Comments on: The Phantom Car of PIE http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie 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/e-maths/the-phantom-car-of-pie#comment-38111 qwerty1106 Tue, 22 Jun 2010 18:10:39 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-38111 Do physic simpler leh... i see amath kinematics and its 3x as hard as physics XP Do physic simpler leh... i see amath kinematics and its 3x as hard as physics XP

]]> By: ignorantsoup http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9537 ignorantsoup Sun, 15 Jun 2008 05:34:40 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9537 Omg Miss Loi is so pretty. Haha. I was browsing the papers when I noticed a sexy young math tutor on the front page, and I know it's you. Hahahaha. It's a pretty nice pretty photo. :) Omg Miss Loi is so pretty. Haha. I was browsing the papers when I noticed a sexy young math tutor on the front page, and I know it's you. Hahahaha. It's a pretty nice pretty photo. :)

]]> By: Ordinary Guy http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9536 Ordinary Guy Sun, 15 Jun 2008 02:51:23 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9536 Hi Miss Loi, Congratulations for having been featured in The Straits Times today as being one of five private tutors on the front page....cool. Ordinary Guy Hi Miss Loi,

Congratulations for having been featured in The Straits Times today as being one of five private tutors on the front page....cool.

Ordinary Guy

]]> By: fggffggf http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9530 fggffggf Sat, 14 Jun 2008 16:17:12 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9530 It is good reminding students the ban of graphing calculators. (Actually I am not a Singaporean student so I did not know that, but it does not matter; many thanks to pointing that I missed the units in part 1.) It is good reminding students the ban of graphing calculators. (Actually I am not a Singaporean student so I did not know that, but it does not matter; many thanks to pointing that I missed the units in part 1.)

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9528 Miss Loi Sat, 14 Jun 2008 15:49:40 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9528 Oh and thanks <b>fggffggf</b> for contributing your answers. Great example of multiple approaches to the same question here - though graphical calculators are still banned for the O-Levels! <b>Clarion:</b> If you're a Physics student, as <a href="/questions/a-maths/kinematics-this-is-a-maths-not-physics" rel="nofollow">mentioned previously</a>, please refrain from thinking about those super duper rocket science out-of-syllabus motion equations you've learnt in your physics class when tackling your <em>Maths</em> kinematics questions - you risk getting yourself mightily confused in the end! This is Maths NOT Physics! Oh and thanks fggffggf for contributing your answers. Great example of multiple approaches to the same question here - though graphical calculators are still banned for the O-Levels!

Clarion: If you're a Physics student, as mentioned previously, please refrain from thinking about those super duper rocket science out-of-syllabus motion equations you've learnt in your physics class when tackling your Maths kinematics questions - you risk getting yourself mightily confused in the end!

This is Maths NOT Physics!

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9527 Miss Loi Sat, 14 Jun 2008 15:37:02 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9527 Ok it has been a looong day ... :D Was about to say that graphical calculators are still banned in O-Level exams so graphing solutions are out - even though <b>fggffggf</b>'s answers are correct. In order to solve the smirk-erasing Part 4, one has to understand that: <span class="highlight">At the time when the car overtakes the lorry (and vice versa), they are at the same position i.e. their distance traveled since <var>t</var> = 0 is THE SAME.</span> <span class="fineprint">*Assuming that both car and lorry started at the same position when <var>t</var> = 0 (Miss Loi added this in the question but sometimes they don't specify - it's good to state this assumption in your working)</span> So to find the overtaking time, you'll need to express the distance travelled by the car and lorry in terms of <var>t</var>, equate them and solve for <var>t</var>. A. Distance traveled by lorry in time <var>t</var> = 15<var>t</var> ----- (1) B. You can express the distance traveled by car in time <var>t</var> straightaway using the trapezium area formula as shown by <b>fggffggf</b> above OR do it part by part just to check that you're on the right track: <img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2008/06/speed-time-graph-answer.gif" alt="Speed-Time Graph Answer" /> As can be seen from the diagram: <ol> <li>When <var>t</var> = 10, distance covered by car < distance covered by lorry ⇒ car hasn't yet overtaken lorry.</li> <li>When <var>t</var> = 40, distance covered by car > distance covered by lorry ⇒ car has overtaken lorry.</li> <li>⇒ car overtook lorry somewhere 10 < <var>t</var> < 40</li> <ol> ∴ distance expression for car = total distance traveled in 1st 10 sec + distance traveled for 0 < <var>t</var> < 40 <span class="highlight">⇒ 100 + (<var>t</var> - 10)(20)</span> ----- (2) Equate (1) & (2) and solving you'll get <var>t</var> = 20s ;) As to whether the lorry overtakes the car again, the answers in Parts 2 and 3 already show that both of them traveled the same distance in 60 sec, so the lorry did overtake the car again at <var>t</var> = 60s because the lorry is still continuing at a constant speed while the car has come to a stop (presumably by more traffic jam on her lane!) Ok it has been a looong day ... :D

Was about to say that graphical calculators are still banned in O-Level exams so graphing solutions are out - even though fggffggf's answers are correct.

In order to solve the smirk-erasing Part 4, one has to understand that:

At the time when the car overtakes the lorry (and vice versa), they are at the same position i.e. their distance traveled since t = 0 is THE SAME.

*Assuming that both car and lorry started at the same position when t = 0 (Miss Loi added this in the question but sometimes they don't specify - it's good to state this assumption in your working)

So to find the overtaking time, you'll need to express the distance travelled by the car and lorry in terms of t, equate them and solve for t.

A. Distance traveled by lorry in time t = 15t ----- (1)

B. You can express the distance traveled by car in time t straightaway using the trapezium area formula as shown by fggffggf above OR do it part by part just to check that you're on the right track:

Speed-Time Graph Answer

As can be seen from the diagram:

  1. When t = 10, distance covered by car < distance covered by lorry ⇒ car hasn't yet overtaken lorry.
  2. When t = 40, distance covered by car > distance covered by lorry ⇒ car has overtaken lorry.
  3. ⇒ car overtook lorry somewhere 10 < t < 40

    ∴ distance expression for car = total distance traveled in 1st 10 sec + distance traveled for 0 < t < 40
    ⇒ 100 + (t - 10)(20) ----- (2)

    Equate (1) & (2) and solving you'll get t = 20s ;)

    As to whether the lorry overtakes the car again, the answers in Parts 2 and 3 already show that both of them traveled the same distance in 60 sec, so the lorry did overtake the car again at t = 60s because the lorry is still continuing at a constant speed while the car has come to a stop (presumably by more traffic jam on her lane!)

]]> By: clarion-x http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9524 clarion-x Sat, 14 Jun 2008 13:24:55 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9524 reminds me of physics... reminds me of physics...

]]> By: fggffggf http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9520 fggffggf Sat, 14 Jun 2008 09:24:15 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9520 Many apologies for the crude "formulas" above. Hope they do not cause much readability problems. I finally derived the algebraic solution to part 4, as follows: Let <i>t</i> s be the required time for the car to be at the same position as the lorry. .'.[pmath]15t={{((t-10)+t)/2}*20}[/pmath] [pmath]15t=10(2t-10)[/pmath] [pmath]15t=20t-100[/pmath] [pmath]100=5t[/pmath] [pmath]t=20[/pmath] .'. When the time is just over 20 s, the car overtakes the lorry. As both vehicles arrive at the same location when time = 60 s, the lorry does not actually overtake the car. Illustrated in the graph. When I saw part 4 of this question, my instinct was not to use an equation, thus I plotted a graph. However the algebra did not seem anywhere obvious in the graph, so I resorted to using the equation. 无奈，但很有用。 Many apologies for the crude "formulas" above. Hope they do not cause much readability problems.
I finally derived the algebraic solution to part 4, as follows:

Let t s be the required time for the car to be at the same position as the lorry.
.'.15t={{((t-10)+t)/2}*20}
15t=10(2t-10)
15t=20t-100
100=5t
t=20
.'. When the time is just over 20 s, the car overtakes the lorry.
As both vehicles arrive at the same location when time = 60 s, the lorry does not actually overtake the car. Illustrated in the graph.

When I saw part 4 of this question, my instinct was not to use an equation, thus I plotted a graph. However the algebra did not seem anywhere obvious in the graph, so I resorted to using the equation. 无奈，但很有用。

]]> By: fggffggf http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9506 fggffggf Fri, 13 Jun 2008 15:47:20 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9506 Miss Loi, I have attempted parts 1 to 4 of your question. Part 1: Acceleration = {20-0}<span class="highlight">m/s</span>/{10-0}<span class="highlight">s</span> = 2 <strong class="highlight">m/s<sup>2</sup></strong> <div class="highlight"> Yes in a linear speed-time graph, the acceleration (=rate of change of speed) over a period of time is the <em>gradient</em> of the graph within this period. But remember to include the unit in you answer (see above)! P.S. It's also worth noting that when the gradient is <em>negative</em> (i.e. at the <var>t</var>=40-60s period in the graph), the car is <em>decelerating</em> i.e. slowing down. </div> Part 2: Distance travelled by the car = 1/2*((60-0)+(40-10))*20 = 900 m <div class="highlight"> Yes as mentioned, the distance covered in a speed-time graph will be the area under the curve which is a trapezium for the range of 0-60s. So using the area of trapezium formula (i.e. 1/2 * sum of parallel sides * height) you'll get the total distance of 900m. For those who've somehow forgotten the trapezium area formula, you can also add up the areas of the triangle (<var>t</var>=0-10s), rectangle (<var>t</var>=10-40s), and triangle (<var>t</var>=40-60s) and you should get the same answer. Such a peanut question right? </div> Part 3: Distance travelled by the lorry = 15*60 = 900 m <div class="highlight"> Miss Loi will knock your head if you don't know how to find the area of the rectangle for <var>t</var>=0-60s! But beware of careless mistakes here as students can sometimes get double-vision and confused as to which graph are they dealing with now - we're dealing with the lorry not the car in this part! This is also the time when Miss Loi's students start smirking. Tsk tsk. </div> For part 4, I plotted a graph on computer. I derived some equations that fit the given speed-time graph, then I integrated them. Hope it does not matter. The graph is titled "pix1" in my <a href="http://photo.xanga.com/fggffggf" rel="nofollow">public photo album</a>. <span class="highlight">Oops class starting ... will be right back :P</span> Miss Loi, I have attempted parts 1 to 4 of your question.
Part 1: Acceleration = {20-0}m/s/{10-0}s = 2 m/s2

Yes in a linear speed-time graph, the acceleration (=rate of change of speed) over a period of time is the gradient of the graph within this period. But remember to include the unit in you answer (see above)!

P.S. It's also worth noting that when the gradient is negative (i.e. at the t=40-60s period in the graph), the car is decelerating i.e. slowing down.

Part 2: Distance travelled by the car
= 1/2*((60-0)+(40-10))*20
= 900 m

Yes as mentioned, the distance covered in a speed-time graph will be the area under the curve which is a trapezium for the range of 0-60s. So using the area of trapezium formula (i.e. 1/2 * sum of parallel sides * height) you'll get the total distance of 900m.

For those who've somehow forgotten the trapezium area formula, you can also add up the areas of the triangle (t=0-10s), rectangle (t=10-40s), and triangle (t=40-60s) and you should get the same answer.

Such a peanut question right?

Part 3: Distance travelled by the lorry
= 15*60 = 900 m

Miss Loi will knock your head if you don't know how to find the area of the rectangle for t=0-60s! But beware of careless mistakes here as students can sometimes get double-vision and confused as to which graph are they dealing with now - we're dealing with the lorry not the car in this part!

This is also the time when Miss Loi's students start smirking. Tsk tsk.

For part 4, I plotted a graph on computer. I derived some equations that fit the given speed-time graph, then I integrated them. Hope it does not matter.
The graph is titled "pix1" in my public photo album.

Oops class starting ... will be right back :P

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9504 Miss Loi Fri, 13 Jun 2008 12:17:25 +0000 http://www.exampaper.com.sg/questions/e-maths/the-phantom-car-of-pie#comment-9504 <b>Pacey:</b> Think Miss Loi's assessment books will be mighty thick if she gets to set the questions since they're so <i>chiong hei</i> lol <b>Cockcroach:</b> Students need to be able to recite the formulae first <em>BEFORE</em> they can chant "WE WILL SCORE A1s!" i.e. have to learn to walk first before flying ;) <b>Krisandro:</b> You don't like Techno? Minus 100 marks! F9 for you! *Casts a bone-chilling glance at <b>Soupie</b>* *Casts another bone-chilling glance at <b>Huifen</b>* <b>Clarion:</b> Got. Depends on which school you're from ;) Pacey: Think Miss Loi's assessment books will be mighty thick if she gets to set the questions since they're so chiong hei lol

Cockcroach: Students need to be able to recite the formulae first BEFORE they can chant "WE WILL SCORE A1s!" i.e. have to learn to walk first before flying ;)

Krisandro: You don't like Techno? Minus 100 marks! F9 for you!

*Casts a bone-chilling glance at Soupie*

*Casts another bone-chilling glance at Huifen*

Clarion: Got. Depends on which school you're from ;)

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