Comments on: The Tuition Enquiry From Hell http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Wed, 24 Apr 2013 20:25:50 +0000 hourly 1 By: Li-sa http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11743 Li-sa Thu, 14 Aug 2008 01:01:14 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11743 I don't really care about that "mistake" because there are no actual reports of jiang shi anyway. Only spirits that possess humans and make them go crazy. I don't really care about that "mistake" because there are no actual reports of jiang shi anyway. Only spirits that possess humans and make them go crazy.

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11712 Miss Loi Tue, 12 Aug 2008 16:40:38 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11712 Thank you so much <b>Li-sa</b> for saving Miss Loi from the 僵屍! But there's a big mistake in your comment: in the movies, sticking yellow papers to their foreheads only stop them temporarily, they most certainly don't VANISH! Wah <b>Naomi</b>, you actually tried this question ... finished my E-Maths homework already? Anyway, high chance that students will encounter such a <del>僵屍</del> <var>T</var><sub><var>r</var>+1</sub> in your exams too! Thank you so much Li-sa for saving Miss Loi from the 僵屍!

But there's a big mistake in your comment: in the movies, sticking yellow papers to their foreheads only stop them temporarily, they most certainly don't VANISH!

Wah Naomi, you actually tried this question ... finished my E-Maths homework already?

Anyway, high chance that students will encounter such a 僵屍 Tr+1 in your exams too!

]]> By: Li-sa http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11708 Li-sa Tue, 12 Aug 2008 13:42:16 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11708 <span class="highlight">Miss Loi is quietly looking at your workings from inside the closet ...</span> The 5th term is a constant. Let the (r+1)th term be [pmath]{{}^n}C_r (x^2)^{n-r}(-2/x)^r [/pmath] The fifth term = [pmath]{{}^n}C_4 (x^2)^{n-4}(-2/x)^4 [/pmath] <div class="highlight"> The good thing about <em>Binomial</em> questions is that there's not many formula you need to work with. So to get the coefficient of the middle term in this question, you'll first need to find the value of <var>n</var> BEFORE you can even know WHICH is the middle term. The only clue given is that the 5th term is independent of <var>x</var> ⇒ the power of <var>x</var> in <var>T</var><sub>5</sub> is zero. <div class="attention">So the key here calculate <var>n</var> by EQUATING the power of the <var>x</var>-component in <var>T</var><sub>5</sub> with zero.</div> From the calculations using the <var>T</var><sub><var>r</var>+1</sub> formula above, the <var>x</var> component of <var>T</var><sub>5</sub> is (<var>x</var><sup>2</sup>)<sup><var>n</var>-4</sup><var>x</var><sup>-4</sup> Using a bit of <a href="/tag/indices" rel="nofollow">indices</a> magic, you can simplify the above into <var>x</var><sup>2(<var>n</var>-4)-4</sup> and you'll get your <var>n</var> as follows: </div> As the fifth term is a constant, power of x of this term = 0 = 2(<var>n</var>-4)-4, <var>n</var> = 6 <div class="highlight"> <div class="attention">Always, always pinch/slap/remind yourself that a binomial expansion of (<var>a</var> + <var>b</var>)<sup>n</sup> contains a total of <strong><var>n</var> + 1</strong> terms.</div> So since <var>n</var> is 6, the middle term of 0, 1, 2, 3, 4, 5, 6 is actually the 4th term <var>T</var><sub>4</sub>, which also means that the value of <var>r</var> has to be 3! N.B. There's no middle term if <var>n</var> happens to be an odd number ;) </div> Now coefficient of the middle term (or 4th term) = [pmath]{{}^6}C_3 (-2)^3 = 20(-8) = -160[/pmath] <span class="highlight">Note that you don't have to bother with the <var>x</var> terms in the <var>T</var><sub><var>r</var>+1</sub> formula, since we're only interested in the coefficient.</span> *hurls a yellow Post-It note with "-160" on it and totally covered in paste at 僵屍's forehead and bullseye! 僵屍vanishes* Exciting question but it seems that most visitors above this comment are just singing: "wo~wo~wo~wo~Everybody was 僵屍 fighting~" <!--It's just a variation of Kung Fu Panda theme song. If you've only watched the trailer you'll still get the joke.--> Ha, thinking of this yellow paper thingy, in my earlier secondary school days, the yellow paper was a warning that one has broke too many times of a certain school rule; break only 1 more time and get a demerit. Seems at that time everyone was really a 僵屍............................ Miss Loi is quietly looking at your workings from inside the closet ...

The 5th term is a constant. Let the (r+1)th term be
{{}^n}C_r (x^2)^{n-r}(-2/x)^r

The fifth term
= {{}^n}C_4 (x^2)^{n-4}(-2/x)^4

The good thing about Binomial questions is that there's not many formula you need to work with.

So to get the coefficient of the middle term in this question, you'll first need to find the value of n BEFORE you can even know WHICH is the middle term.

The only clue given is that the 5th term is independent of x ⇒ the power of x in T5 is zero.

So the key here calculate n by EQUATING the power of the x-component in T5 with zero.

From the calculations using the Tr+1 formula above, the x component of T5 is (x2)n-4x-4

Using a bit of indices magic, you can simplify the above into x2(n-4)-4

and you'll get your n as follows:

As the fifth term is a constant, power of x of this term = 0 = 2(n-4)-4, n = 6

Always, always pinch/slap/remind yourself that a binomial expansion of (a + b)n contains a total of n + 1 terms.

So since n is 6, the middle term of 0, 1, 2, 3, 4, 5, 6 is actually the 4th term T4, which also means that the value of r has to be 3!

N.B. There's no middle term if n happens to be an odd number ;)

Now coefficient of the middle term (or 4th term)
= {{}^6}C_3 (-2)^3 = 20(-8) = -160 Note that you don't have to bother with the x terms in the Tr+1 formula, since we're only interested in the coefficient.

*hurls a yellow Post-It note with "-160" on it and totally covered in paste at 僵屍's forehead and bullseye! 僵屍vanishes*

Exciting question but it seems that most visitors above this comment are just singing:
"wo~wo~wo~wo~Everybody was 僵屍 fighting~"

Ha, thinking of this yellow paper thingy, in my earlier secondary school days, the yellow paper was a warning that one has broke too many times of a certain school rule; break only 1 more time and get a demerit. Seems at that time everyone was really a 僵屍............................

]]> By: NAOMI! http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11704 NAOMI! Tue, 12 Aug 2008 08:19:08 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11704 I tried but can't! ): I tried but can't! ):

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11678 Miss Loi Mon, 11 Aug 2008 16:08:44 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11678 Night has fallen ... time to hide in closet again ... *closes closet door quietly* Night has fallen ... time to hide in closet again ... *closes closet door quietly*

]]> By: ignorantsoup http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11669 ignorantsoup Mon, 11 Aug 2008 12:05:09 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11669 OMG. By the time you finish solving the question you kena sucked liao. OMG. By the time you finish solving the question you kena sucked liao.

]]> By: DK http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11661 DK Mon, 11 Aug 2008 03:52:30 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11661 wah.... didn't know need to use Amath to fight 僵屍 nowadays. I sure die 1. wah.... didn't know need to use Amath to fight 僵屍 nowadays. I sure die 1.

]]> By: |c3^sNoW http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11659 |c3^sNoW Mon, 11 Aug 2008 03:12:46 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11659 wah miss loi is environmentally friendly! i like! this sounds like my A lvl last time leh! forgot how to do liao. wahaha. sorry cant save u miss loi >.< wah miss loi is environmentally friendly! i like!
this sounds like my A lvl last time leh! forgot how to do liao. wahaha. sorry cant save u miss loi >.<

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11629 Miss Loi Sun, 10 Aug 2008 16:27:16 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11629 <b>Cockroach:</b> *holds breath* ... ... ... *exhales after 10 secs* *僵屍 resumes hopping* *Strikes out Krisandro's name from the cast coz he didn't take AMaths* Cockroach: *holds breath* ... ... ... *exhales after 10 secs* *僵屍 resumes hopping*

*Strikes out Krisandro's name from the cast coz he didn't take AMaths*

]]> By: krisandro http://www.exampaper.com.sg/questions/a-maths/the-tuition-enquiry-from-hell#comment-11628 krisandro Sun, 10 Aug 2008 15:44:58 +0000 http://www.exampaper.com.sg/miss-loi-the-tutor/the-tuition-enquiry-from-hell#comment-11628 *scratch head* *scratch armpit* *catch no balls* *scratch head*

*scratch armpit*

*catch no balls*

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