maths past paper qs

answer

rewrite to get y=x^-2

dy/dx=-2x^-3-1

-2/x³

we know the period of sinπ=2π

so sinπn=2π/π =2

so therefore sinnπ/2=2×2=4

logs question

make y equal to the question

get rid of e by doing ln of one side so lny=x-4

rearange to get x as x=4+lny

f(-x)=4+lnx where x is greater than 0

a=make it into algebraic format

see that the first part is not 1 so need to pull it out to get 2x(1 + x^1/2 /4) to the power of -1/2

get equation as

1/2(1+(-1/2)x/4- -(1/2)(-3/2)(x/4)²/2!

b=see difference is x³

replace every x term to x³

½ +x³/16 +3x^6/256

a-using pythagrus find every lengths by doing (x-x)²+(y-y)²

the length that ads together to give you one is the answer

b-Use the circle theorem that the angle subtended by a diameter at the circumference is 90°.

c-find radius by doing square root of answer/2

find centre by doing midpoint

find distance by doing (x-x)²+(y-y)² and the answer tells if above or below squared radius