kumon test Questions & Answers Already Graded A+

log₂(4/3) + 2log₂(√12) - Answer-log₂(4/3×12)=log₂16=4 (log₂3+log₄9)(log₃2+log₉4) - Answer- (log₂3+(log₂9/log₂4))((log₂2/log₂3)+(log₂4/log₂9))=(log₂3+(2log₂3/2))((1/log₂3)+(2/2log₂3))=2log₂3×(2/log₂ 3)=4 log₃(x-2)+log₃(x-4)<1 - Answer-log₃(x-2)(x-4)<1 log₃(x²-6x+8)<1 (x²-6x+8)<3 x²-6x+5<0 (x-1)(x-5)<0 1<x<5 x-2>0, x-4>0 x>2, x>4 4<x<5 log₁₀5(x+1)>2-log₁₀(2x-1) - Answer-log₁₀5(x+1)+log₁₀(2x-1)>2 5(x+1)(2x-1)>100 (x+1)(2x-1)>20 2x²+x-21>0 (x-3)(2x+7)>0 -7/2<x>3 x>-1 x>1/2 x>3 y=(2x+3)² - Answer-4x²+12x+9=8x+12y=(2x²+3)(2x²-3) - Answer-4x⁴-9=16x³ ∫³₀dx - Answer-[x]=3 ∫³_₃dx - Answer-[x]=3-(-3)=6 ∫³₀xdx - Answer-[½x²]³₀=9/2 f(x)=x³-9x²+24x-15 - Answer-f'(x)=3x²-18x+24=3(x-2)(x-4) x=2,4 x=2, f(2)=5 x=4, f(4)=1 At x=2, max is 5 At x=4, min is 1 y=x³-6x²+9x - Answer-f'(x)=3x²-12x+9=3(x-1)(x-3)=0 x³-3x-1=0 - Answer-y'=3x²-3=3(x+1)(x-1) f(0)=-1 1 positive root 2 negative roots ∫(x+1)(x+2)dx - Answer-∫(x²+3x+2)dx=1/3x³+3/2x²+2x+C y=x²(x³+1) - Answer-2x(x³+1) + x²×3x²=2x⁴+2x+3x⁴=5x⁴+2x y=(x²-2x)(x+1) - Answer-(2x-2)(x+1)+(x²-2x)=2x²-2+x²-2x=3x²-2x-2y=(2x²+1)(3x²-1) - Answer-4x(3x²-1)+(2x²+1)6x=12x³-4x+12x³+6x=24x³+2x y=x³-2x-2 (x=-1) - Answer-y'=3x²-2 f'(-1)=1 f(1)=-1 y+1=x+1 y=x y=x²-2x+4 (x=1) - Answer-f'(1)=0 f(1)=3 y-3=0 y=3 y=-2x²+8x-4 - Answer-f'(x)=-4x+8 -4x+8=4 -4x=-4 x=1 f(1)=2 Tangent Line:y-2=4(x-1) Point of Contact:(1,2)