2022-2023学年上海市闵行区七年级（上）开学数学试卷（五四学制）（附答案详解）

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2022-2023
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ᦪᔁᑴ1.a3•a3=.2.(-%)3%•(!")2=.3.ᵨ$ᨵxḄ'ᦪ(⊤*7+,xḄ3-.Ḅ/0.4.2345=5,6Ij2/n=.5.73a771=3,bm=5,ᑣ(a2b3)?nḄ9:.6.232%=a,2ஹ=da,ᓃ⊤*5♦233+2,!6
8"2y:.7.>?=2@'ᦪ(a/ᓝB!3Ḅ9:5,>?=1@'ᦪ((2Q/+ᓃ?!5),Ḅ9:.8.73x—5=y+4=z+l,'ᦪ((y—%)2+(z—%)2+(y—z)2Ḅ9:.9.ᵨDE0F24x32x53+326X0.1256X(-0.25)5+(|+^)100x(|+^)99=.10.#Ty+(3-n)xyn-2-nxn-3y+4xn-4y3-mx2yn-4+(n-3)GᐵIxJyḄKL⚗(,ᑣ(-s=11.73x=57,y=75,ᵨ$x,yḄ'ᦪ(⊤*257-4935+3535:.12.Oᑡᔜ(R!xyz+1,S/Ryr-1,£!1,G[⚗(Ḅᨵ()A.1UB.2UC.3UD.4U13.OᑡVWXḄG()A.4x3-2x2=6x2B.3x2-2x3=6x6C.(-3x5)•(-2x2)2=-12x9D.-x-(—x)12(—x3)3=—x1914.Y8/+5.y2b-3.(-o.25ya+5xb)-2/y3ᑣa-bḄ9:()A.—1B.5C.1D.—515.Oᑡ\FWXḄUᦪG()জ%2y,|x2y2,|xy,xy2ᑖ^G[⚗(/y-1_2y2!|a+1ᑐc2Ḅ⚗;ঝᐵIfḄ[⚗(4nx+t+3GLK⚗(g+ঞY!|/y"TJ7%2y7Gij⚗Rᑣ=8;nটLK[⚗(mnᨵ!⚗:LKᓫ⚗(.A.1UB.2UC.3UD.4U16.a-(—a5)•(—a6)•(—a)7/(—a)2.17.9(xy)3•(!2y)2+(ߟ%2y)2+(!%2y)3.y2X18.(3a)3•(an-1)2•(a2)2+n.(!p2f19.(—x2)•x3•(-2y)3+(2xy)2•(—x)3-y.

120.0.125(%-y)3-(y-x)4-0.875(y-x)•(y-%)64-|(x-y)2•(y—x)3+0.5(y-%)7.21.(-x2•%3)2-(0.5x2-1.5x2)5!(-x2)3-[(-%)3]2-[(-%)4]2.22.73|(a—5)4+11—1|=0,ᓄD'ᦪ(M—(a3—[7a2b+4ab2—(Sab2-2b3+52)]9.23.73=4প2%+3yফ☟4x-2yḄ9.24.73a?"=4,a3n-(a3)2nḄ9.25.732,3•16”=222,2X+3_zx+i,(!:L33=64826.7342*.52X+1-42X+1-52X=203x-4,Ḅ9.x27.:ᢕᖪRA,Bᨴ¡RYAᨴ¡10¢RBᨴ¡5¢R◤⌕600ᐗgYAᨴ¡5¢R8ᨴ¡3¢R◤⌕330ᐗ.¦§¨6000ᐗᐰªᵨᩭᨴ¡Rὃ⇋®◤R⌕Aᨴ¡Ḅᦪ¯°nIBᨴ¡ᦪ¯6-R±°²8ᨴ¡ᦪ¯Ḅ8-.Y├´µ¢Aᨴ¡¶·ᑭ20ᐗR├´µ¢8ᨴ¡¶·ᑭ30ᐗR¹᪵»¼0ᫀ¾¿ÀÁ·ᑭᨬᜧÄᨬᜧᑭÅG[nᐗÄ

2ÆᫀÇÈ᪆1.ூÆᫀ௃஺6ூÈ᪆௃È:a3-a3=a6.ᦑÆᫀ:஺6.᪷ÐiÑᦪÒÓFRÑᦪ°ÔᢣᦪÖRᓽ¶¨Æᫀ.Ø⚪Ú⌕ὃÛiÑᦪÜḄÓFRᙠÈ⚪@⌕¿ᮣßàᵨiÑᦪáḄÓFFᑣRâãäåVឋçGÈ⚪Ḅᐵè.2.ூÆᫀ௃-x6ூÈ᪆௃È(-X)3-X•(-X)2=-X3-X-X2=—X6.ᦑÆᫀ:!!.ᐜëḄÓ0ḄVRìiÑᦪíḄÓFḄVᓽ¶.Ø⚪Ú⌕ὃÛiÑᦪáḄÓFRÈÆḄᐵèGîÖàḄVFᑣḄäå.3.ூÆᫀ௃(7-3x)3ூÈ᪆௃Èï⚪ðᨵ(7-3x)3.ᦑÆᫀ:(7-3x)3.ᐜ⊤*xḄ3-Rì⊤*ᦪḄ.Rì⊤*.Ḅ/0.Ø⚪ὃÛᑡ'ᦪ(ñò⚪Jᦪ¯ᨵᐵḄóôRᵨ$ᨵᦪõஹõöÇV÷øḄ(ù⊤*¨ᩭRúGᑡ'ᦪ(.4.ூÆᫀ௃250ூÈ᪆௃Èû/n=5,A2x9n=2(x3n)3=2x53=2x125=250,ᦑÆᫀ:250.ᑭᵨýḄÓ0ḄFᑣRᓽ¶Á¨Æᫀ.Ø⚪ὃÛëḄÓ0JþḄÓ0RäåëḄÓ0ḄFᑣGÈò⚪Ḅᐵè.5.ூÆᫀ௃1125ூÈ᪆௃ÈYam=3,bm=5,(a2b3)m

3=a2mb3m=(a--.=32X53=9x125=1125,ᦑᫀ1125.ᑭᵨḄḄḄᑣᓽ"#$ᫀ.%⚪ὃ()*ḄḄ+,-ḄḄḄᑣ./01⚪Ḅᐵ3.6.ூᫀ௃5a3b2-6a3b6ூ/᪆௃/27=a,2y=b,5-23x+2y-6-8x+2y=5-23x-22y-6-8X-82y=5•(2X)30)2-6.0)3.(2»=5a3b2—6a3b6,ᦑᫀ5a3b2-6a3b6.ᑭᵨ-ḄḄḄᑣᓽ"#$ᫀ.%⚪ὃ()8ḄḄ+,-ḄḄḄᑣ./01⚪Ḅᐵ3.7.ூᫀ௃1ூ/᪆௃/•••:x=2;<ᦪ>ax2+bx-3Ḅ?5,•••4a+2b=8,2a+b=4,.•.:x=1;<ᦪ>(2a/+bx-5)4=(4-5)4=1.ᦑᫀ1.@ABx=2<ᐭD#$4a+2b=8,EBx=1<ᐭF$ᫀ.G⚪H⌕ὃ()<ᦪ>F?JKLM>NO./⚪ᐵP.8.ூᫀ௃126ூ/᪆௃/Qx-5=y+4=z+l,••z-x=-6,y—x=9,y—z=-3,Bz—x=-6,y—x=-9,y—z=-3<ᐭ(y—x)2+(z-x)2+(y—z)2=81+36+9=126,ᦑᫀ126.ᐜSTF$z-x=-6,y-x=-9,y-z=-3,D<ᐭ/ᓽ".

4G⚪H⌕ὃ()<ᦪ>F?JKLM>NO./⚪ᐵ3.9.ூᫀ௃179966ூ/᪆௃/24x32x53+326x0.1256x(-0.25)5++1)100x(|+^)9956=(2x5)3x(2x32)+4x(86x0.1256)x(-4x0.25)5+(-)100x(-)"556=103x(2x9)+4x(8x0.125)6x(-1)5+-x(-x-)"=1OOOx184-4xl6x(-1)+fx1"65=18000+4x1x(-1)+-x165=18000-4+-65=17996-.6ᦑᫀ17996.6ᐜE◀ᨬWSTXYZ[\ᢥ^_ᑮaḄbcX᝞eᨵgh⌕ᐜighᑁḄ[.%⚪ὃ()ᨵᳮᦪḄlᔠ[ᨵᳮᦪlᔠ[bcᐜE◀ᨬWSTXYZ[\ᢥ^_ᑮaḄbcX᝞eᨵgh⌕ᐜighᑁḄ[.ᨵᳮᦪḄlᔠ[;noᔜq[rḄ[ᵨs[tu#ᑮvᓄ.10.ூᫀ௃1ூ/᪆௃/Mx⚗>.zq{|}⚗>ᨬ~⚗.x"Ty,•**n—1+1—5,
•
n=5,
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M>=x4y—2xy3—5x2y+4xy3—mx2y+2=x4y+(-2xy34-4xy3)—(5x2y+mx2y)+2=x4y+2xy3—(54-m)x2y+2,:.—(m+5)=0:.m=-5,y)5=T=(5=i,ᦑᫀi.ᐜ᪷Mx⚗>.zq{|}⚗>#$”Ḅ?<ᐭM>W᪷M>}⚗>#$”Ḅ?,ᨬWB஻”<ᐭ(z§5F/ᓽ".%⚪ὃ()ᑖ>Ḅ◀x⚗>/⚪Ḅᐵ3.x⚗>|ᦪ.x⚗>|ᦪᨬ~Ḅ⚗Ḅ|

5ᦪ.11.ூᫀ௃x2-y14+x5y7ூ/᪆௃/Qx=57,y=7s,257-4935+3535=(52)7_02)35+(5X7)35=(57)2_(5)14+07)5.05)77=x2—y14+x5y7,ᦑᫀx2-y14+x5y7.ᑭᵨḄḄḄᑣᓽ"#$ᫀ.%⚪ὃ()ḄḄ+,ḄḄḄᑣ./01⚪Ḅᐵ3.12.ூᫀ௃Bூ/᪆௃/ᑡᔜ>-xyz+l,—r2,7r-1,--1,1803x.x⚗>Ḅᨵ-xyz+l,7T-1,ᡠᐳᨵ2qᦑ⌱:B.᪷x⚗>Ḅᓽ"/.%⚪ὃ()x⚗>¡¢+,x⚗>Ḅ./⚪Ḅᐵ3.13.ூᫀ௃Cூ/᪆௃/Aஹ4X3-2X2=8X5,ᦑ4¥¦ᔠ⚪oXBஹ3%2.2/=6/ᦑ8¥¦ᔠ⚪oXCஹ(ߟ3x5)•(ߟ2x2)2=—12x9,ᦑC¦ᔠ⚪oXDஹ—X•(ߟx)12(—x3)3=x22,ᦑ஺¥¦ᔠ⚪oXᦑ⌱C.ᑭᵨᓫ⚗>ᓫ⚗>ḄᑣY±ᦪ-ḄḄᑣḄḄᑣ²ᔜ⚗[ᓽ".%⚪H⌕ὃ(Y±ᦪ-Ḅ/Ḅᐵ3.²³\Ḅ[ᑣḄ+,.14.ூᫀ௃Dூ/᪆௃/:1■18xa+s-y2b~3■(ߟ0.25ya+5xb)=-2x4y3,..._2a+b+5y2b-3+a+5—_2x4y3,x.(a+b+5=4“l2b-3+a+5=3'/#=3=2

6ᦑab=—3—2=/5.ᦑ⌱D.@Aᑭᵨᓫ⚗>ᓫ⚗>[ᑣ#$ᐵ¹a,஻ḄuºD#$ᫀ.G⚪H⌕ὃ()ᓫ⚗>ᓫ⚗>[JK+,³ᐵ[ᑣ./⚪ᐵ3.15.ூᫀ௃Cூ/᪆௃/জ/y,-1x2y2,-fxy,jxy2ᑖ¾ij.x⚗>À2ÁzX/Á2z|%Á+%Ã2Ḅ⚗ᦑMÄ┯ÆXঝᐵ¹xḄx⚗>È᮱+4nx+C+3.}|Ê⚗>ᦑMÄJKXঞÌz12yn-l7%2Ã7.YÎ⚗ᑣ=8,ÄJKXnট}|x⚗>ÐÑᨵz⚗}|ᓫ⚗>ÄJKXᡠÄJKḄqᦪ.3q.ᦑ⌱C.ᑖÒ᪷x⚗>ஹᓫ⚗>YÎ⚗Ḅ⌲zᑨÕᓽ".%⚪ὃ()ᓫ⚗>ஹx⚗>YÎ⚗+,³ᐵ./%⚪Ḅᐵ3.16.ூᫀ௃/a■(—a5)•(—a6),(-a)7,(-a)2=a•(—a5)•(—a6)•(—a7)1a2=—a21.ூ/᪆௃ᑭᵨY±ᦪÖḄḄᑣ[ᓽ".%⚪H⌕ὃ(Y±ᦪ-Ḅ/Ḅᐵ3.²³\Ḅ[ᑣḄ+,.17.ூᫀ௃/M>=9/Á3.S%4y2+/y2+(_”y3).%Á2=x7y5+x4y2—x7y5—x4y2.ூ/᪆௃@AᑭᵨḄ[ᑣᓫ⚗>ᓫ⚗>[ᑣEᔠØ#$ᫀ.G⚪H⌕ὃ()Ḅ[ᓫ⚗>ᓫ⚗>[JK+,³ᐵ[ᑣ./⚪ᐵ3.18.ூᫀ௃/M>=27a3,a2n-2.42n.(_)2n-la+a=-27a6n+4.ூ/᪆௃@Aᑭᵨ-ḄḄ[ᑣஹᓫ⚗>ᓫ⚗>[ᑣᑖÒᓄv#$ᫀ.G⚪H⌕ὃ()Ḅ[ᓫ⚗>ᓫ⚗>[JK+,³ᐵ[ᑣ./⚪ᐵ3.

719.ூᫀ௃/:M>=%2•%3-8y3—4x2y2-x3-y=8x5y3—4x5y3=4%Sy3.ூ/᪆௃᪷ḄÙY±ᦪÚḄᑣF/ᓽ".%⚪ὃ()ÛḄÙY±ᦪ-Ḅ/%⚪Ḅᐵ3.+,ÛḄÙY±ᦪḄᑣ.20.[ᫀ]/0.125(x-y)3.(y-x)4-0.875(y-x)-(y-x)6+|(x-y)2-(y-x)5+0.5(y-x)73=0.125(%—y)7+0.875(%—y)7--(x—y)7—0.5(%—y)73=(0.125+0.875)(x-y)7+(-2-0.5)(%-y)7=(x-y)7-2(y-x)7=—(y_%)7.ூ/᪆௃᪷Y±ᦪ-ḄᑣᓄvWEᔠØYÎ⚗ᓽ".%⚪ὃ()᦮>Ḅlᔠ[+,Y±ᦪÖḄᑣ./%⚪Ḅᐵ3.21.ூᫀ௃/(-%2•%3)2-(0.5%2-1.5%2)5-(-%2)3-[(-x)3]2-[(-x)4]2=%10•(ߟ%10)—(ߟ%6)-X6-X8=-X20+X20=0.ூ/᪆௃ᑭᵨ-ḄḄ[ᑣᓽ"/.%⚪ὃ()ÛḄḄÞK¡¢ᙢ./⚪Ḅᐵ3.22.ூᫀ௃/
.•ᐸáz5)4+[ãäz1|=0a—5=0>-b=—1,2/#a=5,b=-2,M>=a3-a34-7a2b+4ab2-Sab2+2h3-5a2b=2a2b—ab2+2b3,:a=5,b=-2;M>=2x52x(-2)-5x(-2)2+2x(-2)3=-100-20-16=—136.

8ூ/᪆௃ᑭᵨåæᦪḄឋèF$஺äḄ?M>éghᔠØᓽ"<ᐭᓽ"F$?.G⚪ὃ()᦮>ḄST-ᓄvF?åæᦪḄឋè¡¢+,[ᑣ./%⚪Ḅᐵ3.23.ூᫀ௃/•••êz74%—2y=2%+3y,2%=5y,5•x=-y,পM>=ìᔆîফM>=(◤ñ-òH…*ூ/᪆௃ᓄvᑖ>"#x=|y,<ᐭ"F/.%⚪ὃ()ᑖ>Ḅlᔠ[ᓄvᑖ>#ᑮö=|y./⚪Ḅᐵ3.24.ூᫀ௃/•••(÷”=%va2n=22,••an=2,
.a3n-(a3)2n=(4>-(an)6=23-26=-56.ூ/᪆௃ᑭᵨÖḄḄ[ᑣᓽ"/.%⚪ὃ()8ḄḄÞK¡¢ᙢ./⚪Ḅᐵ3.25.ூᫀ௃/•2-8n-16n=2-23n-24n=27n+1,•••2-8n16n=222,7n+1=22>■■n=3,32X+3_2X+1=9.2X+1_2X+1=8.32X+1,333...2X+3_2X+1=648,3332X+1=81=3஺2%+1=4,3•••x=-,2...(r)n=(z|)3=-pூ/᪆௃ᑭᵨ-ḄḄ[ᑣᓽ"/.%⚪ὃ()*ḄḄÞK¡¢ᙢ./⚪Ḅᐵ3.

926.ூᫀ௃/•42X-52x+1-42X+1-52X=5x42x.52x-4x42x-52x=202x,v42X-52X+1-42X+1•52x=203X-4,•2x=3x—4,
■x=4.ூ/᪆௃ᑭᵨᗩḄḄ[ᑣᓽ"/.%⚪ὃ()ýḄḄÞK¡¢ᙢ./⚪Ḅᐵ3.27.ூᫀ௃/þA,8ÿᨴᑖxᐗyᐗ.pOx+5y=6005x+3y=330'••
A,8ᨴᑖ30ᐗ60ᐗᵨ6000ᐗAᨴ஺8ᨴZ?ᑣ96a=200-2b=160,?!ᑭᨬᜧḄ@ᫀAᨴ160Bᨴ20ᨬᜧᑭB3800ᐗ.ூ᪆௃ᐜGHA,8ᨴḄIᵨ6000ᐗAᨴ஺8ᨴ6├ᢇᨴ!ᑭwᐗ᪷$JᑭB=4BᨴᑭBKLᑡHNᦪ᪆*P᪷$⚪&GH”,஻KSḄᐵUᑭᵨNᦪḄឋWGXᓽY.Z⚪ὃ\]^ᐗ^_`a*bஹ4ᐗ^_`a*bḄdᵨ.eZ⚪Ḅᐵfgh⚪&iᑮkᔠ⚪&ḄmdḄᐵU*en⚪Ḅᐵfo&p4ndG᦮ᦪ.