*☢ᑁ-./ᔠ123Ḅ45ᐵ78A.ᚖ2B.*:C.ᚖ2ᡈ*:D.?@ᡈ*:4.2஺Ḅ<=A.—2B.0C.ID.25.ᑡABC-.D⚪ḄA.1FGH3IᨬKB.*:t)23Ḅ123*:C.LMA,B
D.ᑁ┯vw?x6.᝞O-PᙢR:STᑜ-ᙠᩩWXYZ[ᨵ]-^⌕`abcd-eᨵAஹBஹCஹ஺gaᙢFhi⌱k.m⌕n]opbcdᨬq-ᑣbcds`ᙠA.FAᜐB.F8ᜐC.FCᜐD.F஺ᜐ7.z{x>y,ᑡ.x|C┯}ḄA.x+10>y+10B.x-2>y—2C.3x>3yD.-5%>—5y8.᝞O-23a஻b,41=66஺-ᑣ42xt()A.66°B.33°C.24°D.14°9.ᑡḄA.a2+a3=a5B.a6a3=a2C.(a2)3=asD.(ab2)3=a3b610.ᑡx|ᑮḄ-|ᑖḄA.(x+y)(x—y)=x2—y2B.x2—2x+1=(x—l)2C.x2+2x+2=(x+l)2+1D.12xy2=2x-6y211.avḄᑖ=xஹ3ஹ4,xḄ<()A.11

112.ᓅH2022
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225.᝞ᡠᩩAB஻CE,ᑣḄᩩAEB26.(஺-2)2+|281|=0,ᑣ஺2஺22,021Ḅ.27.!"#$ᡈ&'(প!"#$:+,g(2)!&'(:2%-3
ᑶ.28.ᐜᓄ012(x—y)2+(x—y)Q+y),ᐸ4x=3,y=i.29.5ᡂ7☢Ḅ9:.᝞;ZiABC,29z/1+ZF+ZC=180°.9:<=8cᑮ஺?CE஻@B,VCE//AB,••Z.A=(),B=().•••B4CB+41+42=180஺(CDḄEF)Z.A+Z.B+Z.ACB=180°().30.᝞AD//BE,41=42,29Z.A=Zf.31.HIJK“MNᐰPᦻ:RI”TUVWXᵬZᝄ\]2BZᝄ\ᐳ◤220ᐗWX2ᵬZᝄ\]3BZᝄ\ᐳ◤360ᐗ.(1)2`ᵬZᝄ\]`BZᝄ\Ḅabᑖdefᐗg(2)hiᑜWXᵬZᝄ\]BZᝄ\ᐳ30klᵨ&en2300ᐗopᨬfrWXᵬZᝄ\efg32.AABC4জ44BஹCḄCᑖtuvnM,ঝ4NBஹNCḄ᜜DCᑖtuvnN.

3পhNA=80°,4BMC=°,Z.BNC=(2)hB4=/?,yᵨ/?⊤NBMC]/BNC.4⚓ᐳ14⚓

4}ᫀ]!᪆1.ூ}ᫀ௃Aூ!᪆௃!A⌱⚗ᨵᦪᨵᦪḄ⚗Ḅᦪ1,ᔠ⚪B⌱⚗xḄᦪ2,&ᔠ⚪C⌱⚗&᦮("#&ᔠ⚪஺⌱⚗&ᦪ&ᔠ⚪ᦑ⌱A.᪷ᐗ"#ḄEFᑨᓽr.⚪ὃ¢£ᐗ"#ḄEF¤¥ᐗ"#ḄEF!⚪Ḅᐵ§ᨵᦪᨵᦪḄ⚗Ḅᦪ1,¨©᪵Ḅ"#«¬ᐗ"#.2.ூ}ᫀ௃Cூ!᪆௃!a3-a2=a5.ᦑ⌱C.®ᑭᵨ°±ᦪ²Ḅ³´µ¶´ᑣi¶·¸}ᫀ.¹⚪º⌕ὃ¢£°±ᦪᗩḄ³´µ¶½¾¤¥µ¶´ᑣ!⚪ᐵ§.3.ூ}ᫀ௃Dூ!᪆௃!ᙠ°C☢ᑁᩩtÂᨵZÃÄᐵÅᓽCÆᡈuv.ᦑ⌱D.ᑭᵨ°C☢ᑁᩩtḄÃÄᐵÅ!}°C☢ᑁᩩtḄÃÄᐵÅᨵZ:CÆஹuv.⚪º⌕ὃ¢£°C☢ᑁᩩtḄÃÄᐵÅ!⚪Ḅᐵ§ÇᚖuvḄZᱯÊËÌ&ÍᓫÏ?Ð.4.ூ}ᫀ௃Cூ!᪆௃!(-2)0=1.ᦑ⌱C.᪷Óᢣᦪ²Ḅµ¶´ᑣ2¸(-2)஺Ḅὃ¢£ÓᢣᦪÕa஺=l(a0),ᵫ^am=l,amam=am-m=a஺rÙ¸a஺=l(aRO),Ç0°ᱏ1.5.ூ}ᫀ௃Cூ!᪆௃!@ßàátâᨬ,ã⚪⌱⚗&ᔠ⚪8ஹCÆn°tḄtCÆã⚪⌱⚗&ᔠ⚪

5Cåæ®A,Bß&ã⚪⌱⚗ᔠ⚪஺ஹᑁ┯Du'ã⚪⌱⚗&ᔠ⚪ᦑ⌱C.᪷ã⚪ḄEFᑨᓽr.⚪ὃ¢ã⚪èEᳮ!⚪Ḅᐵ§¤¥ã⚪ᑨêËḄëìín4ὃîὃ⚪ï.6.ூ}ᫀ௃Cூ!᪆௃!NᙠßCᜐ᪷ᚖtâᨬ,ᦑ⌱C.᪷ᚖtâᨬ,·¸ᓽr.⚪ὃ¢£ᚖtâᨬ,òó¤¥ᚖtâᨬ,ḄTß!¹⚪Ḅᐵ§.7.ூ}ᫀ௃Dூ!᪆௃!A⌱⚗&'(õ10,&'öḄ"ᔣ&øᦑù⌱⚗½¾&ᔠ⚪B⌱⚗&'(õú2,&'öḄ"ᔣ&øᦑù⌱⚗½¾&ᔠ⚪C⌱⚗&'(õ³3,&'öḄ"ᔣ&øᦑù⌱⚗½¾&ᔠ⚪஺⌱⚗&'(õ³-5,&'öḄ"ᔣᦋøᦑù⌱⚗┯üᔠ⚪ᦑ⌱D.᪷&'(Ḅýឋÿᑨ
ᓽ.⚪ὃḄឋḄᡈ◀ᦪḄᔣᦋ#.8.ூ'ᫀ௃Aூ+᪆௃+-•.•/0a஻b,:.z.2=Z.1=66°.ᦑ⌱-A.ᑭᵨAB0ḄឋCᳮEFᓽ.⚪ὃḄGAB0Ḅឋ+⚪ḄᐵIGJKLM/0ABNOPQ.9.ூ'ᫀ௃Dூ+᪆௃+-AஹTQ3UVNW⚗Yᔠ[ᦑA\ᔠ⚪]Bஹa6-T-a3=a3,ᦑ8\ᔠ⚪-Cஹ(a2)3=a6,ᦑC\ᔠ⚪]Dஹ(ab2)3-a3b6,ᦑ஺\ᔠ⚪]ᦑ⌱-D.a6⚓ᐳ14⚓

6ᑭᵨᔠ[NW⚗ḄdᑣNfᦪgḄ◀dḄdᑣhḄTiḄḄdᑣjᔜ⚗lBmnᓽ.⚪o⌕ὃNfᦪqḄ◀dᔠ[NW⚗gḄTiḄ+'ḄᐵIGjQrḄmndᑣḄLM.10.ூ'ᫀ௃Bூ+᪆௃+-4stᑮvḄ#wG᦮dUVyᑖ+ᦑ⌱⚗\ᔠ⚪{]AstᑮvḄ#wUVyᑖ+ᦑ⌱⚗\ᔠ⚪]C.stᑮvḄ#wUVyᑖ+ᦑ⌱⚗\ᔠ⚪]஺.stᑮvḄ#wUVyᑖ+ᦑ⌱⚗\ᔠ⚪]ᦑ⌱-B.᪷}yᑖ+~G⚗ᓄ᦮ḄiḄwḄCᑨ
ᑭᵨ᣸◀d+.⚪ὃyᑖ+ḄW⚪ḄᐵIᙠVGᔲrᵨᑖ+yḄCᩭᑨ
.11.ூ'ᫀ௃Bூ+᪆௃+-•••PwḄᑖXஹ3ஹ4,4—3

7¯⚪ὃ+ᐗ¾·JKLM·Ḅ+dG+⚪ḄᐵI.14.ூ'ᫀ௃Cூ+᪆௃+-y41=58஺NB=60஺ᡠ42=zl+Z.S=58°+60°=118°,ᦑ⌱-C.᪷}Pw᜜PḄឋ¶42=41+Én+.⚪o⌕ὃPw᜜PḄឋLMPw᜜PḄឋG+⚪ḄᐵI.15.ூ'ᫀ௃Dx—y=1জூ+᪆௃+-Ëy—z=1ঝx+z=6ঞঝ+ঞ¶-x+y=7®,জ+ট¶-2x=8.ᓽx=4,x=4Òᐭজ¶-y=3,x=4Òᐭঞ¶-z=2,%=4ᑣÕ·Ḅ+y=3,2=2ᦑ⌱-D.Õ·ᑭᵨÖ×Øᐗd+ᓽ.⚪o⌕ὃ+ᐗ¾Õ·+ᐗ¾Õ·ḄdGᑭᵨÒᐭdᡈÖ×dØÙÚÛᦪ¶ᑮÜᐗ¾Õ·ᯠÞ+Üᐗ¾Õ·ÚÛᦪḄßaÚÛᦪḄ.16.ூ'ᫀ௃Bூ+᪆௃+-^ACD+/.CAB=180°,vZ.ACD=40°,.•.NCAB=180°-40°=140°,•••4EAᑖ"AB,•••Z.EAB=70°,•••AB"CD,•••Z.AEC==70°,ᦑ⌱-B.᪷}AB0ឋ/CABḄåᦪ᪷}PAᑖ0NEABḄåᦪ᪷}AB0ឋæ4ECḄåᦪᓽ.a8⚓ᐳ14⚓

8⚪ὃPAᑖ0CAB0ឋḄrᵨ+⚪¥-ᩩAB0èaᩩ/0ᡠéNêᑁPì⊡.17.ூ'ᫀ௃(a+l)(a—1)ூ+᪆௃+-a2-1=a2-I2=(a+l)(a-1).ὃjA»Ḅᳮ+⚪UVẠ⚪.⚪¤A⚗Ḅ\Qò/ómᵨA»ᑖ+y.⚪ὃ»dᑖ+yJYᵨA»ᑖ+yḄ⚗Ḅᱯõᓽ“⚗ஹ÷ஹAw”Gøù┯ᵨA»Ḅᨵᦔd.18.ூ'ᫀ௃3%<4ூ+᪆௃+-ᵫ⚪¶-3x<4.ᦑ'ᫀG-3x<4./ó⊤¢xḄ3ÿ3x,4,ᓽ.⚪⌕ὃᵫ▭⚪ᐗ!ᑡᐵ$%&⚪ᐵ'.19.ூ,ᫀ௃y=3x+5ூ&᪆௃&4563x-y+5=0,&4y=3x+5.ᦑ,ᫀ4y=3x+5.:x;<=>ᦪ@)ᓽ.⚪ὃ&Bᐗ56&⚪Ḅᐵ'%DEF>ᦪ;<=>ᦪ@GEF>ᦪ.20.ூ,ᫀ௃-3ூ&᪆௃&4•JKB:1%562%—Qy=—lḄE&:_:RSᐭ562%—ay——142+a=-1,&4Q=-3,ᦑ,ᫀ4-3.:VJ:Sᐭ562x-ay=-12+a=-1,X@56Ḅ&ᓽ•Y⚪ὃBᐗ56Ḅ&Z&ᐗ56[᪷]⚪^ᐵaḄᐗ56%&⚪Ḅᐵ'.21.ூ,ᫀ௃36஺ூ&᪆௃&4•••41a42%b⚔d•••Z1=Z2.)•:N1+42=72",

9•-241=72°.zl=36°.ᦑ,ᫀ436஺.᪷]b⚔dḄឋi&j⚪.Y⚪⌕ὃb⚔dklmnb⚔dḄឋi%&jY⚪Ḅᐵ'.22.ூ,ᫀ௃0ஹ1ஹ2ூ&᪆௃&4pJ:4Ḅ&q1“vᜧxᜧKvxKᜧᜧyz{Kᜧᜧ{ᑮ”Ḅᑣ%&,⚪Ḅᐵ'.23.ூ,ᫀ௃12ூ&᪆௃&4=y=3,aAax+y=ax-ay=4x3—12,ᦑ,ᫀ412.᪷]vᦪḄᑣᓽ.Y⚪ὃvᦪḄklmnvᦪḄᑣ%&⚪Ḅᐵ'.24.ூ,ᫀ௃15ூ&᪆௃&:(x+y)(x-y)=x2-y2,xz-y2=5x3=15,ᦑ,ᫀ415.ᑭᵨ(x+y)(x—y)=/2ᓽ.Y⚪ὃᦪḄᐰ5Ḅ&⚪ᐵ'ᙠ!Ḅ.25.ூ,ᫀ௃zB=N0CE(,ᫀ)ூ&᪆௃&4Ḅᩩ¡448=4஺(K/,ᫀ),:Z.B-Z.DCE,[4B஻CE(v£d¤¥¦§)ᦑ,ᫀ44B=4DCE(,ᫀ).᪷]§Ḅᑨ}}ᳮ@&ᓽ.ª10⚓ᐳ14⚓

10⚪ὃ§Ḅᑨ}aឋik§Ḅᑨ}}ᳮ%&⚪Ḅᐵ'.26.ூ,ᫀ௃2ூ&᪆௃&4■.•(a-2)2+|2h-l|=0,••a—2=0,2b-1=0,&4a=2,b=Iᑣa2022.2021=22022.(-1)2021=2X(2X1)2021=2.bᦑ,ᫀ42.ᑭᵨ³´ᦪḄឋi@aaᓃḄ¶Sᐭᓽᑮ·¸.⚪ὃ³´ᦪḄឋiᳮ&Ꮤ5Zºb¶Ḅ³´ឋ%&Y⚪Ḅᐵ'.27.ூ,ᫀ௃&4(1){?+K=*&3x-2y=3ঝজX2+ঝ4llx=33,&x=3,Dx=3Sᐭজ412+y=15,&y=3,B56pḄ&Â;(2)ÄᑖÆ46x-9

11Y⚪ὃ᦮Ḅàᔠ-ᓄÞ@¶á!klᙢ%&⚪Ḅᐵ'.29.ூ,ᫀ௃¥¦§ᑁ┯d¤42¥¦§v£d¤åSᣚூ&᪆௃çè4éêBCᑮ஺§Ḅឋi%&,⚪Ḅᐵ'.30.ூ,ᫀ௃çè4•••AD//BE,:.Z.A=z3,vzl=z2,•DE//AC,•E=43,:.Z-A=EBC=Z-E.ூ&᪆௃ᵫᑮð4=43,÷ð1=42ᑮOE஻71C,ᵫçèNE=43,åSᣚᓽçè⚪ù·ô.⚪ὃḄ%§ḄឋiᯠÝ᪷]§Ḅᑨ}ZåSᣚúᓄ@ç.31.ூ,ᫀ௃&4î1ïûü¡ᵬþᝄḄxᐗᝄḄyᐗ⚪:0,:ᵬᝄḄ60ᐗᝄḄ80ᐗ.2!"#$ᵬᝄ%ᑣ#$ᝄ30-Tn!⚪60m+8030-m!<2300,771>5.ᨬ45#$ᵬᝄ5.ூ᪆௃1!"ᵬᝄḄxᐗᝄḄ!ᐗᑭᵨ;=ᓫxᦪ?@ᔠ“#$CᵬᝄD2ᝄᐳ◤220ᐗ#$2ᵬᝄD3ᝄᐳ◤360ᐗ”ᓽ5IᐵKX,!ḄMᐗCNOPQ,Rᓽ5I@STU12⚓ᐳ14⚓

12(2)"#$ᵬᝄWᑣ#$ᝄ(30-X)ᑭᵨ;=ᓫxᦪ?@ᔠ;Z[K2300ᐗᓽ5IᐵK஻ḄCᐗCNZ]^R_ᐸaḄᨬbcᓽ5I@S.d⚪ὃfgMᐗCNOPQḄhᵨijCᐗCNZ]^Ḅhᵨ⚪Ḅᐵkl(1)no]?ᐵpqrᑡIMᐗCNOPQT(2)᪷uᔜᦪ?RwḄᐵpqrᑡICᐗCNZ]^.32.ூᫀ௃13050ூ᪆௃(1)᝞zজ•,aNCḄ|ᑖ~KM,Z.MBC=-/-ABC,^MCB=-^ACB,22•MBC+MCB=+ACB),•(MBC+Z-MCB+BMC=180°,(ABC+ACB+=180°,MBC+Z.MCB=180°-BMC,Z.ABC+ACB=180°-•BMC=90°+*4,2V4=80°,BMC=130°T᝞zঝ.48ஹ4c᜜Ḅ|ᑖ~KN,♦NBC=-PBC,NCB=.(QCB,•NBC+NCB=1(NPBC+QCB),vNBC+NCB+BNC=180°,Z-PBC=4+(ACB,QCB=4/+/-ABC,:.NBC+Z-NCB=180°-BNC,PBC+QBC=+Z.ABC+^ACB+=180°+44,A180°-(BNC=1(180°+44),ᓽ4BNC=90°—4A,•LA=80°,:.BNC=50°Tᦑᫀ130T50T(2)᝞zজNBஹ஺Ḅ|ᑖ~KM,♦MBC=-Z.ABC,MCB=-Z-ACB.22M4MBC+MCB=^Z.ABC+ACB),.(MBC+MCB+BMC=180°,Z-ABC+ACB+4=180°,•MBC+MCB=180°-BMC,Z.ABC+ACB=180°-A-•(BMC=90°+M4=90°+2᝞zঝ••NBஹNC᜜Ḅ|ᑖ~KM

13:•NBCPBC,NCB=4QCB,22yNBC+ANCB="NPBC+QCB),•:NBC+4NCB+BNC=18஺°,4PBe=4+4CB,^QCB=zX+zXBC,4NBC+Z.NCB=180°-Z.BNC,PBC+Z.QBC=Z.A+/.ABC+Z.ACB+Z.A=180°+4,180°-BNC=*180°+NA),ᓽNBNC=90஺|N4=90°(1)ᵫ|ᑖ~Ḅ5NMBC+MCB=^^ABC+4ACB),ᑭᵨḄᑁDᳮ54"=90஺+R஽1,5Tᵫ|ᑖ~Ḅ5NNBC+NNCB=*4P8C+NQCB),ᑭᵨḄᑁDᳮ5ZN=90஺C[45T(2)ᵫ|ᑖ~Ḅ5NMBC+NMCB=/N4BC+N4CB),ᑭᵨḄᑁDᳮ54M=90஺+5Tᵫ|ᑖ~Ḅ5NNBC+/NCB=)"BC+“CB),ᑭᵨḄᑁDᳮ5NN=90஺C14,5.d⚪⌕ὃf|ᑖ~ḄḄᑁDᳮ᜜ḄឋᮣᵨᑁDᳮḄᐵp^⚪Ḅᐵk.U14⚓ᐳ14⚓