All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.
Specimen paper 1
Specimen paper 1 answer booklet
Numerical Answers (click the questions for workings/explanation)
Question 1: 
Question 2: 
Question 3: 
Question 4: 792 cm; 73 bounces, 2400cm
Question 5: 
is a maximum, 20
Question 6: 
Question 7: 
Question 8: 
Question 9: 
Question 10: 
Question 11: 
, where 
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.
. Thus, the required number of bounces is 73.
![= 160 + \frac{2(160)(\frac{7}{8}) \big[ 1 - (\frac{7}{8})^{72} \big]}{1 - \frac{7}{8}}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-0843475ae8f876c3ca5b4e136f52ea96_l3.png "Rendered by QuickLaTeX.com")
.
, we have that 
.
![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.
.
. 
lies on a line passing through the position 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")
radians about the Origin.
.
.
.
.
, applying binomial series from MF27
, since 
is small.
, ![\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-a2e5a6c059134361dcf05dc527e183e4_l3.png "Rendered by QuickLaTeX.com")
and using GC, 
, where 
Relevant materials
KS Comments
The specimen paper 1 was useful to provide us with a glimpse of what is to be expected of the updated syllabus. The last two questions, in particular, showed us the extent of applications. It is definitely different from the previous 9758 H2 Mathematics Syllabus as the questions are more intuitive and seek to push students’ imaginations more.
In this paper, Question 9 and Question 11 serve to be the application questions. Question 4 is a contextual/ application question that involves modelling solution. Question 8 test students on application of Mathematics and generally involves a brief statement to test the application. Question 7 tests complex number geometry.
[…] Paper 1 […]