2018年河南省豫南九校高三下学期第一次联考试题理科数学(图片版）.zip

g1594g3128g3316g3888g271g2360g272g1235g803 g1307 1 g3994g271g1643 8 g3994g272 豫南九校2017—2018学年下学期第一次联考 高三数学（理）参考答案 g1078g573g17983g6431g20174 1g2525DCBBB 6g25210ACCAB 11g25212AC 1g714D g463g16403g7616g464g3344g1130 1{ | }2A x x= ≥ g712 { | 1 1}B x x= − ≤ ≤ g712g6256g1301A B∩ = 1 12x x ≤ ≤  g714 2g714C g463g16403g7616g464 1 3 1 1z i= + − = g714g708 3 1 1Z i= − − = g709 3g714B g463g16403g7616g464122 2 2 27π π 2 1log cos log cos log log 24 4 2 2−   = = = = −      g296 g712g7029g17977Bg714 4g714B g463g16403g7616g464g6347g10393g13551 22x py= ( 0)p g11444g7735g2038g7145g12347g1130 2 12y xp= g712g7029g17977Bg714 5g714B g463g16403g7616g464g2093g7072 πsin 4y x = −  g13567g1384g19375g2568g6546g5575 1 πsin 2 4y x = −  g712g1981g1420g5283g12331g2568g6546g55751 π πsin2 6 4y x  = − −     1 πsin2 3x = −  g712g7029g17977Bg714 6g714 A g463g16403g7616g464g1485g20168g5951g2591g11797g1081g7969g19285D ABD′− g2467g1130g16917g2064g1413g1411g708g4018g3374g709g712g7235g5575g16917g2064g1413g1411g11444g16024g19858g12319g1130 2 1+ g714 7g714C g463g16403g7616g464g16403g8965g1072g726 0, 0, 1, 1i S x y= = = = g5424g4091g6295g15996g712g10086g2622 11, 1 1, 2, 2i S x y= = + = = ⋅⋅⋅ 1 1 1 1 15, (1 2 4 8 16) (1 ) 33, 32,2 4 8 16 32i S x y= = + + + + + + + + + ′∈ xfxxfx 时，时， g714 0)1()( =≤∴ fxf g708g5507g1092g1269g5507 g257g7206g2566g256== 1x g709 g708g6214g11105 “g1212g13527g13571g16874”g11797 1−= xy g1130 ）处切线，在点（ 0,1ln xy = g7235g11797 0)( ≤xf g5762g6208g12539g709 g7029 .0)(,0)( 21 ≤≤ xfxf g2121g5621g7481 ,0)()( 21 == xfxf g1594g3128g3316g3888g271g2360g272g1235g803 g1307 3 g3994g271g1643 8 g3994g272 g2467=+−=−+1532132yxyx g16403g5575==71274yxg712g7029 716=+ yx g714 g1218g573g3745g12464g20174g313g7141 14g714 12 15g714 94 16g714 ①② 13g714g463g16403g7616g464g11105g5154g11797g7569g1318g712g2591g15996g3599g2410g3599g1130g1081g16386g5522g714g1958g1117g1081g1114g20134g9961g2102g2139g1130 5 4(1,0),(1,2),( , )3 3 g712g6330g1081g1114g9961g2102g2139g1299g1941z x y= − g7920g20668g5575g726g5507 1, 0x y= = g7206g712zg2566g5575g7472g3927g16441g714 14g714g463g16403g7616g464g11105 ( ) 3a b a− = −g712g2591g5575 2 3 1a b a a b⋅ − = − ⇒ ⋅ =g712g6256g1301g2625g18431b g3416a g7145g2625g1082g11444g6341g5537g1130 12a ba⋅ = g714 15g714g463g16403g7616g464g3382g5619g1130(2, 1)− g712g2121g1299g1941g11556g13551g5575g7262 2 2a b+ = g712g2467 1a b+ = g712g16370g4623g6256g8818g5439g4480g5522g5439g727g1085g4056g1300 2, 1m a n b= + = + g712g2121 4 1 112 1 4 4 4m n m n n ma b m n m n+ ++ = + = + + ++ + 5 92 4 4 4n mm n≥ ⋅ + = g714(g5507g1092g1269g5507 ,4n mm n= 即m=2n时g712g1238g2467 2a b= 时，g2566“=”g727g8596g72062 13 3a b= =, g714) 16g714g463g16403g7616g464g311 g712 g712g5507g1092g1269g5507 g7206g2566g12665g2599g714g7029“ ”g7263“ ”g11444g1909g2102g1085g5621g16305g7569g1318g714 g3 g312g2591g1134g1467 1.1, 1.21a x= = g712g1238g2591g7072g5522g13571g2616g11797g5621g4488g3416 xaxa ax log,0,1 使得 g6208g12539g714 g3 g313 ( )f x g2591g1301g4671g12140g712g1398g5621g20139g7481g3927g12140g11444g18200g2102g712g1092 ( ) 0f x g11444g7458g13551g3364g6208g11444g19858g12319g8708 ( ) 0f x qq g712 g11105g20168g5951g712g557534 121 1 1 1813( )a a qa q a q a a q = = + = +…………………2g2102 g16403g5575 133aq= = …………………3g2102 g6256g1301 11 3n nna a q −= = ………………4g2102 g1594g3128g3316g3888g271g2360g272g1235g803 g1307 4 g3994g271g1643 8 g3994g272 g7082g709g11105g708Ig709g5575 2 13log 3 2 1nnb n−= = − g712 ………………5g2102 21( ) [1 (2 1)]2 2nnn b b n nS n+ + −= = = g714 ………………6g2102 g295 21 1 1 14 1 2 2 1 2 1nc n n n = = − − − +  , …………………8g2102 g295 1 1 1 1 1 112 3 3 5 2 1 2 1 2 1n nT n n n      = − + − + + − =      − + +      ⋯ ,……10g2102 g14613 2 1n nT n λ ∈+ g5762g6208g12539g712 g2121 max1( )2 1nλ + ,g6256g1301 13λ ………………12g2102 18g714g16403g726 g7081g709g16887g8971g1078g726g16878ABg1117g9961g1130Og712g17934g6613POg712 g11105g5154g11797PA=PBg712g6256g1301POg309ABg712 g13884g5283g19858PABg309g5283g19858ABCDg712g1236g13551g1130AB g7029POg309g5283g19858ABCD g1301Og1130g2511g9961g451OPg1130zg17828g712OBg1130yg17828g712g4018g3374g5418g12539g12458 g19492g11556g16386g3456g7735g13099g712g5286g16878PO=hg712 g2121P(0g7120g712h)g712B(0g7121g7120)g712C( 2 g7121g7120)g712 D( 2 g712g7131g7120) g6256g1301PC =( 2 g7121g712g713h)g712BD =( 2 g712g7132g7120) 0=⋅ BDPC g6256g1301PCg309BD…… 6g2102 g16887g8971g1218g726g16878ABg1117g9961g1130Og712g17934g6613POg712g11105g5154g11797 PA=PBg712g6256g1301POg309ABg712 g13884g5283g19858PABg309g5283g19858ABCDg712g1236g13551g1130AB g7029POg309g5283g19858ABCDg712g1278g13884BDg309PO……g311 g3416g11801g5522ABCDg1117g712g17934g6613COg712g16878COg1086BDg1236g1214Mg712 g2121g11105CD: CB=BC:BOg11797g440BCD g440OBCg712g6256g1301g287BCO=g287CDB g6256g1301g287BCM+g287CBM=g287CDB +g287CBM=90°g712g7029BDg309CO……g312 g11105g311g312g11797BDg309g5283g19858PCO g6256g1301PCg309BDg714 g7082g709g11105ADg309ABg712g5283g19858PABg309g5283g19858ABCDg712g1236g13551g1130ABg712g2591g5575ADg309g5283g19858PABg712 g6256g1301g5283g19858PABg309g5283g19858PADg712g1236g13551g1130PA g17911Bg1420BHg309PAg712g3506g17379g1130Hg712g2121BHg309g5283g19858PAD BDg1086g5283g19858PADg6256g6208g11444g16386g2467g1130g16386g287BDH g6256g1301BH= 22BD= 3622 =×g1278g13884g1081g16386g5522PABg1130g12665g17897g1081g16386g5522g712PO= 3 …… 8g2102 g708g1167g2591g11096g2625g18431g8965g8818g2090POg712g16878P(0g7120g712h)g712g2121A(0g712g7131g7120)g712B(0g7121g7120)g712g712D( 2 g712 g1594g3128g3316g3888g271g2360g272g1235g803 g1307 5 g3994g271g1643 8 g3994g272 g7131g7120)g712g2591g8818g5575g5283g19858PADg11444g1072g1114g8965g2625g18431g1130p =(0g712hg712g7131)g712g13884 )0,2,2( −=BD g712g11105 cos=sin45°g2591g16403g5575h= 3g709 g16878g5283g19858BPCg11444g1072g1114g8965g2625g18431g1130mg712g2121=⋅=⋅00BCmBPm g712 )0,0,2(),3,1,0( =−= BCBP g712g2591g2566m =(0g712 3g7121) g16878g5283g19858DPCg11444g1072g1114g8965g2625g18431g1130ng712g2121=⋅=⋅00DCnDPn g712 )0,2,0(),3,1,2( =−= DCDP g712g2591g2566n =(g713 3g7120g712g713 2 ) g1214g7263cos=g713 1010 g712…… 11g2102 g7029g1212g19858g16386B-PC-Dg11444g1417g5462g1644g1130g713 1010 …… 12g2102 19g714g16403g726 g7081g709g11105g20168g712 3.56t 1+ 2 + 3+ 4 + 5 + 6= = g712 76y 6.6 + 6.7 + 7 + 7.1+ 7.2 + 7.4= = g712 61( )( )i iit t y y=− −∑ ( 2.5) ( 0.4) ( 1.5) ( 0.3) 0 0.5 0.1 1.5 0.2 2.5 0.4 2.8= − × − + − × − + + × + × + × = g712 621( )iit t=−∑ 2 2 2 2 2 2( 2.5) ( 1.5) ( 0.5) 0.5 1.5 2.5 17.5= − + − + − + + + = g714 g6256g1301 2.8 0.1617.5b = =ɵ g712g2552ɵa y bt= − ɵ g712g5575ɵ 7 0.16 3.5 6.44a = − × = g712 g6256g1301yg1955g1214tg11444g13551g5719g3342g5506g7145g12347g1130ɵ 0.16 6.44y t= + g714 6g2102 g7082g709g311 g11105g7081g709g11797ɵ 0.16 6.44y t= + g712g5507 7t = g7206g712ɵ 0.16 7 6.44 7.56y = × + = g712 g24672018g5284g16917g1996g1239g2801g11444g1239g18431g11307g71456g1079g2648g714 g312 g5507g5284g1239g18431g1130yg7206g712g19248g2910g20173 3 2 3(4.5 0.3 ) 10 ( 0.3 4.5 ) 10S y y y y= − × = − + × g708g1079g1907g709g712 g5507 7.5y = g7206g712g2093g7072Sg2566g5575g7472g3927g1644g712g2552g3344 { }6.6 6.7 7 7.1 7.2 7.4 7.56y ∈ g712 g712g712 g712 g712 g712 g712 g16849g12743g5575g5507 7.56y = g712g2467 7t = g7206g712g24672018g5284g19248g2910g20173g7472g3927g714 12g2102 20g714g16403g726 g7081g709g11105g5154g11797g5575g726 1NF NM= g712g6256g1301 1 2 2 4NF NF MN NF+ = + = g2552 1 2 2 2F F = g712g6256g1301g9961N g11444g17816g17961g7263g1301 1 2,F F g1130g10070g9961g712g19375g17828g19375g12665g12144g11444g8029g3382g712 g6256g1301g9961N g11444g17816g17961g7145g12347g72632 214 2x y+ = g714…………3g2102 g7082g709g5507kg4488g3416g7206g712g16878g11556g13551 ( ): 1 0AB y kx k= + ≠ g712 ( )1 1,A x y g712 ( )2 2,B x y g712g2121 ( )2 2,B x y′ − g712 g1594g3128g3316g3888g271g2360g272g1235g803 g1307 6 g3994g271g1643 8 g3994g272 g13956g12539g11556g13551ABg1086g8029g3382g55752 22 41x yy kx + == + g712…………5g2102 g5575( )2 21 2 4 2 0k x kx+ + − = g712…………6g2102 g295( )21 2 21 2 28 1 4 0,4 ,1 221 2kkx xkx x k∆ = +  −+ = +− = +…………7g2102 g295 1 21 2ABy ykx x′−=+ g712g6256g1301g11556g13551 ( )1 21 11 2: y yAB y y x xx x−′ − = −+ g712 g6256g1301g1300 0x = g712g5575 1 2 2 11 2x y x yyx x+=+ g712…………9g2102 ( ) ( )1 2 2 1 1 21 2 1 21 1 2 1 2x kx x kx kx xx x x x+ + += = + =+ + g712 g6256g1301g11556g13551AB′g17911g4554g9961 ( )0,2Q g712g708g5507kg1085g4488g3416g7206g1277g17970g2616g709…………10g2102 g6256g1301 PAB′∆ g11444g19858g12319 1 2 2212 1 2PQB PQA kS S S x x k′∆ ∆= − = + = + 2 21 22 kk= ≤+g712g5507g1092g1269g5507 22k = ± g7206g712g12665g2599g6208g12539g714 …………11g2102 g6256g1301 PAB′∆ g19858g12319g11444g7472g3927g1644g7263 22 g714…………12g2102 21g714g16403g726 g7081g709g11105f(x)g729exg711asin xg711bg712 g5507ag7291g7206g712g5575f′(x)g729exg711cos xg714 g5507xg281[0g712g711∞)g7206g712ex≥1g712cos xg281[g7131g7121]g712g1092g5507cos xg729g7131g7206g712xg7292kπg711πg712kg281Ng712g8596g7206ex1g714 g6256g1301f′(x)g729exg711cos x0g712g2467f(x)g3416[0g712g711∞)g1082g2437g16947g17986g3790g712 g6256g1301f(x)min g729f(0)g7291g711bg712 g11105f(x)≥0g5762g6208g12539g712g55751g711b≥0g712g6256g1301b≥g7131g714 ……………………5g2102 g7082g709g11105f(x)g729exg711asin xg711bg5575 f′(x)g729exg711acos xg712g1092f(0)g7291g711bg714 g11105g20168g5951g5575f′(0)g729e0g711ag7291g712g6256g1301ag7290g714 g2552(0g7121g711b)g3416g2103g13551xg713yg7131g7290g1082g714 g6256g13010g7131g713bg7131g7290g714g6256g1301bg729g7132g714 g6256g1301f(x)g729exg7132g714 g1594g3128g3316g3888g271g2360g272g1235g803 g1307 7 g3994g271g1643 8 g3994g272 g1912g16881exg7132xg7131g712g2467exg713xg71310(x0)g712 g1300g(x)g729exg713xg7131(x0)g712 g2121g′(x)g729exg71310g712 g6256g1301g(x)g3416(0g712g711∞)g7263g3790g2093g7072g714 g6256g1301g(x)g(0)g7290g712g2467exg7132xg7131g714g311 g1981g16881xg7131≥ln xg712g2467xg7131g713ln x≥0(x0)g712 g1300φ(x)g729xg7131g713ln xg712 g2121φ′(x)g7291g7131xg729 1x x− g712 φ′(x)g7290g7206g712xg7291g712φ′(x)0g7206g712x1g712φ′(x)ln xg712g2467f(x)ln xg3416(0g712g711∞)g1082g6208g12539g714…………12g2102 22g714g16403g726 g7081g709g296g3382Cg11444g7601g3456g7735g7145g12347g1130 )32cos(4 πθρ −= g712 g295 )cos21sin23(4)32cos(42 θθρπθρρ −=−= g712 g2552g296 222 yx +=ρ g712 θρ cos=x g712 θρ sin=y g712 g295 xyyx 23222 −=+ g712 g295g3382Cg11444g7326g17994g7145g12347g1130 032222 =−++ yxyx g727…………5g2102 g7082g709g16878 yxz += 3 g712 g7029g3382Cg11444g7145g12347 4)3()1(0322 2222 =−++⇒=−++ yxyxyx g712 g295g3382Cg11444g3382g5619g7263 )3,1(− g712g2426g5556g72632g712 g4662+=−−=tytx213231g1299g1941 yxz += 3 g5575 tz −= g712 g2552g296g11556g13551lg17911 )3,1(−C g712g3382Cg11444g2426g5556g72632g712 g295 22 ≤≤− t g712g295 22 ≤−≤− t g712g2467 yx +3 g11444g2566g1644g14643g3364g7263 ]2,2[− g714……10g2102 23g714g16881g7230g726 g7081g709g8965g1072g726(1g7112x4)g713(2x3g711x2) g7292x3(xg7131)g713(xg7111)(xg7131) g729(xg7131)(2x3g713xg7131) g729(xg7131)(2x3g7132xg711xg7131) g729(xg7131)[2x(x2g7131)g711(xg7131)] g729(xg7131)2(2x2g7112xg7111) g1594g3128g3316g3888g271g2360g272g1235g803 g1307 8 g3994g271g1643 8 g3994g272 g729(xg7131)2 2 xg711122g71112 ≥0g712 g6256g13011g7112x4≥2x3g711x2g714 g8965g1212g726(1g7112x4)g713(2x3g711x2) g729x4g7132x3g711x2g711x4g7132x2g7111 g729(xg7131)2·x2g711(x2g7131)2≥0g712 g6256g13011g7112x4≥2x3g711x2g714 ……………………5g2102 g7082g709g16881g7230g726g3344g11306g729xg7112yg7113z≤ x2g711y2g711z2· 1g7114g7119g712g708g11105g7711g16303g1085g12665g5439g5575g709 g6256g1301x2g711y2g711z2≥187g712 g5507g1092g1269g5507xg729y2g729z3g2467xg72937g712yg72967g712zg72997g7206g712x2g711y2g711z2g7481g7472g4671g1644187g714……10g2102