All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.
Numerical Answers (click the questions for workings/explanation)
Question 1: 
Question 2: 
Question 3: 
Question 4: 1277cm, 3400cm
Question 5: 
is a maximum, 20
Question 6: 
Question 7: 
Question 8: 
Question 9: 
Question 10: 
Question 11: 
and 
be the circumference and area of the ink-blot at time 
respectively.
, 
.
(3 d.p.)
be the maximum height of the ball after the first bounce.
![= 200 + \frac{2(200)(\frac{8}{9}) \big[1 - (\frac{8}{9})^4 \big]}{1-\frac{8}{9}} - 200( \frac{8}{9})^4](http://theculture.sg/wp-content/ql-cache/quicklatex.com-2680bb5aa85ccc5caf7ca25b55e60e06_l3.png "Rendered by QuickLaTeX.com")
. Thus, the required number of bounces is 85.
![= 200 + \frac{2(200)(\frac{8}{9}) \big[ 1 - (\frac{8}{9})^{84} \big]}{1 - \frac{8}{9}}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-846b3e638d8ef0d1218f2d93be16186e_l3.png "Rendered by QuickLaTeX.com")
.
is a maximum.
![A = \bigg[ \frac{1}{4} (\text{ln}x)^4 \bigg]_e^{e^3}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-65c13355c93f14e734e5884384fba152_l3.png "Rendered by QuickLaTeX.com")
is parallel to 
since 
is also a nonzero vector.
.
. 
and parallel to the direction vector 
, where 
is a scalar parameter.
![(1+i) \bigg[ -2i + \big( 1 + \frac{i}{2} \big) w \bigg] + (2+i)w = 3](http://theculture.sg/wp-content/ql-cache/quicklatex.com-5beffb8bc3c1ec1f20289bf967b18665_l3.png "Rendered by QuickLaTeX.com")
.
.
depends only on 
.
.
, ![\bigg[ \begin{pmatrix} 0\\-1\\2 \end{pmatrix} + \lambda \begin{pmatrix} 2\\-3\\1 \end{pmatrix} \bigg] \cdot \begin{pmatrix} 2\\-3\\1 \end{pmatrix} = - 9](http://theculture.sg/wp-content/ql-cache/quicklatex.com-5e3c276e185de2881b22b9aad5785ead_l3.png "Rendered by QuickLaTeX.com")
for some 
.
be the reflection of 
on 
.
and 
![\vec{PF} = \frac{1}{14} \bigg\{ \bigg[ \begin{pmatrix} 4\\-5\\10 \end{pmatrix} - \begin{pmatrix} -2\\2\\1 \end{pmatrix}\bigg] \cdot \begin{pmatrix} 2\\-3\\1 \end{pmatrix} \bigg\} \begin{pmatrix} 2\\-3\\1 \end{pmatrix}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-b073d125d9359c3ec69a9a3db70a863a_l3.png "Rendered by QuickLaTeX.com")
.Relevant materials
KS Comments
The specimen paper 1 was useful to provide us with a glimpse of what is to be expected of the upcoming syllabus. The last two questions, in particular, showed us the extent of applications. It is definitely different from the old 9740 H2 Mathematics Syllabus as the questions are more intuitive and seek to push students’ imaginations more.
