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	<title>Jφss Sticks &#187; A-Maths Questions</title>
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	<description>Sassy O Level Maths Tuition, Questions &#38; Tips from Singapore&#039;s Favourite Private Tutor</description>
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		<title>Once In 50 Years</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/once-in-50-years</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/once-in-50-years#comments</comments>
		<pubDate>Mon, 09 Aug 2010 13:33:29 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[differentiation]]></category>
		<category><![CDATA[maxima & minima]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/?p=1594</guid>
		<description><![CDATA[<p>It caught everyone by surprise when it came. And Miss Loi scrambled her way to the nearest shelter, where she stood and watched with fear as little streams of water on the floor merged into a raging river, carrying away anything in its path that had a lower density than water. And then ...</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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			<content:encoded><![CDATA[<p>The <a rel="external nofollow" href="http://www.asiaone.com/News/AsiaOne+News/Singapore/Story/A1Story20100713-226662.html">sea of little flags</a> proudly perched on all manner of vehicles serves to remind us that, once again, <a rel="external nofollow" href="http://www.ndp.org.sg/">National Day</a> is here.</p>
<p>Falling magnanimously on a long weekend, it&#8217;s also the perfect opportunity for patriotic families to <del>flee</del> leave the country <i>en masse</i>, thereby affording Miss Loi the opportunity to scale down this weekend&#8217;s <i>joss sticks</i> sessions in exchange for more leisurely activities like watering her plants, folding her clothes, and heading to town to catch some <a rel="external nofollow" href="http://www.etour-singapore.com/fireworks-in-singapore.html">fireworks display</a>.</p>
<p>With her <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Johor–Singapore_Causeway">Woodlands Customs</a>-trained bumper-to-bumper driving skills, she managed to navigate her way out of the ubiquitous traffic jams, and promptly found what was arguably the last vacant (and legal) parking lot deep in the lowest basement of a carpark. <span class="fineprint">(<a href="/miss-loi-the-tutor/a-nation-celebrates-miss-loi-bemoans-her-fate">Couldn&#8217;t just anyhow park at the roadside</a> you see, even though it&#8217;s a holiday.)</span></p>
<p>Soon, she was standing among the huge crowd at a prime spot with eyes transfixed at the night sky. And before long &#8230;</p>
<blockquote><p>Ooooooooh!!!!!</p></blockquote>
<p>A collective cheer greeted the first of the fireworks as it lit up the sky.</p>
<blockquote><p>AAAAhhhhhh!!!!!</p></blockquote>
<p>Another one went up, streaking the heavens with brilliant <var>y</var> = <var>k</var> ln(<var>x</var><sup>2</sup>), <var>k</var> ∈ ℝ arcs.</p>
<blockquote><p>WAAAAhhhh!!!!!</p></blockquote>
<p>The next one was fierce, with straight explosive <var>y</var> = <var>k</var><var>x</var>, <var>k</var> ∈ ℝ lines shooting out in all directions.</p>
<blockquote><p><strong>ALAMAK!!!!!</strong></p></blockquote>
<p>The night sky masked the storm clouds. The electrifying atmosphere absorbed all scent of impending rain. So when it came, the sudden, massive downpour caught everyone by surprise, and Miss Loi became an instant panicky member of the &#8220;<i>Forget to Bring Umbrella</i>&#8221; Club as she scrambled her way to the nearest shelter.</p>
<p>Shivering in the confines of the shelter, she stood and watched with fear as little streams of water on the floor merged into a raging river, carrying away anything in its path that had a lower density than water. And then &#8230;</p>
<blockquote><p><strong>NOOOOOOOOO!!!!!</strong></p></blockquote>
<p>A sudden realization dawned upon her, and the scene in her mind shifted quickly from the flash flood before her to her hapless car parked &#8220;deep in the lowest basement&#8221;.</p>
<p>With <a href="/questions/a-maths/novena-under-water">history about to repeat itself</a>, she sacrificed her <a rel="external nofollow" href="http://www.charleskeith.com/">Charles &#038; Keith</a> platform shoes (again) and ran in the relentless rain towards the direction of the carpark.</p>
<p>Her worst nightmare was realized when she found the entrance to the carpark cordoned off by the police, and she had to be subsequently restrained by the police officer when she tried to barge her way through.</p>
<blockquote><p>Let me in! My car is at the basement! LET ME IN!!!</p></blockquote>
<blockquote><p>Mdm! Get a hold of yourself! The flood water is rising inside! It&#8217;s too dangerous!</p></blockquote>
<blockquote><p>Let me in! My insurance doesn&#8217;t cover &#8220;Acts of God&#8221;! Let me in!!!</p></blockquote>
<p> and she began to wail uncontrollably.</p>
<p>Perhaps it was her poor 凄凉 face that moved him, or perhaps it was her eerie wailing voice (in combination with her &#8216;gothic&#8217; look created by her melting makeup) that spooked him. Either way, the police officer softened his stance &#8230;</p>
<blockquote><p>I think I know you. Aren&#8217;t you that famous Sunday Times Maths Super Tutor?</p></blockquote>
<div class="question">
<p>A <a rel="external nofollow" href="http://www.pub.gov.sg/">PUB</a> government scholar has predicted that the height <var>y</var> (in cm) of the flood water in the lowest basement carpark will vary with time <var>t</var> (in minutes) as follows:</p>
<p><img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_981_49df4cf72034a9c73f93f4b08eb8cf96.png" style="vertical-align:-19px; display: inline-block ;" alt="y = 40+ln { [ { te^{-{t-4}/2}}/{8-t} ]^{1/2} }" title="y = 40+ln { [ { te^{-{t-4}/2}}/{8-t} ]^{1/2} }"/>, <var>t</var> &gt; 0.</p>
<ol>
<li>As it&#8217;s only safe to enter when the water level is neither rising nor falling, find the first value of <var>t</var> for which <var>y</var> is a stationary point and determine the nature of this stationary point.</li>
<li>Once you reach your car, it is only safe to drive out when the water level is falling. Find the set of values of <var>t</var> for which <var>y</var> is a decreasing function of <var>t</var>.</li>
</ol>
</div>
<p>With that, the police officer held her shoulders, looked into her eyes and said,</p>
<blockquote>
<p>Listen Mdm! This is a test of your understanding of the <span class="highlight">methods</span> involved to obtain stationary points in a function! Do not use your illegal <acronym title="Graphical Calculator">GC</acronym> or exotic iPhone app to plot the curve as you won&#8217;t be able to obtain your answer this way!</p>
<p>Good luck and Happy National Day! </p>
</blockquote>
<div class="attention">
<p><strong class="highlight">Afterword:</strong> So it didn&#8217;t rain tonight. But you still must help Miss Loi rescue her car in this <em>INCEPTION</em>-esque 9th August alternate reality <img src='http://www.exampaper.com.sg/blog/wp-includes/images/smilies/icon_razz.gif' alt=':P' class='wp-smiley' /> </p>
<p>*totem spinning*</p>
</div>
<p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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		<slash:comments>9</slash:comments>
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		<item>
		<title>M Is For Miracle</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/m-is-for-miracle</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/m-is-for-miracle#comments</comments>
		<pubDate>Sat, 06 Mar 2010 12:45:35 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[matrices]]></category>
		<category><![CDATA[simultaneous equations]]></category>

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		<description><![CDATA[<p>Night has fallen when the Maths Tutor reached her car. Just as she was about to start the engine and drive away, the street lamps began to flicker wildly. A great sense of foreboding filled the air, as a strange vision suddenly flashed before her eyes ...</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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			<content:encoded><![CDATA[<p><span class="fineprint"><i>Continuing from <a href="/questions/e-maths/hell-hath-no-fury-like-an-ah-beng-scorned">last week&#8217;s episode</a> &#8230;</i></span></p>
<p>Night has fallen when the Maths Tutor reached her car.</p>
<p>Just as she was about to start the engine and drive away, the street lamps began to flicker wildly. </p>
<p>A great sense of foreboding filled the air, as a strange vision suddenly flashed before her eyes &#8230;</p>
<div class="question">
<p>In an imaginary grid, a man walks along a straight street defined by the equation: <var>m</var><var>x</var> + (<var>m</var> &minus; 1)<var>y</var> = 10</p>
<p>At the same time, a black car zooms furiously along a straight road defined by the equation: (<var>m</var> &minus; 2)<var>x</var> + 3<var>m</var><var>y</var> = 20</p>
<p>The car will hit the man <em class="highlight">if</em> their paths meet &#8230;</p>
</div>
<p>A scream snapped her out of her trance before her vision was complete, and she blinked her eyes in time to see a frightened woman pushed a man away under the glare of the bright street lamps.</p>
<p>The man <span class="fineprint">(who happens to be our <a href="/questions/e-maths/hell-hath-no-fury-like-an-ah-beng-scorned">young henchman</a> if you&#8217;ve been following the previous episodes)</span> then turned around and walked away with his head bowed, looking dejected. </p>
<p>In a shocking realization of her déjà vu experience, she recognized the man as the walking man in her vision just moments ago. </p>
<p>And in that very moment, the silence of the night was broken by the unmistakable roar of a speeding car&#8217;s engine, while the Maths Tutor could only cover her eyes and pray for a miracle &#8230;</p>
<div class="question">&#8230; <strong>find the &#8216;miracle&#8217; value of <var>m</var> where the paths of the car and the man would never meet.</strong></div>
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<p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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		<title>Inglourious *BEEP* Chapter Two: The Insane Bugis Junction Carpark Ah Lian</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian#comments</comments>
		<pubDate>Thu, 01 Oct 2009 06:43:06 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[Rate of Change]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/questions/a-maths/inglourious-beep-chapter-two-the-insane-bugis-junction-carpark-ah-lian</guid>
		<description><![CDATA[<p>Of rate of change and an insane Ah Lian at the Bugis Junction carpark. Based on another true story. BOOMZ! </p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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			<content:encoded><![CDATA[<p>Based on another true story &#8230;</p>
<div class="img-div">
<p><img style="border:solid 1px #333" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/bugis-junction-1.gif" alt="Scene 1" /></p>
<p><img style="border:solid 1px #333" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/bugis-junction-2.gif" alt="Scene 2" /></p>
<p><img style="border:solid 1px #333" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/bugis-junction-3.gif" alt="Scene 3" /></p>
<p><img style="border:solid 1px #333" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/bugis-junction-4.gif" alt="Scene 4" /></p>
<p><img style="border:solid 1px #333" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/bugis-junction-5.gif" alt="Scene 5" /></p>
<p><img style="border:solid 1px #333" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/bugis-junction-6.gif" alt="Scene 6" /></p>
<p><img style="border:solid 1px #333" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/bugis-junction-7.gif" alt="Scene 7" /></p>
<p><img style="border:solid 1px #333" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/bugis-junction-8.gif" alt="Scene 8" /></p>
</div>
<div class="question">
<p><img class="right" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/10/inverted-cone-diagram.gif" alt="Inverted Cone Question Diagram" /></p>
<p>Given that Little Miss Loi&#8217;s &#8230; umm &#8230; <del>bla</del> *water container comes in the form of an inverted cone of height 30 cm and base radius 20 cm, and that the water in the container is rising at a constant rate of 20 cm<sup>3</sup>s<sup>&minus;1</sup>.</p>
<ol>
<li>Express the volume of water in the container, <var>V</var>, in terms of: <var>&pi;</var> and the depth of water in the container, <var>h</var>.</li>
<li>If the depth of water is currently at 24 cm, find the rate of increase of <var>h</var> at this very instant.</li>
<li>Find the number of seconds left for Little Miss Loi to reach the toilet (i.e. when the water container fills up fully and begins to &#8230; umm &#8230; <em>leak</em>).</li>
</ol>
<p><span class="fineprint">*For hypothetical use only.</span></p>
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<p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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		<slash:comments>13</slash:comments>
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		<title>The Facebook Friend</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/the-facebook-friend</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/the-facebook-friend#comments</comments>
		<pubDate>Fri, 11 Sep 2009 17:50:40 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[plane geometry]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/questions/a-maths/the-facebook-friend</guid>
		<description><![CDATA[<p>A plea for mathematical help from a stranger on Facebook made Miss Loi click the 'Confirm' button without hesitation, totally failing to notice her long unkempt hair, and her Japanese-sounding first name. A while later this appeared on Miss Loi's wall, and this was what she saw ...</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
<br/>
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			<content:encoded><![CDATA[<p>It&#8217;s <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Hungry_Ghost_Festival">that time of the year</a> again.</p>
<p>It&#8217;s the season when the stifling scent of joss sticks fills the air, and a pall of smoke hangs over the land. A time when little kids are told in no uncertain terms to say &#8216;<i>excuse me</i>&#8216; before they go <i>peepee</i> in the bushes.</p>
<div class="img-div right"><a href="http://www.flickr.com/photos/miss-loi/3908781911/" class="tt-flickr tt-flickr-Small"><img src="http://farm3.static.flickr.com/2615/3908781911_59b2aba690_m.jpg" alt="Formula Sheets" width="240" height="180" /></a>
<div class="caption">Kawaii, aren&#8217;t they?</div>
</div>
<p>Shaken by last year&#8217;s harrowing encounter with the <a href="/questions/a-maths/the-tuition-enquiry-from-hell">Binomial Zombie</a>, Miss Loi decided not to stay too late at <a href="/miss-loi-temple">The Temple</a> tonight, preferring to do up her colourful cutie set of formula sheets within the relative safety of her home this time round.</p>
<p>After a marathon workout session with the laptop, a tired Miss Loi did what most <del>skiving</del> teenagers at her age would do when they take a break from studying: login to <a rel="external nofollow" href="http://www.facebook.com/celineloi">her Facebook account</a>.</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-friend-requests.gif' alt='Facebook Friend Requests' /></p>
<p>Sieving through the many <del>dodgy</del> friend requests that invariably showed up, she was drawn to this particular one:</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-sadako-friendship-request.gif' alt="Sadako's Friendship Request" /></p>
<p>The helpless-looking plea triggered her mathematical maternal instinct, and coupled with her excitement at meeting another Loi, made her click the &#8216;Confirm&#8217; button without hesitation, totally failing to notice her long unkempt hair, and her Japanese-sounding first name.</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-sadako-friendship-confirmed.gif' alt="Sadako's Friendship Confirmed" /></p>
<p>A while later this appeared on Miss Loi&#8217;s wall</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-sadako-wall-1.gif' alt="Sadako's 1st Wall Post" /></p>
<p>Miss Loi duly replied:</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-sadako-wall-2.gif' alt="Miss Loi's reply" /></p>
<p>And she replied:</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-sadako-wall-3.gif' alt="Sadako's 2nd Wall Post" /></p>
<p>And then Miss Loi replied again:</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-sadako-wall-4.gif' alt="Miss Loi's 2nd reply" /></p>
<p>And finally she replied:</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-sadako-wall-5.gif' alt="Sadako's 3rd Wall Post" /></p>
<p>And this was what Miss Loi saw &#8230;</p>
<p><object type="application/x-shockwave-flash" width="400" height="324" data="http://www.youtube.com/v/mnbQOVU0e28&#038;hl=en&amp;fs=1"><param name="movie" value="http://www.youtube.com/v/mnbQOVU0e28&#038;hl=en&amp;fs=1" /></object></p>
<p>At the very moment a stunned Miss Loi finished viewing the video, the Facebook notification icon at the bottom-right of her screen popped up with a message &#8230;</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-notification.gif' width="100" alt='Facebook Notification' /></p>
<p>&#8230; and she found this message waiting for her in her inbox</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/facebook-sadako-message.gif' alt="Sadako's Final Message" /></p>
<p>Now that <strong class="big highlight">YOU</strong> have watched the video, you have seven days to post up the solution here in order to save yourself from being dragged into your monitor screen by Sadako Loi!</p>
<p><img src='http://www.exampaper.com.sg/blog/wp-content/uploads/2009/09/sadako-likes-this.gif' width="400" alt='Sadako Likes This!' /></p>
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<p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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		<slash:comments>18</slash:comments>
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		<item>
		<title>Tora! Tora! Tora!</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/tora-tora-tora</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/tora-tora-tora#comments</comments>
		<pubDate>Sat, 15 Aug 2009 14:53:50 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[differentiation]]></category>
		<category><![CDATA[linear law]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/questions/a-maths/tora-tora-tora</guid>
		<description><![CDATA[<p>After parking her newly-waxed car, Miss Loi slowly walked away, turning her head every few steps to admire its shine. Before long the area was gradually draped by a large shadow that caused her to stop in her tracks, look up, and stare in utter horror at a huge fleet of birds flying towards her direction in an aggressive-looking formation, each with its ... umm ... "crosshairs" trained on the car.</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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			<content:encoded><![CDATA[<div class="img-div right"><a href="http://www.flickr.com/photos/miss-loi/3821607039/" class="tt-flickr tt-flickr-Small"><img src="http://farm3.static.flickr.com/2324/3821607039_1a0c0a960f_m.jpg" alt="My Dirty Car" width="240" height="180" /></a>
<div class="caption">Miss Loi&#8217;s neglected car<br/><a href="http://www.flickr.com/photos/miss-loi/3821607039/">click</a> to see how horribly dirty it is</div>
</div>
<p>With the return of the <a rel="external nofollow" href="http://www.asiaone.com/News/AsiaOne%2BNews/Singapore/Story/A1Story20090808-159988.html">haze</a> and Miss Loi&#8217;s recent absence away in the <a href="/questions/a-maths/trapped-in-the-plane-of-geometry">Plane of Geometry</a>, the poor car is looking a little neglected these days.</p>
<p>Dismayed and feeling depressed like a guilty parent each time she saw the dismal state of its paintwork, Miss Loi decided to send the car for a long-overdue wash plus pamper it with one of those much-touted &#8220;car grooming&#8221; sessions.</p>
<p>When she collected her car later in the day, her depression was cured instantly by the uplifting sight of its dazzling shine.</p>
<p>Words could not describe the silky sensation as she ran her slim fingers slowly across its smooth immaculately-waxed body, now free of the minuscule scratches and parabolic swirls that once scarred it.</p>
<p>It was almost like getting a new car, and this feeling stayed with her throughout her drive to a new student&#8217;s home, situated at the end of a straight road in a carpark-deprived area, for her next tuition session.</p>
<div class="img-div right"><img class="content-img" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/08/birds-eye-view.jpg" alt="Bird's Eye View" />
<div class="caption">Bird&#8217;s eye view <br/>- Miss Loi&#8217;s somewhere down there</div>
</div>
<p>As she slowly walked away, turning her head every few steps to admire the shine of her parked car, little did she realize that this glint of a shine would attract the attention of a little bird perched on a large tree at the end of the road.</p>
<p>Before long the area was slowly draped by a large shadow that caused Miss Loi to stop in her tracks, look up, and stare in utter horror at a huge fleet of birds flying towards her direction in an aggressive-looking formation, each with its &#8230; umm &#8230; &#8220;crosshairs&#8221; trained on the car.</p>
<p>The air raid siren in her mind sounded, and it was sheer luck that got her to the car in time before these terrors in the sky rained destruction upon the land.</p>
<div class="img-div right"><img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2007/01/ractis.jpg" alt="Pitter-patter" />
<div class="caption">When heroes are born</div>
</div>
<p>In heroic scenes that followed, left and right she swerved her car as she strived to save it from the relentless onslaught, narrowly avoiding bomb after bomb of waste matter that whistled through the air before landing with a sickening *splat* inches away from her.</p>
<p>Just when it seemed certain the car would be martyred on this very day, the flock began to turn back, as Miss Loi charged her way to freedom beyond the bombing range, immensely relieved that her superb driving skills had somehow saved her from the pounding.</p>
<p>But now she&#8217;s stuck at the end of the road, in a tense face-off with the evil birds on the tree at the opposite end readying themselves for the next bombing run, while her new student waits patiently for her in her house &#8230;</p>
<div class="question">
<div class="img-div"><img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/08/linear-law-question-diagram.gif" alt="Linear Law Question Diagram" /></div>
<p>Noticing the pattern of the impact points along the road, Miss Loi suspects that their distance <var>d</var> from the centre of the road and the distance <var>x</var> <em>along</em> the road is connected by the equation <img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_972_f43463d91f6493513f30b65871339225.png" style="vertical-align:-28px; display: inline-block ;" alt="d={ax}/{bx^2+5}" title="d={ax}/{bx^2+5}"/></p>
<p>Bravely measuring a few samples along certain intervals on the road, Miss Loi recorded the following sets of values:</p>
<table>
<tr>
<th><var>x</var> (m)</th>
<td>5</td>
<td>10</td>
<td>15</td>
<td>20</td>
<td>25</td>
<td>30</td>
</tr>
<tr>
<th><var>d</var> (m)</th>
<td>2.50</td>
<td>0.9</td>
<td>3.21</td>
<td>2.85</td>
<td>2.50</td>
<td>2.20</td>
</tr>
</table>
<p>Given there&#8217;s nowhere else she can park her car other than along the centre of the narrow road (inside the bombing range), *use a suitable graph to examine the validity of Miss Loi&#8217;s equation, and estimate the values of <var>a</var> and <var>b</var>.</p>
<p>At which point (<var>x</var>) along the road should Miss Loi park her car to minimize the chances of it being hit i.e. where <var>d</var> is maximum?</p>
<div class="fineprint">*This is a <em>Linear Law</em> question requiring you to plot a graph on a piece of graph paper. You may <a rel="external nofollow" href="http://incompetech.com/graphpaper/multiwidth/">generate a piece of graph paper online</a> should you not to have one with you.</div>
</div>
<p>As Miss Loi doesn&#8217;t have any graph paper with her (shame on her!), can you please help her find the safest spot to park her shiny car so that she can start her new student&#8217;s tuition session on time with peace of mind?</p>
<p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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		<slash:comments>13</slash:comments>
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		<title>Trapped In The Plane Of Geometry</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/trapped-in-the-plane-of-geometry</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/trapped-in-the-plane-of-geometry#comments</comments>
		<pubDate>Fri, 07 Aug 2009 16:30:55 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[geometry]]></category>
		<category><![CDATA[plane geometry]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/questions/a-maths/trapped-in-the-plane-of-geometry</guid>
		<description><![CDATA[<p>After staring for what seemed like an eternity while trying to solve a nasty Plane Geometry question, a circle in the diagram seemed to grow larger and larger as it beckoned Miss Loi to lean closer and closer ... so close that she felt almost at one with the question and could almost feel the closeness of the solution that she desperately sought. Suddenly, an unknown force reached out and, to her horror, pulled her headfirst into the circle!</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
<br/>
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			<content:encoded><![CDATA[<p>It was noon at <a href="/miss-loi-temple">The Temple</a> when Miss Loi was totally engrossed in trying to obtain the proof in a nasty <a href="/tag/plane-geometry">Plane Geometry</a> question sent earlier by a student.</p>
<p>After staring for what seemed like an eternity at the question&#8217;s diagram, her <a href="/tuition-notes/a-maths-tips/the-yin-yang-eye-of-plane-geometry">阴阳眼</a> simply would not come and she was beginning to get very tired, partly due to the <a rel="external nofollow" href="http://twitter.com/MissLoi/status/3171052981">ridiculous phone call</a> that cut short her sleep in the morning. </p>
<p>Never one to give up easily in the face of adversity <del>and face the ignominy of hearing a &#8220;<i>Haha! Miss Loi also dunno how to do!</i>&#8220;</del>, she rubbed her eyes and continued to stare intensely at the diagram.</p>
<p>So intense was her gaze that a circle in the diagram seemed to grow larger and larger as it beckoned her to lean closer and closer &#8230; so close that she felt almost at one with the question and could almost feel the closeness of the solution that she desperately sought.</p>
<p>Suddenly, an unknown force reached out and, to her horror, pulled her headfirst <em>into</em> the circle!</p>
<p>In the harrowing moments that followed, she was whisked through a tunnel lined with circles, triangles, tangents, secants, chords and all manner of grotesque polygons from the <a rel="external nofollow" href="http://www.seab.gov.sg/SEAB/oLevel/syllabus/2009_GCE_O_Level_Syllabuses/4038_2009.pdf">O-Level A-Maths Syllabus</a>.</p>
<p>After what seemed like an eternity, she landed with a big thump right in front of a weathered-looking Right-Angled Triangle (RAT), who muttered</p>
<blockquote><p>Oh boy here comes another 走火入魔 one.</p></blockquote>
<blockquote><p>Who are you? Where am I?</p></blockquote>
<p>asked Miss Loi as she meticulously checked for any facial scar arising from the rough landing.</p>
<blockquote><p>You&#8217;re at the Plane of Geometry. The realm of all killer Plane Geometry questions. And you, of all people, should know that I&#8217;m the <strong class="highlight">Right-Angled Triangle alias Pythagoras Theorem</strong> &#8211; introduced to most during Sec One/Two and some say even PSLE! But they hardly think about me anymore.</p></blockquote>
<blockquote><p>Can you show me the way back to The Temple?</p></blockquote>
<p>The RAT continued to grumble.</p>
<blockquote><p>These days all the young people here only care about the &#8216;latest&#8217; fads like the Tangent-Secant Theorem etc. They hardly think about me anymore.</p></blockquote>
<blockquote><p>Uncle! I really need your help! I&#8217;ve got a class to teach in a few hours&#8217; time! AND I WANT MY NATIONAL DAY LONG WEEKEND!!!</p></blockquote>
<blockquote><p>I will show you the way if you can show me the following:</p></blockquote>
<div class="question">
<p><img class="right" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/08/plane-geometry-question.gif" alt="Plane Geometry Question Diagram" /> </p>
<p><var>P</var> is a point outside the circle such that <var>PA</var> and <var>PB</var> are tangents to the circle of centre <var>O</var>. <var>M</var> is the mid-point of <var>AB</var> and the secant line <var>PDC</var> cuts the chord <var>AB</var> at <var>E</var>.</p>
<p>Show that:</p>
<ol>
<li>&Delta;<var>PMA</var> is similar to &Delta;<var>BMO</var></li>
<li><var>PA</var>&times;<var>BM</var> = <var>BO</var>&times;<var>PM</var></li>
<li><var>PE</var>&sup2; = <var>PD</var>&times;<var>PC</var> &minus; <var>DE</var>&times;<var>CE</var></li>
</ol>
</div>
<p>As Miss Loi has somehow lost her <a href="/tuition-notes/a-maths-tips/the-yin-yang-eye-of-plane-geometry">阴阳眼</a> ability, can you help her find her way back to The Temple?</p>
<p>Meanwhile the RAT continued to mumble &#8230;</p>
<blockquote><p>They hardly think about me anymore &#8230;</p></blockquote>
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		<title>The Terrifying O1NK Virus Outbreak</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/the-terrifying-o1nk-virus-outbreak</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/the-terrifying-o1nk-virus-outbreak#comments</comments>
		<pubDate>Tue, 07 Jul 2009 08:57:42 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[indices]]></category>
		<category><![CDATA[logarithms]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/questions/a-maths/the-terrifying-o1nk-virus-outbreak</guid>
		<description><![CDATA[<p>It started with a little "oink!" from a student when asked "Who was the former President of the United States?" by his teacher in class. Appalled by this apparent display of rudeness, he was sent to stand outside the classroom. Shocked and puzzled by his dismissal, the student couldn't hold back a sneeze at a passing group of giggly girls, who giggled all the way to the tuckshop, where one of them sneezed at the fish ball noodles aunty, who in turn sneezed at a passing kitten, who in turn let out a BIG KITTY SNEEZE while being caressed by a large gathering of girls, since it was, after all, the school's resident kitty.</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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			<content:encoded><![CDATA[<div class="center"><strong class="big">如有雷同纯属巧合</strong></div>
<p>It started with a little &#8220;<i>oink!</i>&#8221; from a student when asked &#8220;Who was the former President of the United States?&#8221; by his teacher in class.</p>
<p>Appalled by this apparent display of rudeness, the teacher sent the student to stand outside the classroom.</p>
<p>Shocked and puzzled by his dismissal, the sad student cut a forlorn figure outside his classroom, and couldn&#8217;t hold back a sneeze at a passing group of giggly girls.</p>
<p>That group of giggly girls giggled at their exclusive naughty joke all the way to the tuckshop, where one of them sneezed while taking her bowl of fish ball noodles from the stall aunty, who in turn sneezed while disposing her stall&#8217;s leftovers at the rubbish dump, startling a passing kitten, who in turn let out a BIG KITTY SNEEZE later amidst all the &#8220;<i>SOOOOO CUTE!!!</i>&#8221; while being caressed by a large gathering of girls, since it was, after all, the school&#8217;s resident kitty.</p>
<div class="img-div right"><img class="content-img" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/07/oink-victim.gif" alt="O1NK Victim" />
<div class="caption">O1NK victim at late stage of the disease</div>
</div>
<p>After the dust had settled, the giggles turned into a series of <i>oinks</i>, the kitty spooked everyone with an <i>oink</i>, and students thought the stall aunty was selling <a rel="external nofollow" href="http://lifestylewiki.com/Bak_Chor_Mee"><i>bak chor</i> mee</a>. </p>
<p>When certain portions of the school assembly sounded like a pig farm as they sang the National Anthem the following morning, the school principal was sufficiently alarmed to hastily convene a staff meeting, where the Biology <acronym title="Head of Department">HOD</acronym> stood up and said,</p>
<blockquote>
<p>Sir, I have grave news.</p>
<p>Using my lab&#8217;s sophisticated equipment, we&#8217;ve concluded that the students and the cat have been infected by a new, highly-contagious O1NK strain of the influenza virus. </p>
<p>We believe the first student caught it via contact with Aussie pigs in his Australian Farmstay tour during the school holiday. </p>
<p>As per the H1N1 virus, steps are being taken to set up checkpoints at our school gate. Anyone found to reply &#8220;oink&#8221; when asked for his/her name will be turned away.</p>
</blockquote>
<p>In addition, the following info was obtained from contact tracing:</p>
<div class="question">
<p>The school has a total 1500 students. The spread of the virus, since the first student was discovered at Monday 5:00pm is given by </p>
<p><img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_976_ff4816c24b24b474dff3215c4c5b4163.png" style="vertical-align:-24px; display: inline-block ;" alt="y = {1500}/{1+1499e^{-0.1 alpha t}}" title="y = {1500}/{1+1499e^{-0.1 alpha t}}"/>, </p>
<p>where <var>y</var> is the total number of students infected after <var>t</var> hours, and <var>&alpha;</var> is obtained by the solution of</p>
<p><img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_993_dd180f61bcc39f064090776a45e5a4ae.png" style="vertical-align:-7px; display: inline-block ;" alt="27*3^{lg alpha} = 9^{1+lg(alpha-20)}" title="27*3^{lg alpha} = 9^{1+lg(alpha-20)}"/></p>
<ol>
<li>It&#8217;s now 16 hours since the first student first came to school. How many students are infected now (correct to the nearest whole student)?</li>
<li>Given that announcements are scheduled at the beginning of every hour (e.g. 10:00am, 11:00am etc.), and that according to the Education Ministry&#8217;s guideline, the school principal will need to make an announcement to close the school at the hour in which the number of infected students is expected to cross the 45% mark. What time should the principal schedule his announcement?</li>
</ol>
</div>
<p>Unfortunately, the school principal had returned all his math knowledge to his teacher (shame on you!). Hence in order to solve the above problem, he had to rely on his Mathematics <acronym title="Head of Department">HOD</acronym>, who promptly stood up and said </p>
<p>&#8230; <i>OINK</i>!</p>
<hr />
<div class="attention">
<p>As part of your AMaths <em>Exponential &#038; Logarithmic Functions</em> chapter, you are almost certain to see in your O-Level exam a question (or part of a question) concerning the <span class="highlight">application of an exponential or logarithmic function</span> on some scary-looking real-life situations that may involve the likes of a exploding/shrinking population, multiplying bacteria, decaying radioactive substances, cooling temperatures etc.</p>
<p>While the calculation part is usually pretty straightforward i.e. sub the relevant values into the given formula and use what&#8217;s stated in <a href="/tuition-notes/a-maths-tips/sergeant-lois-mid-year-boot-camp-2008-fall-in-for-logarithm-training">Sergeant Loi&#8217;s Logarithm Training Program</a> and <i>ln/lg both sides</i> etc., it&#8217;s vital that you <span class="highlight">read the question carefully</span> before submitting your final answer.</p>
</div>
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		<title>The Night Nothing Stood Still</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/the-night-nothing-stood-still</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/the-night-nothing-stood-still#comments</comments>
		<pubDate>Sun, 26 Apr 2009 14:47:40 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[kinematics]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/questions/a-maths/the-night-nothing-stood-still</guid>
		<description><![CDATA[<p>The howling started at 11pm on Wednesday night, filling The Temple with an air of fear that was quickly followed by eerie rattling sounds coming from the roof above. The curls of her hair were instantly straightened by a mighty gust of wind the moment she stepped outside, to be greeted by an extraordinary scene unlike any she had ever witnessed.</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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			<content:encoded><![CDATA[<p>The howling started at 11pm on Wednesday night, filling <a href="/miss-loi-temple">The Temple</a> with an air of fear that was quickly followed by eerie rattling sounds coming from the roof above, as if its tiles were being systematically peeled away by whatever&#8217;s behind these ungodly noises.</p>
<p>With thoughts of being in a scene of a Korean horror flick (where the actress usually dies) flooding her mind, Miss Loi decided to abandon the <a href="/tag/kinematics">Kinematics</a> question she was doing and quickly closed shop for the night.</p>
<p>The curls of her hair were instantly straightened by a mighty gust of wind the moment she stepped outside the Temple Gates, to be greeted by an extraordinary scene unlike any she had ever witnessed: leaves, twigs, plastic bags and whatever &lt;1 kg were strewn everywhere as <a rel="external nofollow" href="http://www.channelnewsasia.com/stories/singaporelocalnews/view/424439/1/.html">gale-forced winds</a> lashed through Novena. </p>
<div class="img-div right"><a href="http://www.flickr.com/photos/miss-loi/3475734311/" class="tt-flickr tt-flickr-Small"><img src="http://farm4.static.flickr.com/3652/3475734311_4d426b463d_m.jpg" alt="Fallen Tree" width="240" height="180" /></a></div>
<p>Closing her agape mouth just in time to prevent any unwanted debris for supper, Miss Loi recovered her composure and tried to make a dash for her car under the deafening roar of the wind.</p>
<p>Oh it was not a pretty sight as her hair parting constantly changed directions as the wild tempest battered her from all directions &#8211; with flying twigs that threatened to scar her precious face, and NTUC plastic bags &#038; the odd flying underwear that threatened to smother her at every turn &#8211; all while being mocked by <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Ivy_Lee_(actress)">Ivy Lee</a> in brochures blown from the neighbourhood slimming centre.</p>
<p>When she finally hit the road on her way home (albeit with a new hairstyle), she found to her dismay the roads perilously littered with leaves and branches, with huge fallen trees blocking her way <img src='http://www.exampaper.com.sg/blog/wp-includes/images/smilies/icon_sad.gif' alt=':(' class='wp-smiley' /> </p>
<div class="question">
<p>Miss Loi&#8217;s car first passed a big tree located along the way at a fixed point <var>O</var> at a speed of 210 m/min. </p>
<p>Assuming that she moved in a straight line and that her acceleration <var>a</var> m/s<sup>2</sup> at <var>t</var> minutes after passing <var>O</var> is given by <var>a</var> = 60<var>t</var> &minus; 240,</p>
<ol>
<li>Calculate her <em>speed</em> at the second minute.</li>
<li>Given that she had to turn back immediately to the direction she came from upon encountering a fallen tree, find the value(s) of <var>t</var> when she had to turn back.</li>
<li>If the big tree at <var>O</var> was felled by the wind at the tenth minute, will she be able to pass it before it fell? Calculate the total distance she would have travelled in 10 minutes.</li>
</ol>
</div>
<div class="attention">
<p>To further what&#8217;s being taught in its EMaths counterpart, AMaths <em>Kinematics</em> introduces the terms <strong>displacement</strong> (<var>s</var>) and <strong>velocity</strong> (<var>v</var>) which may be <em>very loosely</em> considered as distance and speed involving <span class="highlight">direction</span> respectively.</p>
<p>So instead of that headstrong cyclist/car/train in your E-Maths <em>Kinematics</em> who somehow lost its reverse gear and end up moving in only one direction, you&#8217;ll find in AMaths modern cars like Miss Loi&#8217;s (or more commonly &#8216;particles&#8217;) that can move back and forth like a maniac in opposite directions, with the following relationships between displacement (<var>s</var>), velocity (<var>v</var>) and acceleration (<var>a</var>):</p>
<p><img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_976_c3f0e8e1dbf594f2e7df9fba0538c60a.png" style="vertical-align:-24px; display: inline-block ;" alt="s = int{}{}{v} dt doubleleftright v = ds/dt" title="s = int{}{}{v} dt doubleleftright v = ds/dt"/><br />
<img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_976_2d274644c5ca77d2f5e16234d9a21eff.png" style="vertical-align:-24px; display: inline-block ;" alt="v = int{}{}{a} dt doubleleftright a = dv/dt" title="v = int{}{}{a} dt doubleleftright a = dv/dt"/></p>
</div>
<div class="img-div"><a href="http://www.flickr.com/photos/miss-loi/3475734055/" class="tt-flickr tt-flickr-Small"><img src="http://farm4.static.flickr.com/3563/3475734055_af84cf88db_m.jpg" alt="Aftermath of the Squall" width="240" height="180" border="0" /></a>
<div class="caption">Singapore&#8217;s Earth Day 2009 Celebration</div>
</div>
<p>P.S. Most of the above story is true, except the part on the flying underwear. Maybe Mother Nature was trying to tell us something on <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Earth_Day">Earth Day</a> 2009?</p>
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		<slash:comments>11</slash:comments>
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		<title>The Great Tiger Prawn Massacre</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/the-great-tiger-prawn-massacre</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/the-great-tiger-prawn-massacre#comments</comments>
		<pubDate>Mon, 06 Apr 2009 14:00:00 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[geometry]]></category>
		<category><![CDATA[plane geometry]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/questions/a-maths/the-great-tiger-prawn-massacre</guid>
		<description><![CDATA[<p>小妹! WHAT’S YOUR PROBLEM?! LAST TIME THOSE *BEEP* ANG MOHS CAME AND GIVE PROBLEM! NOW A SEXY GIRL LIKE YOU COME AND GIVE PROBLEM! YOU SAY WE OVERCHARGE YOU - WHERE’S YOUR PROOF?!</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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			<content:encoded><![CDATA[<div class="center"><strong class="big">如有雷同纯属巧合</strong></div>
<p>As <a href="/study-break/the-mathematics-of-love">reported previously</a>, Miss Loi has been working late nights (yes, yes, yes you&#8217;ll hear about <a href="/exam-papers">them</a> <em>real</em> soon).</p>
<div class="img-div right"><img class="content-img" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/04/tiger-prawns.jpg" alt="Tiger Prawns" />
<div class="caption">Scene from The Great Tiger Prawn Massacre<br/>[<a rel="external nofollow" href="http://thesingaporepost.blogspot.com/2009/03/local-news-newton-stall-charges-239-for.html">Source</a>]</div>
</div>
<p>When strange sounds were heard coming from the direction of her tummy last night, she finally decided to end the day&#8217;s work and drove to the nearest hawker centre (from <a href="/miss-loi-temple">The Temple</a>, Novena) that was still open at this late hour, for a sinful late night dinner to appease her stomach.</p>
<p>There was barely time to savour the sweet aroma at the smoke-filled hawker centre when she was <del>forcibly</del> promptly ushered by a helper to a table beside a BBQ seafood stall, where rows of tiger prawns were on display and were being advertised at a price of $10 each.</p>
<p>Feeling extremely hungry by now, Miss Loi succumbed to the juicy sight of these succulent prawns. And in a classic <i>don&#8217;t-care-3-7-21</i> (不管三七二十一) rash moment, she decided to throw her entire dieting plan to the wind by ordering a whopping total of <strong>FOUR</strong> tiger prawns.</p>
<p>Upon completing her messy massacre of the prawns, it was Miss Loi&#8217;s turn to be massacred when a bill of <strong>$120</strong> was presented to her by the stall owner.</p>
<p>When questioned, the owner shrugged and said</p>
<blockquote><p>小妹! These are premium prawns! $30 each! Bigger, <span class="highlight">longer</span> and better than those $10 ones!</p></blockquote>
<p>Miss Loi, however, was adamant that wasn&#8217;t the case.</p>
<blockquote><p>But they look exactly like the $10 ones.</p></blockquote>
<p>The owner became agitated.</p>
<blockquote>
<p>小妹! WHAT&#8217;S YOUR PROBLEM?! LAST TIME WE CHARGE BY WEIGHT AND THOSE *BEEP* <a rel="external nofollow" href="http://www.straitstimes.com/Breaking%2BNews/Singapore/Story/STIStory_351102.html">ANG MOHS</a> CAME AND GIVE PROBLEM! NOW WE CHARGE BY <span class="highlight">LENGTH</span> AND A SEXY GIRL LIKE YOU COME AND GIVE PROBLEM!</p>
<p>YOU SAY WE OVERCHARGE YOU &#8211; WHERE&#8217;S YOUR <strong>PROOF</strong>?!</p>
</blockquote>
<p>With that he took a $10 prawn from the display and placed it, in an oblique manner, beside Miss Loi&#8217;s last unfinished prawn on a dish.</p>
<blockquote><p>NAH! SEE?! YOUR *BEEP* PRAWN IS MUCH LONGER! <strong>PROVE</strong> IT TO ME IF YOU THINK IT&#8217;S NOT!</p></blockquote>
<p>When Miss Loi tried to align the prawns properly, four well-built men (who looked to be in their 40s) appeared from nowhere and blocked her access to the dish.</p>
<blockquote><p>OI! *BEEP*! WHO SAY YOU CAN TOUCH?! I ASKED YOU TO <strong>PROVE</strong> NOT TOUCH!</p></blockquote>
<div class="question">
<p>The prawns, whose lengths are represented by the lines <var>ABC</var> and <var>ADE</var>, are placed in such a way that <var>ABC</var> and <var>ADE</var> are secants of the circular dish as shown in the diagram below.</p>
<p>Given that <var>BC</var> = <var>DE</var>, prove that <var>AB</var> = <var>AD</var>.</p>
<p><img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/04/tiger-prawn-plane-geometry.gif" alt="Tiger Prawn Plane Geometry" /></p>
</div>
<blockquote>
<p>YOU SO SMART YOU COME AND <strong>PROVE</strong> LAH! *BEEP*! YOU THINK WE HAWKERS GOOD TO BULLY IS IT?! *BEEP*! IF YOU CAN&#8217;T <strong>PROVE</strong> DON&#8217;T EXPECT TO LEAVE THIS PLACE TONIGHT! MUAHAHAHAHAHA!!! </p>
<p>*BEEP* *BEEP* *BEEP* *BEEP* *BEEP*</p>
</blockquote>
<p>Given that that her <a href="/tuition-notes/a-maths-tips/the-yin-yang-eye-of-plane-geometry">阴阳眼 Of Plane Geometry</a> is refusing to work <acronym title="Overtime">OT</acronym> since it&#8217;s already late at night, and that this question is similar to an evil <em>tricky</em> one contributed by a student <span class="fineprint">(actually this IS the question, minus the prawns)</span>, and that she&#8217;s being surrounded by more and more well-built men (who looked to be in their 40s), can you please help Miss Loi (with the aid of the sheet below) prove the above and escape from the hawker centre? <img src='http://www.exampaper.com.sg/blog/wp-includes/images/smilies/icon_sad.gif' alt=':(' class='wp-smiley' /> </p>
<div class="img-div"><a href="http://www.exampaper.com.sg/blog/wp-content/uploads/geometric-formulae-for-plane-geometry.pdf"><img class="content-img" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2008/10/geometric-formulae-for-plane-geometry.gif" alt="Geometric Formulae For Plane Geometry" /></a></div>
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<p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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		<title>The Unfortunate Plight Of A National Icon</title>
		<link>http://www.exampaper.com.sg/questions/a-maths/the-unfortunate-plight-of-a-national-icon</link>
		<comments>http://www.exampaper.com.sg/questions/a-maths/the-unfortunate-plight-of-a-national-icon#comments</comments>
		<pubDate>Wed, 04 Mar 2009 15:25:30 +0000</pubDate>
		<dc:creator>Miss Loi</dc:creator>
				<category><![CDATA[A-Maths Questions]]></category>
		<category><![CDATA[angles of elevation]]></category>
		<category><![CDATA[coordinate geometry]]></category>
		<category><![CDATA[curves]]></category>

		<guid isPermaLink="false">http://www.exampaper.com.sg/questions/a-maths/the-unfortunate-plight-of-a-national-icon</guid>
		<description><![CDATA[<p>What has angles of elevation and coordinate geometry has to do with the Merlion getting struck by lightning.</p><p><small>&copy; 2007-2011 <a href="http://www.exampaper.com.sg">Jφss Sticks</a>. Copycats will be mercilessly hunted down.</small>
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			<content:encoded><![CDATA[<div class="img-div right"><img class="content-img" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/03/old-merlion.jpg" alt="Old Merlion" />
<div class="caption">Balancing proudly in his prime</div>
</div>
<p>He was there when it all began.</p>
<p>Guarding fiercely the old mouth of the Singapore River, he witnessed the meteoric rise and rise of a glorious nation, as modern skyscrapers rose around him, and old warehouses turned into trendy <a rel="external nofollow" href="http://www.zoukclub.com/">dance clubs</a>, and students began using calculators in their <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Primary_School_Leaving_Examination">PSLE</a>, while he dutifully maintained law and order in the river by keeping errant <i>sampans</i> in line with his lethal water spout.</p>
<p>As the years went by, however, he slowly felt forgotten by the relentless pace of progress, as the <i>sampans</i> themselves got transformed into <a rel="external nofollow" href="http://www.rivercruise.com.sg/home.htm">tour boats</a>.</p>
<p>He spouted a watery sigh of sadness while he looked on as one by one, his old friends like the <a rel="external nofollow" href="http://infopedia.nl.sg/articles/SIP_1027_2006-08-12.html">Satay Club</a> and the <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Old_National_Library_Building">National Library</a> went the way of the bulldozers.</p>
<p>More spouts of resignation were to follow when he learnt that younger and mightier <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Merlion#Merlion_statues">clones</a> (including a <a rel="external nofollow" href="http://www.sentosa.com.sg/explore_sentosa/attractions/gallery_merlion/gallery.html">Godzilla-like monster</a> that can shoot laser beams from its eyes) were recruited across the island to perform his job, and that the only occasions he was ever mentioned were in jokes involving drunk patrons of pubs and clubs.</p>
<p>But still he kept his dignity in defiance of the changing times, and continued his balancing act in a forgotten corner of Singapore to spray his jet of water with pride, even when they cruelly deprived him of his daily sunrise viewing by building a <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Esplanade_Bridge">huge bridge</a> across his face.</p>
<div class="img-div right"><img class="content-img" src="http://www.exampaper.com.sg/blog/wp-content/uploads/2009/03/merlion-and-tourists.jpg" alt="Merlion with Sunglasses" />
<div class="caption">That Last Straw</div>
</div>
<p>In the end, the straw that broke the Merlion&#8217;s back came when he was <a rel="external nofollow" href="http://en.wikipedia.org/wiki/Merlion#Relocation_of_original_statue">relocated</a> against his will to another location. The loss of his spiritual home, combined with his inability to get used to being photographed and molested left, right and center by daily hordes of <i>kawaii</i> teeny trigger-happy tourists in this ironically spanking new location, finally pushed him over the edge.</p>
<p>And so, on a dark sunless day, he turned (as far as he could) to take a final look at his son (and discovered to his further horror that he hasn&#8217;t really grown all these years), before closing his eyes and imploring the heavens to put him out of his misery.</p>
<p>A passing 雷公 aka Lightning God heard his plea, and proceeded to plot his target coordinates &#8230;</p>
<div class="question">
<p>The Merlion&#8217;s water spout follows a path defined by the curve <var>y</var><sup>2</sup> = 4<var>x</var> + 64, <var>y</var> &gt; 0 and the lightning bolt (that travels in a <em>straight line</em>) is poised to strike the Merlion&#8217;s head at the point (0, 8), which lies on the path of the water spout.</p>
<p>On the seaward side, a group of tourists are snapping photos of the Merlion&#8217;s <em>front</em> from a <a rel="external nofollow" href="http://www.rivercruise.com.sg/home.htm">Singapore River Cruise</a> boat, with a line of vision that&#8217;s tangent to the water sprout at (0, 8).</p>
<p>On the landward side, a group of <i>kawaii</i> teeny Japanese tourists are snapping photos of the Merlion&#8217;s <em>rear</em> with an angle of elevation of 60&deg; from them to the point (0, 8).</p>
<p>Given that the straight line lightning bolt is so powerful that it can travel through the Merlion&#8217;s head and harm anything beyond, find the range of possible values of its gradient so that the tourists will be safe from harm. </p>
</div>
<p>While this should ultimately be a straightforward enough problem involving the special <span class="highlight"><var>y</var><sup>2</sup> curve</span> that made its way to the <a rel="external nofollow" href="http://www.seab.gov.sg/SEAB/oLevel/syllabus/2009_GCE_O_Level_Syllabuses/4038_2009.pdf">new A-Maths Syllabus</a> last year, please make sure you sketch out the right graphs in this scenario in order to prevent the 雷公 from making any careless mistake that can lead to tragic consequences for the innocent tourists!</p>
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