2021-2022学年河南省平顶山市卫东区八年级（上）第一次月考数学试卷（附答案详解）

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2021-2022
ᓭḕ⚔ὶ᪥
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3ᨵᳮᓄtqr᪷t◀\᪵ᳮJ᝞J+=K==—7+4.\᪵*+ᑖ|ஹᑖ¡igt|¢ᑖ:Ḅ᪷ᓄ£ᡈ¢᪷:Ḅᑖᓄ£¥¦ᑖᨵᳮᓄ.§⚪J(1)4-᜛Ḅᨵᳮᓄt,ᜓᑖᨵᳮᓄ.(2),-Jজ¬x=®1y=ᗩ|A/+y2Ḅ±Tঝ1+V2+V2+V3+V3+V4+…+V1999+V2O0023.᝞41,Rt^ABC,AC1CB,AC=15,4B=25,஺²6³´.(1)᝞42,+஺µDE_LAB¶CBE,·¸AE,¹AEºᑖ4CABACET(2)᝞43,ᙠ஺Ḅ»´+¼:·¸C஺>½4C0¾ῪÀÁ7A40.123

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5஺ஹ0ḄUR᪷QR᪷lq!ᦑ@⌱⚗`a.ᦑ⌱4B.4.ூLᫀ௃Dூ᪆௃4AஹrstZvwxy᪷z!{ᔠ|ᡂ~⚗!ᦑ@⌱⚗┯h!+ᔠ⚪Bஹ4V3-3V3=V3,ᦑ@⌱⚗┯h!+ᔠ⚪Cஹ2V3x2V3=12,ᦑ@⌱⚗┯h!+ᔠ⚪஺ஹV27^-V3=V9=3,ᦑ@⌱⚗`a!+ᔠ⚪ᦑ⌱4D.᪷6xy᪷zḄᑣᑨ4᪷6xy᪷zḄᑣᑨB᪷6xy᪷zḄᑣᑨC᪷6xy᪷zḄ◀ᑣᑨD.@⚪ὃCDxy᪷zḄ◀!FGᑣ⚪ḄᐵI.5.ூLᫀ௃Aூ᪆௃4Aஹ={s&ᔠ|!ᦑ@⌱⚗`aBஹ{sᔠ|!ᦑ@⌱⚗┯hCஹV20=2V5,{sᔠ|!ᦑ@⌱⚗┯h஺ஹV02=y,{sᔠ|!ᦑ@⌱⚗┯h.ᦑ⌱4A.᪷6xy᪷zḄឋ:ᓄ!ᯠ᪷6{ᔠ|Ḅxy᪷zdvwxy᪷zᑨ.@⚪ὃCvwxy᪷zḄᭆ!vwxy᪷zᓄdᨬxy᪷z!RᦪlvḄxy᪷zdvwxy᪷z.6.ூLᫀ௃Cூ᪆௃4•••[a-b]2+|a2+b2-c2|=0,.a-b=0,a2+b2-c2=0,4a=b,a2+b2=c2,ABCḄ¤dqῪᦑ⌱4C.✌ᐜ᪷6⚪ᵫ¨pᦪḄឋ:<!©ªᑮ஺=«a2+b2=c2,᪷6-./ᳮ⌮/ᳮ<AABCḄ¤dqῪ.¬⚪⌕ὃCD-./ᳮ⌮/ᳮ8¨pᦪḄឋ:!ᐵIFG-./ᳮḄ⌮/ᳮ4᝞°

6Ḅ±²a,b,஺³´a2+/=c2,µ¶·¸.7.ூLᫀ௃Dூ᪆௃ூᑖ᪆௃@⚪ὃC¹ᦪsᦪºஹ-./ᳮq»¼!⚪ḄᐵIᮣ¾¿ᵨ-./ᳮÁACஹAMḄ²!ÂÃÄὃÅὃ⚪Æ.ᐜᑭᵨ-./ᳮÁAC,᪷6AC=AM,Á0M,ᵫ¬ᓽ<ÈÉ⚪.ூL௃4•••Ê±ABCOË!•••/.ABC=90°,vAB=3,AD=BC=1,AC=y/AB2+BC2=V32+l2=<10,•••AM=AC=<10,OA=1,OM=-/10—1,ÌM⊤ÎÌᦪdVTU-1.ᦑ⌱D.8.ூLᫀ௃Dூ᪆௃4᪷6⚪4a+l+2a—7=0,4a=2,ᑣ·`ᦪ(2+I)2=9.ᦑ⌱஺᪷6~`ᦪḄQR᪷ᨵ2!ÏkdlmᦪÁ“Ḅ!ᓽ

7•••BC=14,¬Ò×ᨵØ~ÙÚ.ÓNABCÛÖ!᝞Ò,Ó¬ÙÜÝÖ!BC=9-5=4.ᦑ⌱8.᪷6-./ᳮᐜÁ30ஹ8Ḅ²!ÞÁ8c¸ßà᧕D!âᑖÜÝã?.¬⚪⌕ὃCDÄ-./ᳮḄ¿ᵨ.ᓽj±ḄQRqÃä±ḄQR.10.ூLᫀ௃Bூ᪆௃4ådQ☢çÒè~!ᦑᑖÜÝᑖé!©êᜧìíî!Þ«ᔜðñÄa/ᨬcḄðñ.(1)çô☢ஹõ☢ᑮ²RḄj±d5+4=9cm3cm,ᵫ-./ᳮAB?=(5+4)2+32=90(cm)(2)çô☢ஹø☢ᑮ²RḄj±d4+3=7cm5cm,ᵫ-./ᳮAB?=(3+4)2+52=74(cm)(3)çù☢ஹø☢ᑮ²RḄj±d5+3=8cm4cm,ᵫ-./ᳮAB?=(3+5)2+42=80(czn)ᡠ8ᨬcðý²dgem,ᦑ⌱B.Ḅ☢ᙠ☢ᑁᨬ.ᑭᵨᳮ"A$BḄᓽ'(ᑮ⇪⇩,-Ḅᨬ./.ᙠ012134ᩩ01678Ḅ9:ᩩ01678Ḅ;$ᑭᵨᳮ'"(.<⚪ὃ?Ḅ@☢-ᨬBCD⚪᪷F⚪GHIḄ⊤☢Kᑭᵨᳮ"L@LM⚪ḄᐵO.11•ூMᫀ௃>ூL᪆௃L0.5=,21,

8ᦑMᫀ_>.✌ᐜ0.5b_ᯠdefᡃḄ᦮ᦪjᑖl᪷FmnoᦪᜧqḄrs-mnᓽ'.⚪t⌕ὃ?voᦪḄᜧqmn.⚪w0.5b3_ᑖᦪᯠd᪷FxᳮᦪḄ᦮ᦪjᑖlᩭmnᓽ'LzD⚪.12.ூMᫀ௃V2+1ூL᪆௃LV8+(-l)2020-|-V2|=2V2+1-V2-V2+1.ᦑMᫀ_V2+1.ᐜᓄ|ᔜ~ᯠdls-fᓽ'LM.<⚪ὃ?voᦪḄfᙢᓄ|ᔜ~@L⚪ḄᐵO.13.ூMᫀ௃64ூL᪆௃Ly=Vx-3+V3-x+4,fx-3>0AL3-x>0L(=3,
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y=4,

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•FC=AF=13cm,vAB=18cm,AF—13cm,

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FF=18-13=5(cm),vzF=zF=90°,EC=V132-52=12(cm),vAD=BC=EC,•AD=12cm,ᦑMᫀ_12.ᵫᢚ(EAC=LBAC,AE=AB=18cm,᪷F-ឋ(AF=FC=13cm,l"IEF=5cm,ᑭᵨᳮ"IECḄᓽAOḄ.<⚪@ᢚD⚪ὃ?v3ஹᢚḄឋᜧ¡8¢ὃ⚪£¤¥ᢚ¦dḄ§¨w1©7ª-Ḅᑁ┯1©7(I7Ὺ213᪷F71¨76"I6ḄᑭᵨᳮLzD⚪.15.ூMᫀ௃§ூL᪆௃L®¯AO,4AB=AC=13,BC=10,஺_BC4,AD%BC,BD=^BC=5,AD=TAB?-BD2=12,°DELAB,1i^BD-AD=^AB-ED,BDAD5x1260-'-ED=^r=-=u'ᦑMᫀ_±✌ᐜ®¯A£,ᵫAABC4AB=AC=13,BC=10,஺_BC4ᑭᵨ7Ὺ213Ḅ2ᔠḄឋᓽ'³(AD1BC,ᯠdᑭᵨᳮᓽ'"(ALḄᯠdᑭᵨ☢´rᩭ"OEḄ.⚪ὃ?v7Ὺ213Ḅឋµᳮ.⚪〉4L⚪ḄᐵO@·I¸¹ºGᦪ3»ᔠ¼½Ḅwᵨ.16.ூMᫀ௃L᪷F⚪G'(2a-1=9,3a+b-9=8ᦑa=5,b=2°ᨵ7ீ¿À8,'(c=7ᑣa+2b+c=16ᑣ16ḄfÂ᪷_4.

10ூL᪆௃✌ᐜ᪷F᪷ªÃ᪷ḄᭆÅ'(2a-1ª3a+b-9ḄsÊ'(aஹ6Ḅ¯ḼedḄᜧq'(cḄsÊ'(a+26+c,᪷FfÂ᪷Ḅ"r'(Mᫀ.⚪t⌕ὃ?v᪷ஹÃ᪷ஹfÂ᪷ḄxᳮᦪḄefΤ¥᪷~ḄÏ/2—V2=5V2(2)V(-3)2+V^8+|l-V2|=3-2+V2-l—V2(3)(V3-l)2-(V3-V2)(V3(V3+V2)=3-273+1-(3-2)=3-2V3+l-l=3-2V3V8+7I8=1çভ
—+(V24-0L1L=2+3+2V2——=5+|V2.ூL᪆௃(1)᪷F᪷~Ḅឋªᔠêëì᪷~Ḅrᑣs-fí'(2)᪷F᪷~ḄឋÃ᪷Ḅî¨Ḅឋs-fí'(3)᪷Fïᐰñ~ªòñ~s-fí'(4)᪷F᪷~Ḅ◀rᑣs-fí'.<⚪t⌕ὃ?v᪷~ḄôᔠfÃ᪷ᐵO@õ᪷~Ḅឋ.18.ூMᫀ௃L:Ý~=|—c|+\a—b\+a+—\b—c\f=c+(—a+b)+a+b—(—6+c),=c-Q+b+a+b+b—c,=3b.ூL᪆௃᪷Fø=|a|l»ᔠî¨Ḅឋùî¨lᔠêëì⚗ᓽ'.⚪t⌕ὃ?voᦪḄfᐵO@¤¥î¨Ḅឋ$᪷~Ḅឋ.

1119.ூMᫀ௃L:û1üýABCḄ☢´=4x4-1x2+2-4x3+2-2x4+2=16-1-6-4=5.ᦑBCḄ☢5(2)•.•1,AB2=I2+22=5,AC2=22+42=20,BC2=32+42=25,AB2+AC2=BC2,••.ABC"#$#%.ூ'᪆௃(1)*ᵨᒘ⊡./0%Ḅ☢12$3$#%Ḅ☢/ᓽ567ABCḄ☢8(2)᪷:;<=ᳮ6?A4BCᔜḄ/Aᑭᵨ;<=ᳮḄ⌮=ᳮDEᑨ=/GHIJ?ᑮᐸ%M.N⚪P⌕ὃST;<=ᳮU;<=ᳮḄ⌮=ᳮ/'VW⚪⌕*ᵨ;<=ᳮḄ⌮=ᳮ:Y$#%ABCḄ$Z[+஻=©2,ᑣ$#%ABC_"#$#%.20.ூVᫀ௃'8abA8I◤⌕ᨚfg┝.ᳮᵫ᝞k8᝞l/mCnCD148pD.•••CA1CB,.Z.ACB=90°,sBC=800t/AC=600t,ᡠv/᪷:;<=ᳮᨵ=ᡠ002+6002=iooo(t).sSMBC=\AB-CD=\BC-ACBCAC_800x600ᡠvCO=AB=1000480{t|.ᵫp400t}480t/ᦑ~ᨵᓻ◅,sWA3abI◤⌕ᨚfg┝.ூ'᪆௃mCnCD14Bp஺.᪷:CA1CB,?7NACB=90°,ᑭᵨ᪷:;<=ᳮᨵ4B=1000t.ᑭᵨ=18-CD=gBC-4C?ᑮCD=480t.A᪷:480t400t5vᑨ~ᨵᓻ◅.N⚪ὃST;<=ᳮḄᵨ/'⚪Ḅᐵ_ᑭᵨ"#$#%Ḅឋ67COḄ.21.ூVᫀ௃'8ᙠRtAABD/AB=AD=2+Z.BAD=90°,•••BD=>]AB2+AD2=4,

12VCD=4V3,BC=8,BC2=BD2+CD2,BDC=90°,S./0ABCD=SMBD+S^DCB=2x2ax2-\/2+2x48x4=4+8>/3.ூ'᪆௃✌ᐜ᪷:;<=ᳮ678஺,A᪷:;<=ᳮḄ⌮=ᳮNBDC=90஺,᪷:SᑗBCO:^hABD+SA࠷Bᓽ5'τ5⚪N⚪ὃS;<=ᳮv⌮=ᳮ,$#%Ḅ☢,'⚪Ḅᐵ_ᮣ¡*ᵨᡠ¢'£⚪,¤pὃ¥ὃ⚪¦.22.ூVᫀ௃(4+b)§ூ'᪆௃'8(1)4-bḄᨵᳮᓄs©5v_4+ª,3_3x1_V32V3=2V3xV3=T)ᦑVᫀ84+>/7,ᙛফজ®”°=(6+1)(6-1)_4+2V3(V3-1)(V3+1)=~~_--1_(6±1)(²T)_4-2µ'=V3+1=(V3+1)(V3-1)=-2-2-V5f,x2+y2=(x+y)2—2xy=(2+µ+2-µy-2x(2+V3)x(2-V3)=16-2x1=14.+V2+V5+V3+75+///+Vi999+V2000=V2-1+V3-V2+V4-V3+-+V2000-V1999=72000-1=2075-1.(1)¶7ᔜ©Ḅᑖ¸ᨵᳮᓄs©ᓽ5(2)জ¹xºyᑖ¸ᨵᳮᓄᓄ»¼²ᐭ¾©ᓽ5?ᑮ¿À.ঝ¾©ᔜ⚗ᑖ¸ᨵᳮᓄ/ᔠÄᓽ5?ᑮ¿À.W⚪ὃSTᑖ¸ᨵᳮᓄ,0Å⌱ÇÈ3ÉÊ᪷©,ËÌÍḄÎᔠÏÐa©_'V£⚪Ḅᐵ.23.ூVᫀ௃':(1)%,-AC1CB,AC=15,AB=25.•BC—20,MEÏᑖ448,

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