2021-2022学年天津市高二（上）学业能力调研数学试卷（12月份）（附答案详解）

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2021-2022
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7k2x2—(pfc2+2p)x+2P2=0,ᓽᨵᡭᑐ2=7>•.(3_g(1_ä=?=·=|,:y2=3x.ᦑhᫀny2=3x.᪷å²ᱥy2=2px(p>0)Ḅᯖ&æḄ/½²ᱥ&AஹB,ØAMஹBNᚖ¼&MஹN,᪷|BC|=2|BF|,#|4F|=3,4²ᱥḄ<ç;:8NCB=30°,4(%13%),8(᝞y2)3|BF|=X,é+^=3,X+^=1,#X1X2=Y>(3-ë1-஽)=29np=|,7஻Ḅᓽ²ᱥḄ-..P⚪R[%᫏⚪.ὃ²ᱥḄ<çzGì<ᦪÔ²ᱥḄ᪗¼-..íîᦪKÎᔠḄïðᱯ*Rb᪆òÙS<óÁòÙôKḄẆöz÷Òᓄù.11.ூhᫀ௃-x2+y2+1-4xy-4x-4y=06ூb᪆௃bnᙠú-íABCD-EFGH%û2᝞ôᡠüḄýÑIᙶ᪗,ᑣ4(0,0,0),8(1,0,0),C(l,l,0),஺(0,1,0),£(0,0,1).=ß1,0,0)+*0,1,0)+|(0,0,1)=þ,|),ÿ=(1,0,0),
ᙠᑐḄᢗᔣ||=,|/1£)|4ᑣPᑮABḄ4=|2_|=Uli-^=++yJ111\AB\1y1649166ᡠᑮABḄ!"஺ᙠ$☢ABC஺ᑁ'(Q(x,y,0),ᑣḄ=(x,y,—l),)*EQ+ECᡠᡂ-:'!/ᓃ'1•)=3||)|cosjᓽᨵx+y+1=+72+189*;,᦮ᳮ/+?8⚓'ᐳ15⚓

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©dᵫ(2)°=6n+5,2•%=²+b=+1+6«+5=7«+6,nn(13n+6)c°ᦪᑡ%¢J©¨ᦪᑡᑣ7@=/³=7=´W.ூ᪆௃(1)µ61—an-l=—«$1¶·¸◀஺«@«$icG^----1$=(H>2),n2°n-i2ᓽcfᦪᑡ2
J1✌⚗@v¨Ḅ©¨ᦪᑡ@(2)ᵫᦪᑡb
Ḅ)஻⚗oS=3«2+8n,G=11,®«22ᵫ½=S«-Sn.ilnᦪᑡ«¢Ḅ¾⚗vw@(3)ᵫ(1)cl¿,ᵫ(2)°/=6n+5,Eᐭc=G+b“,᦮ᳮqc°ᦪᑡ%¢J©nanan¨ᦪᑡÁᵫ©¨ᦪᑡḄlovwlᦪᑡ%¢Ḅ)஻⚗o~⚪ὃ©¨ᦪᑡḄ¾⚗vw:)஻⚗oὃÂÃlÄÅJ᫏⚪.C=192ci=1,cGb=l,a=V2,a—y/b2+c2ᡠÆᙊḄÈÉ
f+y2=1@(2)0)*4(Ê0),B(xy),2l2ὶ᦮ᳮcG
(1+2k2)x2+4kmx+2m2-2=0,(,xz+2y'=2''4=16k2m2-4(1+2/c2)(2m2-2)>0,cG⊈2<1+2ήcGm2<2,12⚓ᐳ15⚓

12-4km27n2-2%14-X=Xi1%2=22l+2k2Nl+2kᡠ|4B|=V1+fc2-J(X1+஺)2—4J“X2=V1+/C2-JÒ◥-4=2V2V2k2+l-7n2Vl+k2•1+22஺ᑮH/ḄÚÛd=Vl+fcznr@HI1IniJ1/(I7.22yf2\/2k2+l-m2|m||m|V2k2+l-m2ᡠSrA4°B=3|4B|-d=5-VFFP.7^p=V2——=V2-|?n|-V2-?n2_V2=,22cG•V2—m2=1,᦮ᳮcG—2m24-1=0,Gm?=1,cGm=±1,ᡠæḄ>±1জ)f
ᵫèxéDêë$ᑮHìí2:8í2ḄÚÛî©cG524+^^=°ᓽð+*_=0,%1-1ò$1ᓽ(%2T)+%(%1-1)=03ᵫ(i)cG(k%i+m)(x-1)+(kx+rn)(x-1)=0,221᦮ᳮcG
2kxix?+(m—k)(Xi+x)-2m=0,2ᓽ2k.ᔁ+S-k)•ô$2n=0,lcGm=-2k,ᡠH/ḄÈÉy=kx-2k=k(x-2),cfGH/ឤös(2,0).ூ᪆௃(1)ᵫᯖᙶ᪗ø“&í2☢ûḄᨬᜧ>oa,b,cþḄᐵcG“஺Ḅ>SlmÆᙊḄÈÉ@(2)(i)ὶH/:ÆᙊḄÈÉlm¶᪷
᪷|AB|஺ᑮ/ḄdḄᐭḄ☢ᵫḄ!"Ḅ#(ii)ᵫ⚪%!4&BF2Ḅ'᳛ឤ*+,ᦪ'᳛
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᪷ᐭ!᪷/0Ḅᐵ2ᐭ/Ḅ345!ឤ678.:⚪ὃ<=ᙊḄ34/=ᙊḄ?ᔠAᵨឤ678Ḅ5C☢ḄAᵨDE᫏⚪.18.ூHᫀ௃KL(1)M*=ᙊ஺ḄN*OP᳛*8ᡠR2a=4,-=a2ᡠRQ=2,c=1,b2=a2—c2=3,ᡠR=ᙊḄ34*1+!=1.43(2)ᵫ(1)SF(—1,0),G(2,0),

13X=-1x=-1ᵫ9+1=1!M*HF1\N]G_yNabNE5,ᑣᨵ“(i1,|)lm=m=nᑣ|OS|=1,ᓽS(O,1),|SG|=2|SH|,M*SASMG=6S-HN(B[ji|SA/||SG|sinzMSG=6-j|SW|S/V|sinz/VSH,ᑣᨵ|SM|=3|SN|,MNḄ'᳛ᙠMNḄ34*x=0,ᑣM0,ibN0,ᡠR᦮?=?=2+ᔠ⚪%\SN\y/3-lᡠRMNḄ'᳛ᙠMNḄ34*=1O+1,ὶg21ுW3+4/c2x2+8kx-8=0,3xz+4yz=12/Vx,y,22ᡠR/+ᡭ=ix=-^,X12ᵫ|SM|=3|SN|!=3SN,ᓽi%,1iᨴ=3x,y-122.8kX+X=--T7—1'24k2+3y_='{Xd124H+3Xi=-3X2K!ᓽO=±MᡠRMNḄ34*y=§¨+1ᡈஹ=i/x+1.y=kx+1fy=kx+1{ᐲ—®=1/m_°=o²³y´ᡠ!iᐗ¶·34᪷
+¸¹iº=1ᡃiºiU!½AB/½CQ8ÀᔠঝPX1%Ã?%2ஹ2ᵫ⚪%!ÄÅ%Å஺y=\DP\sinZ.ADQ,y=\DQ\sinZ.ADQ,12ᑣᨵÆ-y=|PQ|sinZj40Q,2ᵫABḄ34x+y-l=0!஻Å4Q=45஺|4Q|=É;=V2y,2M*Ë=3Ìsin/ACQ,ᓽ|4Q|=3y[2\PQ\sin^ADQ,ᡠRÍ2=3aO-2ᡠRÄ=/1,/Ḅ'᳛*஺/Ḅ34*x=5y-2KÆ,y,/Ḅ'᳛*஺ḄÏÐ.2ঞ/Ḅ'᳛ᙠ/Ḅ34*y=mx+2,!C0,2m,Ò14⚓ᐳ15⚓

14ᵫÕÕÕÖ?,8Ḅ8Ḅ×ᙶ᪗="Û,ᵫÜC|,ᵫ|BC|=12mlÞßᓽ.ூK᪆௃(1)᪷áâ7ᩩä=ᙊCḄåNᓽæH.(2)᪷áᩩä8H,SḄᙶ᪗ç!|SG|=2□S|,ᵫ☢7ᳮêẓ=3ì7,ᯠ´ᑖ'᳛ᙠ/ᙠïðᓽçᳮÞßæH.(3)ᑖ᪆ᔜò⚪óïKô+Aò⚪Ḅᐵõᩩäᵨᦪö⊤øᑏᓽ!.:⚪ὃ<=ᙊḄ34/=ᙊḄ+_ò⚪K⚪◤⌕i7ḄÞßüÆDE᫏⚪.