Comments on: GCE A-Level 2009 Oct/Nov H2 Maths 9740 Paper 1 Suggested Answers & Solutions http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: meena http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-34678 meena Sat, 06 Feb 2010 16:15:03 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-34678 as in 2009. thanks especially to paper 1. as in 2009. thanks especially to paper 1.

]]> By: meena http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-34677 meena Sat, 06 Feb 2010 16:12:49 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-34677 hello anyone knows where to find the ans to A level chem our year ? hello
anyone knows where to find the ans to A level chem our year ?

]]> By: Mr Loi http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-33936 Mr Loi Tue, 12 Jan 2010 14:09:17 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-33936 Hello there <b>'Cher</b>. Moved your comment here as I believe you're referring to the <strong>2009</strong> H2 Maths P1 and not the 2008 one. Errr ... for the relevant part of <span class="highlight">Q7(ii)</span>, the binomial expansion of (<var>a</var>+<var>b</var><var>x</var><sup>2</sup>)<sup>−1</sup> is as follows: [pmath](a+bx^2)^-1[/pmath] [pmath]{}={1/a}(1+{b/a}x^2)^-1[/pmath] Since [pmath]{b/a}x^2[/pmath] is the <var>b</var> in (1+<var>b</var>)<sup><var>n</var></sup>, the next term would contain a <var>x</var><sup>4</sup> if we were to 'expand one more time' as follows: [pmath]{}={1/a}[1+(matrix{2}{1}{{-1} 1})({b/a}x^2)+(matrix{2}{1}{{-1} 2})({b/a}x^2)^2 + cdots][/pmath] [pmath]{}={1/a}[1+(-1)(b/a)x^2+(1)(b/a)^2x^4 + cdots][/pmath] From the above we can see that there is no <var>x</var><sup>2</sup> beyond the second term. I suspect that you've taken [pmath](1+{b/a}x^2)[/pmath] instead to be your <var>b</var> in (1+<var>b</var>)<sup><var>n</var></sup>? <strong>stormangel:</strong> This blog post was published on 12 Nov 2009 (two days after your H2 Paper 1) - very late <i>meh</i>? Hello there 'Cher.

Moved your comment here as I believe you're referring to the 2009 H2 Maths P1 and not the 2008 one.

Errr ... for the relevant part of Q7(ii), the binomial expansion of (a+bx2)−1 is as follows:
(a+bx^2)^-1
{}={1/a}(1+{b/a}x^2)^-1

Since {b/a}x^2 is the b in (1+b)n, the next term would contain a x4 if we were to 'expand one more time' as follows:

{}={1/a}[1+(matrix{2}{1}{{-1} 1})({b/a}x^2)+(matrix{2}{1}{{-1} 2})({b/a}x^2)^2 + cdots]
{}={1/a}[1+(-1)(b/a)x^2+(1)(b/a)^2x^4 + cdots]

From the above we can see that there is no x2 beyond the second term. I suspect that you've taken (1+{b/a}x^2) instead to be your b in (1+b)n?

stormangel: This blog post was published on 12 Nov 2009 (two days after your H2 Paper 1) - very late meh?

]]> By: 'Cher http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-33928 'Cher Tue, 12 Jan 2010 09:01:54 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-33928 hi, for qn7ii, you need to expand (a+bx^2)^(-1) one more time as (1+b/a x^2) ^2 will have a term in x^2. hi,
for qn7ii, you need to expand (a+bx^2)^(-1) one more time as (1+b/a x^2) ^2 will have a term in x^2.

]]> By: stormangel http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-33532 stormangel Thu, 31 Dec 2009 01:04:20 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-33532 wah.. so late then it's out.... alrd finish a level liao.... wah.. so late then it's out.... alrd finish a level liao....

]]> By: Mr Loi http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32432 Mr Loi Mon, 16 Nov 2009 15:28:42 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32432 And to elaborate on <b>Labbitan</b>'s method to get the cartesian equation of the plane (let's call it <var>p</var><sub>4</sub>) in <span class="highlight">Q10(iii)</span>, <img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/11/2009-h2-p1-q10-diagram.gif" alt="2009 H2 9740 Paper 1 Q10 diagram" /> We let <var class="vector">d</var><sub>1</sub> be the direction vector of <var>l</var> i.e. <var class="vector">d</var><sub>1</sub> = [pmath](matrix{3}{1}{1 1 {-1}})[/pmath] We're given that (2, 3, 4) lies on <var>p</var><sub>4</sub>, and since we've proven that <var>l</var> lies on <var>p</var><sub>4</sub> ⇒ (0, 1, 0) lies on <var>p</var><sub>4</sub> too ⇒ we can form another direction vector <var class="vector">d</var><sub>2</sub> on the plane as follows: <var class="vector">d</var><sub>2</sub> = [pmath](matrix{3}{1}{2 3 4})-(matrix{3}{1}{0 1 0})=(matrix{3}{1}{2 2 4})=2(matrix{3}{1}{1 1 2})[/pmath] We can then cross <var class="vector">d</var><sub>1</sub> and <var class="vector">d</var><sub>2</sub> to obtain the normal of plane <var>p</var><sub>4</sub>: <var class="vector">d</var><sub>1</sub> × <var class="vector">d</var><sub>2</sub> = [pmath](matrix{3}{1}{1 1 {-1}})*(matrix{3}{1}{1 1 2})=(matrix{3}{1}{3 {-3} 0})=3(matrix{3}{1}{1 {-1} 0})[/pmath] So to get the cartesian equation of <var>p</var><sub>4</sub>: <var class="vector">r</var>⋅[pmath](matrix{3}{1}{1 {-1} 0}) = (matrix{3}{1}{1 0 0})(matrix{3}{1}{1 {-1} 0}) = -1[/pmath] ∴ <var>x</var> − <var>y</var> = −1, <var>z</var> ∈ ℝ (yes <b>passerby</b> it's <var>z</var> ∈ ℝ, I've updated the solution ;) ) <hr/> Lastly, I would like to add that we can also show that line <var>l</var> lies in <var>p</var><sub>3</sub> through the following two expressions: <var>x</var>+<var>z</var> = 0 ⇒ <var>x</var> = −<var>z</var> <var>y</var>+<var>z</var> = 1 ⇒ <var>y</var> = 1−<var>z</var> that's obtained using the RREF function in your <acronym title="Graphical Calculator">GC</acronym> when solving the equations of <var>p</var><sub>1</sub> & <var>p</var><sub>2</sub> in part (ii). We can then sub the above expressions into the equation for <var>p</var><sub>3</sub> as follows: LHS: 2(−<var>z</var>)+(1−<var>z</var>)+3<var>z</var>−1+<var>k</var>(<var>z</var>+2(1−<var>z</var>)+<var>z</var>−2) = 0 = RHS ∴ <var>l</var> lies in <var>p</var><sub>3</sub> for any constant <var>k</var>. And to elaborate on Labbitan's method to get the cartesian equation of the plane (let's call it p4) in Q10(iii),

2009 H2 9740 Paper 1 Q10 diagram

We let d1 be the direction vector of l i.e.
d1 = (matrix{3}{1}{1 1 {-1}})

We're given that (2, 3, 4) lies on p4, and since we've proven that l lies on p4
⇒ (0, 1, 0) lies on p4 too
⇒ we can form another direction vector d2 on the plane as follows:

d2 = (matrix{3}{1}{2 3 4})-(matrix{3}{1}{0 1 0})=(matrix{3}{1}{2 2 4})=2(matrix{3}{1}{1 1 2})

We can then cross d1 and d2 to obtain the normal of plane p4:

d1 × d2
= (matrix{3}{1}{1 1 {-1}})*(matrix{3}{1}{1 1 2})=(matrix{3}{1}{3 {-3} 0})=3(matrix{3}{1}{1 {-1} 0})

So to get the cartesian equation of p4:
r⋅(matrix{3}{1}{1 {-1} 0}) = (matrix{3}{1}{1 0 0})(matrix{3}{1}{1 {-1} 0}) = -1
∴ x − y = −1, z ∈ ℝ
(yes passerby it's z ∈ ℝ, I've updated the solution ;) )

Lastly, I would like to add that we can also show that line l lies in p3 through the following two expressions:

x+z = 0 ⇒ x = −z
y+z = 1 ⇒ y = 1−z

that's obtained using the RREF function in your GC when solving the equations of p1 & p2 in part (ii).

We can then sub the above expressions into the equation for p3 as follows:
LHS: 2(−z)+(1−z)+3z−1+k(z+2(1−z)+z−2) = 0 = RHS
∴ l lies in p3 for any constant k.

]]> By: Mr Loi http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32431 Mr Loi Mon, 16 Nov 2009 15:25:37 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32431 Sorry guys I've been away for the past week as I was busy with my classes and working out the solutions to the rest of the H1/H2 maths papers. Anyway for those of you who are not yet aware, my <a href="http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-h1-maths-8863-h2-maths-9740-paper-2-suggested-answers-solutions" rel="nofollow">H1 Maths Paper 1 and H2 Maths Paper 2</a> are now up. I appreciate your discussions and comments here, and in response to some of the feedback, I've updated the diagrams in <span class="highlight">Q9</span> to more show more accurately that the bisector does indeed pass through the origin and <var>z</var><sub>7</sub>. Sorry guys I've been away for the past week as I was busy with my classes and working out the solutions to the rest of the H1/H2 maths papers.

Anyway for those of you who are not yet aware, my H1 Maths Paper 1 and H2 Maths Paper 2 are now up.

I appreciate your discussions and comments here, and in response to some of the feedback, I've updated the diagrams in Q9 to more show more accurately that the bisector does indeed pass through the origin and z7.

]]> By: Ys http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32384 Ys Sat, 14 Nov 2009 23:42:07 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32384 Oh ok thanks! Do you all mind putting the link here once you all find it? Thanks a million! (: wad ques did you all do for chem? Oh ok thanks! Do you all mind putting the link here once you all find it? Thanks a million! (: wad ques did you all do for chem?

]]> By: wei zhong http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32370 wei zhong Sat, 14 Nov 2009 14:31:21 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32370 Ikes true, JC chem doesn't seem to be covered here. i tried and tried Google using various search terms, but I guess I'll try again tomorrow, when whichever website hosting it gets indexed by Google. thanks for your info! :DD Ikes true, JC chem doesn't seem to be covered here. i tried and tried Google using various search terms, but I guess I'll try again tomorrow, when whichever website hosting it gets indexed by Google. thanks for your info! :D D

]]> By: Nash http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32367 Nash Sat, 14 Nov 2009 13:39:38 +0000 http://www.exampaper.com.sg/mr-loi-the-a-level-tutor/gce-a-level-2009-octnov-h2-maths-9740-paper-1-suggested-answers-solutions#comment-32367 Yes it was an organic spam, every question had it cambridge dosnt like to repeat trends. Just in case u wanna know, P3 had 2 organic question, chem kinetics, protein chem ,grp7. Like i spotted they are gonna put transition for paper 2 and kill alot of ppl like the Cu chem question last year (ugh) Probably Mn or Vanadium this time(might come out as electro though) I don't think Little miss Loi covers JC chem so maybe u should try other websites. Its already out according to my tutor but i dun have the links >_< sorry... Omg i rank highest in the chatter boxers <_<, just noticed... Well its constructive conv anyways (mostly) =P Yes it was an organic spam, every question had it cambridge dosnt like to repeat trends. Just in case u wanna know, P3 had 2 organic question, chem kinetics, protein chem ,grp7. Like i spotted they are gonna put transition for paper 2 and kill alot of ppl like the Cu chem question last year (ugh) Probably Mn or Vanadium this time(might come out as electro though)

I don't think Little miss Loi covers JC chem so maybe u should try other websites. Its already out according to my tutor but i dun have the links >_< sorry...

Omg i rank highest in the chatter boxers <_<, just noticed... Well its constructive conv anyways (mostly) =P

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