Comments on: Tsunami! Run Or Don’t Run?! http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: qwerty1106 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-38120 qwerty1106 Sat, 26 Jun 2010 16:52:19 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-38120 noooooooooooooooo...... I haven learn trigo!! if i'm there, i'll most likely die XP noooooooooooooooo...... I haven learn trigo!! if i'm there, i'll most likely die XP

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1493 Miss Loi Tue, 16 Oct 2007 10:00:08 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1493 <strong>123 & Kiroii</strong>: Gambate!!! 6 (actually 7) more days to burning your A-Maths textbooks! 123 & Kiroii: Gambate!!! 6 (actually 7) more days to burning your A-Maths textbooks!

]]> By: kiroii http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1492 kiroii Tue, 16 Oct 2007 08:24:57 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1492 ya 6days...till i get to whack the paper question by question *charges my power further beyond cream de la cream power levels" ya 6days...till i get to whack the paper question by question *charges my power further beyond cream de la cream power levels"

]]> By: 123 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1491 123 Tue, 16 Oct 2007 07:48:01 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1491 T_T O in 6 days..... stressssssss T_T O in 6 days..... stressssssss

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1489 Miss Loi Mon, 15 Oct 2007 15:54:11 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1489 At least the water's still and there's no hidden whirlpool 'engineered to kill you'. This is something basic and everyone should know this. Moreover you won't be able to sketch the graph properly in part 5 without the answers from part 1. But to be honest Miss Loi did had a premonition that some students will do a simple cos<sup>-1</sup><var>x</var> and call it a day. She actually wanted to put up the SATC diagram within the blog post, but she decided against it as one glance will be enough to hint to you what you should do. But always remember that in your exam, there's no such luxury and nobody will be there to prompt you. So here's the same old naggy tagline: Always know your approach before you jump into the question! At least the water's still and there's no hidden whirlpool 'engineered to kill you'.

This is something basic and everyone should know this. Moreover you won't be able to sketch the graph properly in part 5 without the answers from part 1.

But to be honest Miss Loi did had a premonition that some students will do a simple cos-1x and call it a day. She actually wanted to put up the SATC diagram within the blog post, but she decided against it as one glance will be enough to hint to you what you should do. But always remember that in your exam, there's no such luxury and nobody will be there to prompt you.

So here's the same old naggy tagline: Always know your approach before you jump into the question!

]]> By: kiroii http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1487 kiroii Mon, 15 Oct 2007 15:06:51 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1487 wow..de first question is engineered to kill..that all i gotta say..totally 4got about about your approach..it seemed to easy>.< still waters run deep i guess wow..de first question is engineered to kill..that all i gotta say..totally 4got about about your approach..it seemed to easy>.< still waters run deep i guess

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1488 Miss Loi Mon, 15 Oct 2007 15:05:08 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1488 What a 'hero'! :? What a 'hero'! :?

]]> By: Peter http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1486 Peter Mon, 15 Oct 2007 08:50:31 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1486 If missloi is at ground zero, I'd give her a life jacket :) THEN I'll run! If missloi is at ground zero, I'd give her a life jacket :)

THEN I'll run!

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1483 Miss Loi Mon, 15 Oct 2007 07:42:43 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1483 Kiroii, looks like you've been pretty ravaged by the Tsunami! Please take a look at Miss Loi's comments on your answers as this is a pretty important topic for your upcoming exam. <acronym title="For your information">FYI</acronym> parts 1 and 5 (those without the word <em>state</em>, obviously) carry the most marks, so you'll need to spend the majority portion of your 5 min on these. Parts 2-4 are pretty much *ping* *pong* *poom* i.e. done under a minute! While we're at this, Miss Loi might as well present the sketched graph for part 5: <img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2007/10/2cos4x-1.gif" alt="y=2cos4x-1" /> Note that <em>all</em> answers from parts 1-4 were used and indicated in the sketched graph. And pay attention to the fact that the graph is only sketched for 0 ≤ <var>x</var> ≤ 180, as stated in your question - so always read your question carefully. So, assuming Miss Loi is at Ground Zero (<var>y</var> = 0) do you think she should run? :) Kiroii, looks like you've been pretty ravaged by the Tsunami! Please take a look at Miss Loi's comments on your answers as this is a pretty important topic for your upcoming exam.

FYI parts 1 and 5 (those without the word state, obviously) carry the most marks, so you'll need to spend the majority portion of your 5 min on these. Parts 2-4 are pretty much *ping* *pong* *poom* i.e. done under a minute!

While we're at this, Miss Loi might as well present the sketched graph for part 5:

y=2cos4x-1

Note that all answers from parts 1-4 were used and indicated in the sketched graph. And pay attention to the fact that the graph is only sketched for 0 ≤ x ≤ 180, as stated in your question - so always read your question carefully.

So, assuming Miss Loi is at Ground Zero (y = 0) do you think she should run? :)

]]> By: kiroii http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1481 kiroii Sun, 14 Oct 2007 18:42:23 +0000 http://www.exampaper.com.sg/questions/a-maths/tsunami-run-or-dont-run#comment-1481 eh its 2cos(4x-1) or 2cos(4x) -1 ? de ( ) is tremendously significant anyway i'l juz assume that 1) 0=2 cos(4x-1) 90 = 4x-1 x = 22.71(weird answer..) but if i were to take it as 2cos(4x) -1 x would be 15 <div class="highlight"> For such O-Level A-Maths questions, the equation is usually in the form of <var>a</var>cos<var>b</var><var>x</var> + <var>c</var>, so you should take this as 2 cos(4<var>x</var>)-1. Anyway ... YOU GOT PWNED BY THE TSUNAMI! What you did was f(<var>x</var>) = 2cos(4<var>x</var>) -1 = 0 ⇒ cos(4<var>x</var>) = 1/2 And using your super-duper calculator, you got 4<var>x</var> = 60<sup>o</sup> and then you divide by 4 to find <var>x</var>? NOT SO SIMPLE DUDE! The function lies within the range 0<sup>o</sup> ≤ <var>x</var> ≤ 180<sup>o</sup>. So you'll need to find ALL the values of <var>x</var> that satisfy the condition f(<var>x</var>) = 0 within this range. That 60<sup>o</sup> is just your <strong>basic angle</strong> (= <var>α</var>). Remember this classic <strong>A</strong>ll <strong>S</strong>cience <strong>T</strong>eachers are <strong>C</strong>razy diagram? <img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2007/10/s-a-t-c.gif" alt="SATC" /> Since cos(4<var>x</var>) is POSITIVE, <var>α</var> falls within quadrants <var>A</var> and <var>C</var>. Which means: 4<var>x</var> = 60<sup>o</sup> (in quadrant A), 360<sup>o</sup>-60<sup>o</sup> = 300<sup>o</sup> (in quadrant C). ⇒ 4<var>x</var> = 60<sup>o</sup>, 300<sup>o</sup> N.B. For those who are lost please start referring to your textbook now. But we're not done yet, because we're dealing with 4<var>x</var> here, which means we need to go a total of 4 rounds round the 360<sup>o</sup> circuit, and we've only completed 1 round. But since we're only interested in 0<sup>o</sup> ≤ <var>x</var> ≤ 180<sup>o</sup>, we only need a total of <strong>2 rounds</strong> in the circuit. So to go one more round, 4<var>x</var> = 60<sup>o</sup> (round 1), 300<sup>o</sup> (round 1), 60<sup>o</sup>+360<sup>o</sup> (round 2), 300<sup>o</sup>+360<sup>o</sup> (round 2) ⇒ 4<var>x</var> = 60<sup>o</sup>, 300<sup>o</sup>, 420<sup>o</sup>, 660<sup>o</sup> ⇒ <var>x</var> = 15<sup>o</sup>, 75<sup>o</sup>, 105<sup>o</sup>, 165<sup>o</sup> Please familiarize yourself with this process. It looks involved but it's really straightforward and there's not much trickery. So don't lose marks here! </div> 2) I'll assime its 2cos(4x) -1 if not i dun see how it's possible to do -1< cos4xf(x)>-3 <div class="highlight"> YOU GOT PWNED BY THE TSUNAMI AGAIN! This portion deals with the <var>a</var> portion of your <var>a</var>cos<var>b</var><var>x</var> + <var>c</var> graph. Many students got tricked here. Remember the <strong>amplitude of the trigonometric function does not change even when the graph is shifted up/down</strong>! So since the amplitude should still be <var>a</var> i.e. 2! </div> 3)period = 180 / 4 = 45 (i think..still not quite sure what period is, lazy to check textbook) <div class="highlight"> YOU GOT PWNED BY THE TSUNAMI AGAIN! This portion deals with the <var>b</var> portion of your <var>a</var>cos<var>b</var><var>x</var> + <var>c</var> graph. The period is defined as the interval over which the curve repeats itself. A cos<var>x</var> graph repeats itself over 360<sup>o</sup>, so for cos(4<var>x</var>) the graph repeats itself over 360<sup>o</sup>/4 = 90<sup>o</sup> </div> 4) max =1 , min = -3 <div class="highlight"> OK, the Tsunami didn't get you this time. This portion deals with the <var>c</var> portion of your <var>a</var>cos<var>b</var><var>x</var> + <var>c</var> graph. Since <var>c</var> = -1, the entire graph shifts <em>downwards</em> by 1. Correspondingly the max point (2) and min point (-2) gets shifted down by 1. Hence you're right! </div> eh its 2cos(4x-1) or 2cos(4x) -1 ? de ( ) is tremendously significant anyway i'l juz assume that

1) 0=2 cos(4x-1)
90 = 4x-1
x = 22.71(weird answer..)

but if i were to take it as 2cos(4x) -1
x would be 15

For such O-Level A-Maths questions, the equation is usually in the form of acosbx + c, so you should take this as 2 cos(4x)-1.

Anyway ... YOU GOT PWNED BY THE TSUNAMI!

What you did was f(x) = 2cos(4x) -1 = 0
⇒ cos(4x) = 1/2

And using your super-duper calculator, you got 4x = 60o and then you divide by 4 to find x?

NOT SO SIMPLE DUDE!

The function lies within the range 0o ≤ x ≤ 180o. So you'll need to find ALL the values of x that satisfy the condition f(x) = 0 within this range. That 60o is just your basic angle (= α).

Remember this classic All Science Teachers are Crazy diagram?

SATC

Since cos(4x) is POSITIVE, α falls within quadrants A and C. Which means:

4x = 60o (in quadrant A), 360o-60o = 300o (in quadrant C).
⇒ 4x = 60o, 300o

N.B. For those who are lost please start referring to your textbook now.

But we're not done yet, because we're dealing with 4x here, which means we need to go a total of 4 rounds round the 360o circuit, and we've only completed 1 round. But since we're only interested in 0o ≤ x ≤ 180o, we only need a total of 2 rounds in the circuit.

So to go one more round,

4x = 60o (round 1), 300o (round 1), 60o+360o (round 2), 300o+360o (round 2)
⇒ 4x = 60o, 300o, 420o, 660o
⇒ x = 15o, 75o, 105o, 165o

Please familiarize yourself with this process. It looks involved but it's really straightforward and there's not much trickery. So don't lose marks here!

2) I'll assime its 2cos(4x) -1 if not i dun see how it's possible to do

-1< cos4xf(x)>-3

YOU GOT PWNED BY THE TSUNAMI AGAIN!

This portion deals with the a portion of your acosbx + c graph.

Many students got tricked here. Remember the amplitude of the trigonometric function does not change even when the graph is shifted up/down! So since the amplitude should still be a i.e. 2!

3)period = 180 / 4
= 45 (i think..still not quite sure what period is, lazy to check textbook)

YOU GOT PWNED BY THE TSUNAMI AGAIN!

This portion deals with the b portion of your acosbx + c graph.

The period is defined as the interval over which the curve repeats itself. A cosx graph repeats itself over 360o, so for cos(4x) the graph repeats itself over 360o/4 = 90o

4) max =1 , min = -3

OK, the Tsunami didn't get you this time.

This portion deals with the c portion of your acosbx + c graph.

Since c = -1, the entire graph shifts downwards by 1. Correspondingly the max point (2) and min point (-2) gets shifted down by 1. Hence you're right!

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