高中数学计算限时训练参考答案与讲解

参考答案与讲解1.x-22.-1或一73.2.48×10⁷4.05.一86.2.1×10-77.-1或38.1或-119.158.125元9.—810.8.125元9.—810.14.415.016.3617.418.2919.x(2-y)(2+y)20.921.±2022.723.-1训练41.±42.4(x+y)(x-y)3.3xy(y-3x)(y+3x)49.—8a³+16a⁴-8a⁵10.-211.±212.15,1612.513.114.6√2或2√5或2√215.416.217.(2,5)或(8,20)18.514.-215.略注这里以第6题为例：注这里以第1题为例：S=1×2¹+3×2²十…十(2n—3)2”-¹+(2n—1)2”2S,=1×2²+3×2³+…+(2n—3)2"+(2n-S,=2+2³+2⁴+…+20+1—7.(10,+一)8.9.(-0,-1)3.△=a²+4>0,解方程ax²+(a+2)x+1=0,两根分别为：或4.△=a²—4.(1)当△=a²-4≤0,(2)当△=a²—4>0,注这里以第2题为例：注意，这里的△>0.y11ao112@::训练21训练223.因为训练231.当a≥-4时，单调递增区间是(0,+一)注这里以第2题为例：工2.x-√2y-√3=0注这里以第3题为例：解得m²=1,m=±1.1训练28为半径的圆.3.(24,十0)为半径的圆.2.曲线的形状是以或训练29训练30—训练3112.203.(1)PA:x+y-1=0,PB:7x-y-15=0训练32训练33训练34训练35训练362.4.-2sin2x+2·32r+¹In3训练3712.3.2sin(2x+5)+4.xcos(2x+5)4.(ln3+1)3*e-1n2·25.训练38训练39训练401.K²≈18.1822.K²≈6.593训练41训练42;事由已知得x=5,y=13,事;事训练43工42中42中;:事;:事;;Y05P训练44ξ0234P244X2345P训练452n²+1,所以3">2n²+1(n≥3,n∈N*).注这里以第1题为例：2.5≤r≤63.训练474.(1)(7b—8a)(7b+8a)(2)3a(x+3y)²(3)(7x+2)(训练481.11762.8.534524.(1)2x(x+2)(x—2)(2)(a+2b)(a-2b)(则f(x)>f(0)=0,g(x)>g(0)=0训练49训练50训练51.5.6.(1)(x—1)²+(y+2)²=5(2)(x-2)²+(y(3)(x-m)²+(y+2n)²=m²+4n²7.√58.m=(A²+B²)[(x₀—x)²+(y₀—y)²]训练52或或a=4;(2)2个解：a>4或a=0;(3)1个解：a无解；(4)0个解：a<0.14.(x+2)(x+3)(x-1)(x-2)训练531)(x²-x+1)(x⁴-x²+1)(3)(1-3x)(x+1)(4)(x+2y+3)(x+y+2)66注这里以第4题为例：yybC训练55工)2.y≤13.√54.(1)0(2)2(3)1(4)85.(1)1.12.2或53.—60<a-2b<30;4.a=—6,b=—1;x≤-6或x≥15.a=3,b=6(4)<(5)<10.证明：在平面直角坐标系xOy内作以原点为圆心的单位圆，以Ox为始边作角a,β,它们OA·OB=(cosa,sina)·(cosβ,sinβ)=cosa训练58训练598.i9.1或39.14410.-111.212.2√213.士√514.(48-32√2)π训练608.(1)(x+a+1)(x+1)(2)(ax+1)(x+2)9.训练611.82.3.0.24.5.(-1,2)6.(1)log3.82.5<log2.g2.9<log2.84.6注即训练62训练63训练64训练65训练66训练67训练6889.2-10.89.2-10.(1,+○)14.过定点(1,2)训练69训练70半径为1的圆的一部分(右半圆).4.805.x²+y²+2x-2y=06.圆心坐标是,半径是训练712.是3.(0,2)4.(-1,2)5.9.-210.[0,4]11.(-0,-2)U(-2,1)U(1,+训练72训练732.2(a-2)²3.24.2√35.1106.57.±2√3训练74(3)7或811.证明：因为α+β=π,sina=sinβ,所以训练7512.74.23.-24.(1)(一x²+3)e²-*(2)(3)5.6.(1)训练76训练77训练781.22.83或一853.8.(1)(y-6)²(2)(x+3)²(3)(x-3y)²(x+3y)²(4)(y+2)²(y-2)²(5)2ab(a-b)²(6)(m一训练79工2.[-13,13]3.(1)<(2)<4.必要不充分5.(0,3)6.(1)-1(2)47.x²+y²-6x=08.69.-202210.12.(n+1训练8197.am=2”—18.1209.√210.4tanA+tanB=tan(A+B)(1—tantanA+tanB+tanC=—tanC(1—tanAtan训练82训练83(2)-2<x<1或x>3(3)x<1(4)x<1.52.73.11训练84训练851.2或-12.>3.4454.(-1,0)U(1,+0)5.(-0,4)U(8,+o)6.7.训练86训练87训练88训练89训练90训练91训练92训练9311.(1)(x—5y+2)(x+2y-1)(2)(x+3y-2)训练941.4或±22.{0,1,2}3.124.)5.6.1.(1)(x-a)(x+2)(2)(x-a)(x—1)(3)(x-a)(x+12.Vx∈R,7x²-2x+1>03.O4.0.65.26.167.x=-1,3或x≥48.1+2i9.110.2训练961.72.13或一53.24.-3a²b⁵5.-46.-287.-58.109.10.an=6n—111.a=12.x=0或3x+4y=013.3x+y-6=014.y训练971.-0.14412.(1)(2,3)(2)(-2,-1)U(5,+0)(3)x≤-3或x=3(4)(0(6)2√2(7)(-0,0)U(1,+c)3.4.5.)(k∈Z训练98训练99训练1003.(-c,1)4.3.(-c,1)4.训练1011.82.193.10或4.-85.36.47.28.(-0,1)9.训练1021.(0,+一)2.3.4.2√2+15.6.3x²-3*In37.训练10312.y=2sin(4x-3)13.114训练1043,3√2+3]12.913.(√2,+α)14.略训练1051.3≤≤122.√-x3.104.x<45.[√6,2√3]6.a>c>b