Comments on: The All-in-One Package http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: mathslover http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-24337 mathslover Fri, 17 Apr 2009 16:31:02 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-24337 Ah much clearer now, and it makes use of properties of square root and inequalities too. It is looking more AIO than before. Great answer from you <b>Miss Loi</b> - it's stuff like this that keeps students <strike>like me</strike> interested to probe further into the wonderful world of mathematics. If only there are more such light-at-the-end-of-the-tunnel answers in school instead of 'this is not in syllabus, no need to know', or 'know one method is enough, wait u confused'.. sigh.. :( Since Miss Loi is so nice to answer a 没事找事做 question, I will answer your <a href="http://www.exampaper.com.sg/miss-loi-the-tutor/jc-or-poly-or-just-peer-pressure#comment-24146" rel="nofollow">question</a> too. I am <strike>an auditor of maths questions</strike> some nightmare maths student who loves asking teachers this kind of questions. P.S. I haven't finish <strike>scrutinizing</strike> reading your old<i>er</i> blog posts. Ah much clearer now, and it makes use of properties of square root and inequalities too. It is looking more AIO than before.

Great answer from you Miss Loi - it's stuff like this that keeps students like me interested to probe further into the wonderful world of mathematics. If only there are more such light-at-the-end-of-the-tunnel answers in school instead of 'this is not in syllabus, no need to know', or 'know one method is enough, wait u confused'.. sigh.. :(

Since Miss Loi is so nice to answer a 没事找事做 question, I will answer your question too.

I am an auditor of maths questions some nightmare maths student who loves asking teachers this kind of questions.

P.S. I haven't finish scrutinizing reading your older blog posts.

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-24318 Miss Loi Fri, 17 Apr 2009 03:34:21 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-24318 Oh dear no one told Miss Loi there's an external audit of the old blog posts today?! Alright Miss Loi's original approach was to go for the nearest <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Square_number" rel="nofollow">perfect square</a> which is 4 ⇒ √3 > √4 ⇒ 3√3 > 3√4 ⇒ 3√3 > 3(2) = 6 BUT thanks to your question, Miss Loi now thinks that a more robust approach instead would be to <em>square</em> the original term and find the nearest perfect square that's greater than this squared-term i.e. <div class="attention"> (3√3)<sup>2</sup> = 27 ⇒ nearest perfect square (that's smaller than 27) = 25 = 5<sup>2</sup> ⇒ (3√3)<sup>2</sup> > 5<sup>2</sup> ⇒ 3√3 > 5 <span class="fineprint">(∵3√3 & 5 are both > 1!)</span> ⇒ next integer is 6 <span class="fineprint">(since 6<sup>2</sup> = 36 > 27)</span> </div> With the second approach, we not only confirm that 3√3 is <i>confirm chop stamp</i> greater than 4 (with no common sense used, no cheating by calculator), we can also solve the question even if it's changed to <i>List all integers in the range of 3√<span class="highlight">2</span> to 4π</i>. <span class="fineprint">(Note: the word 'even' is taken out)</span> Great <del>audit</del> question from you <b>mathlover</b> - it's stuff like this that fine-tunes the solutions posted here and keeps <del>Miss Loi on her toes</del> Miss Loi's mind well-oiled. If only there are more such though-provoking questions like this in class instead of "Miss Loi! I dunno how to do!!!" *complete with pouted lips* ... sigh ... Ah ... the power of social media ... Oh dear no one told Miss Loi there's an external audit of the old blog posts today?!

Alright Miss Loi's original approach was to go for the nearest perfect square which is 4
⇒ √3 > √4
⇒ 3√3 > 3√4
⇒ 3√3 > 3(2) = 6

BUT thanks to your question, Miss Loi now thinks that a more robust approach instead would be to square the original term and find the nearest perfect square that's greater than this squared-term i.e.

(3√3)2 = 27
⇒ nearest perfect square (that's smaller than 27) = 25 = 52
⇒ (3√3)2 > 52
⇒ 3√3 > 5 (∵3√3 & 5 are both > 1!)
⇒ next integer is 6 (since 62 = 36 > 27)

With the second approach, we not only confirm that 3√3 is confirm chop stamp greater than 4 (with no common sense used, no cheating by calculator), we can also solve the question even if it's changed to List all integers in the range of 3√2 to 4π. (Note: the word 'even' is taken out)

Great audit question from you mathlover - it's stuff like this that fine-tunes the solutions posted here and keeps Miss Loi on her toes Miss Loi's mind well-oiled. If only there are more such though-provoking questions like this in class instead of "Miss Loi! I dunno how to do!!!" *complete with pouted lips* ... sigh ...

Ah ... the power of social media ...

]]> By: mathslover http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-24308 mathslover Thu, 16 Apr 2009 17:25:46 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-24308 This is a 没事找事做 comment: We are looking for even integers greater than 3√3 right? Assuming we have no clue the approximate value of √3 (and apparently cannot use calculator for this), your comment #12 only mentioned <b>3√3 < 3√4 = 6</b> therefore '6' is part of the answer. It didn't address the problem of <b><i>what if 3√3 < 4</i></b>? Then '4' would be an acceptable answer le. Perhaps you can convince me that <i>common sense</i> says <b><i>√3 > 4/3</i></b> therefore <b><i>3√3 > 4</i></b>? This is a 没事找事做 comment:

We are looking for even integers greater than 3√3 right?

Assuming we have no clue the approximate value of √3 (and apparently cannot use calculator for this), your comment #12 only mentioned 3√3 < 3√4 = 6 therefore '6' is part of the answer.

It didn't address the problem of what if 3√3 < 4? Then '4' would be an acceptable answer le.

Perhaps you can convince me that common sense says √3 > 4/3 therefore 3√3 > 4?

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-1218 Miss Loi Sun, 30 Sep 2007 16:19:10 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-1218 Read the red portion of comment #6 again. The question asks for the nearest integer upwards from 3√3. Now √3 is never an integer. So is √3.1, √3.2 etc. So the nearest integer is √4 = 2 i.e. the nearest <em>perfect square</em> is 4 ⇒ nearest integer from 3√3 is 3√4 = 6 (which happens to be even as well). Read the red portion of comment #6 again. The question asks for the nearest integer upwards from 3√3.

Now √3 is never an integer. So is √3.1, √3.2 etc. So the nearest integer is √4 = 2 i.e. the nearest perfect square is 4

⇒ nearest integer from 3√3 is 3√4 = 6 (which happens to be even as well).

]]> By: kiroii http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-1211 kiroii Sat, 29 Sep 2007 10:16:03 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-1211 3√3 to 4π. eh but if im wrong then how do u calculate 3√3 ? or juz simply guess? 3√3 to 4π.

eh but if im wrong then how do u calculate 3√3 ?
or juz simply guess?

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-772 Miss Loi Sun, 02 Sep 2007 15:29:00 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-772 Thanks for trying out the problem! Please see Miss Loi's comments to some of the workings in <span class="highlight">red</span>. Thanks for trying out the problem!

Please see Miss Loi's comments to some of the workings in red.

]]> By: kiroii http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-757 kiroii Fri, 31 Aug 2007 10:33:41 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-757 nah miss loi is nice she wont mind if u spam unintentionally ( unlike what im doin now lololololol) nah miss loi is nice she wont mind if u spam unintentionally ( unlike what im doin now lololololol)

]]> By: 123` http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-755 123` Fri, 31 Aug 2007 10:31:28 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-755 sorry, didnt mean to spam, coz my comp got crazy, and i accidentally posted twice sorry, didnt mean to spam, coz my comp got crazy, and i accidentally posted twice

]]> By: kiroii http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-754 kiroii Fri, 31 Aug 2007 10:29:35 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-754 well frankly i do believe laurels should go to me eh? =x btw the puberscent geometry q i still dont see the gist off it-.- or rather no point staring at the screen <span class="highlight">Miss Loi: Answered this at <a href="/questions/e-maths/geometry-a-pre-pubescent-question#comment-769" rel="nofollow">this comment in the original post</a>. Please try to post your comment at the relevant post next time.</span> well frankly i do believe laurels should go to me eh? =x btw the puberscent geometry q i still dont see the gist off it-.- or rather no point staring at the screen

Miss Loi: Answered this at this comment in the original post. Please try to post your comment at the relevant post next time.

]]> By: kiroii http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-753 kiroii Fri, 31 Aug 2007 10:28:15 +0000 http://www.exampaper.com.sg/questions/e-maths/the-all-in-one-package#comment-753 and the last question is simply a give away haha? miss loi i bet ur thinking *hah!~ no1 would be as smart as me as to think of how to do this* anyway (root 3) x 3 is basically 3.(something) 4x π is basically 12.(something) to even integers would be 4, 6, 8, 10 <div class="highlight"> Miss Loi: Are you SURE √3 x 3 approximates 3???!!! The nearest <em>higher</em> square root that results in an integer is √4. So your lowest even integer for the range is √4 x 3 = 6. You've rightly approximated π ~ 3, which means the highest even integer for the range is 4 x 3 = 12. But you didn't include this in your answer! So much for giveaways eh? ;) </div> and the last question is simply a give away haha? miss loi i bet ur thinking *hah!~ no1 would be as smart as me as to think of how to do this*

anyway
(root 3) x 3 is basically 3.(something)
4x π is basically 12.(something)

to even integers would be 4, 6, 8, 10

Miss Loi: Are you SURE √3 x 3 approximates 3???!!! The nearest higher square root that results in an integer is √4. So your lowest even integer for the range is √4 x 3 = 6. You've rightly approximated π ~ 3, which means the highest even integer for the range is 4 x 3 = 12. But you didn't include this in your answer!

So much for giveaways eh? ;)

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