f4 maths2

1.
f(x) =x^2 -1
f(a-1)= (a-1)^2 -1 (sub x=a-1)
= a^2-2a+1 -1
= a^2-2a
= a(a-2)

2.
where is the following equations?
x/2 + (x+1)/2 = 54/60
as speed/ distance = time
be careful of units changing

3.
1/2logy= 1+logx
1/2logy= log10+logx (log10=1,log100=2)
1/2logy= log(10x) (logM + logN=logMN & take log for both sides)
y^(1/2)=10x ( square both sides)
y =100x^2

4.
As f(1)=0,
that means f(x) can divided by x-1 { x-1 =0, x=1 }
f(x) =x^3-2x^2-5x+6
= (x-1)(x^2-x-6) {用長除法}
=(x-1)(x+2)(x-3)

5.
log(x-1)=3
log(x-1)=log1000 (log10=1,log100=2)
x-1 =1000
x=1001

6.
f(x)=(2x-1)(x+1)+2x+1
f(-1/2)= {2(-1/2)-1}(-1/2+1) +2(-1/2)+1
= {-1-1}{1/2}-1+1
=(-2)(-1/2)
=1
thus remainder is 1