Hopefully, you guys have started on the Set A. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. 🙂
If you do have any questions, please WhatsApp me. 🙂
Firstly, either consider
or square both sides. Its easier to do the latter (so I will).

![\bigg[ \frac{2x-3}{x+5} \bigg]^2 \le \bigg[ \frac{2}{3} \bigg]^2 \bigg[ \frac{2x-3}{x+5} \bigg]^2 \le \bigg[ \frac{2}{3} \bigg]^2](//s0.wp.com/latex.php?latex=%5Cbigg%5B+%5Cfrac%7B2x-3%7D%7Bx%2B5%7D+%5Cbigg%5D%5E2+%5Cle+%5Cbigg%5B+%5Cfrac%7B2%7D%7B3%7D+%5Cbigg%5D%5E2&bg=ffffff&fg=000&s=0)



Since
for all 




(i)
LHS


RHS.
(ii)


(Showing workings for Method of Difference)

(iii)
As
.
Hence, the series converges to
.



Since arithmetic series is increasing,
,

Common ratio 
Since
, the geometric series converges.
(ii)
First term 


By Pythagoras’ Theorem,


since 
Area, 

Let 


Check with first derivative test.
Hence,
maximises A.

Thus, dimensions are
m and
m (to 3.s.f.).


(i)




, where
is an arbitrary constant.
When
.

(ii)
As
.
Thus, the population of salmon in the fish farm will decrease towards 6,000 in the long run.

For curve to cut the x axis at 2 distinct points,

or 
(i)

(ii)
— (1)
— (2)
Coordinate of 
When 
Observe that
passes through
for all real values of
.
Thus, for line to not intersect C,
.
(iii)


or 
(a)

Firstly, scale by factor
parallel to the y – axis.
Secondly, translate by 3 units in the positive x – direction.
Curve D is a circle.
(b)
(i)

(ii)

(i)


Since 
Using Sine Rule,


So y coordinate is given by 
(ii)
Gradient of 
Since QS is always tangential to hump, gradient of 
Since 

(iii)
Area 
(4dp)