Reflection - size of mirror and image

3D drawing software - Google Sketchup

Found this rather interesting (and free) software: Google Sketchup. Interesting because it enables you to draw in 3 dimension as well as manipulate it around to give you views from different angle.

Perfect for those who have trouble visualising 3D trigonometry problems.

Test your English

Take the test at http://www.helloquizzy.com/tests/the-commonly-confused-words-test.

Here's my result:

Your result for The Commonly Confused Words Test...

Advanced

You scored 93% Beginner, 100% Intermediate, 100% Advanced, and 73%
Expert!

You have an extremely good understanding of beginner, intermediate, and
advanced level commonly confused English words, getting at least 75% of each of
these three levels' questions correct. This is an exceptional score.
Remember, these are commonly confused English words, which means most
people don't use them properly. You got an extremely respectable score.

Thank you so much for taking my test. I hope you enjoyed it!

For the complete Answer Key, visit my blog:
http://shortredhead78.blogspot.com/.

Take The Commonly Confused Words Test at HelloQuizzy

A 'simple' maths problem

A teddy bear has a cost price of $18, and a selling price of $21. One day, a young man decided to buy that bear and gave the shopkeeper a $100 dollar bill.

Unfortunately, the shopkeeper do not have $100 change. Hence he went to change the $100 bill into smaller change from a passer-by and gave the change to the young man.

After some time, the passer-by realise the $100 is a fake and demanded his money back from the shopkeeper! The shopkeeper has no choice but to return $100 to the passer-by.

Question: how much exactly did the shopkeeper lost?

Teacher's Day 2008 'rewards'

Thanks for all the gift!

Egg in a bottle experiment

Make your own balance toy

I have came across an interesting wooden balance toy, usually found in the markets of Vietnam and Thailand. Unfortunately, I lost mine and this is the only similiar picture I can find online:

However, you could make your own balance toy by simply using a piece of cardboard!

Step 1 - Download the picture (click on it and download the full size).

Step 2 - Print the shape on a piece of carboard and cut out the shape.

Step 3 - Bend at the lines to create this:

There you have it! Now watch as it does a seemingly impossible act by balancing on the tip of a pen.

Questions to ponder:

1. Is the toy considered stable?



2. Where do you think is the CG of the toy?



3. Do you think the toy is able to balance if you do not let the 'wings' droop down?

Ans: (highlight the space below with your cursor)

1. Yes, because the toy returns to its original position after being tilted.



2. The C.G. is below the tip (pivot), along the line of gravity pull.



3. No. This is because moving the wings upwards will cause the C.G. to move upwards, resulting in an unstable equilibrium. I.e. the moments created by the weight of the toy when the C.G. is above the pivot will tend to topple it. When the C.G. is below the pivot, the moments created by the weight will tend to move the toy back to the original position.

My posting

I realise I haven't update that I've been posted to Kranji Secondary school. You can find out more from their website: http://www.kranjisec.moe.edu.sg/ A beginning teacher is a very busy person...



Sorry Shuqunites, I did request to go back but I guess Shuqun do not lack Physics teacher. Still, all the best for your 'O's! If you need help just let me know.

Would u believe this is the hair of a secondary school male teacher?

English Pronunciation

Though I do not teach English and neither is my command of the language strong, just wanna post this here to share. Try it!

Source: http://bertc.com/english.htm


English Pronunciation!?!
If you can pronounce correctly every word in this poem, you will be speaking English better than 90% of the native English speakers in the world. After trying the verses, a Frenchman said he'd prefer six months of hard labour to reading six lines aloud. Try them yourself.


Dearest creature in creation,

Study English pronunciation.
I will teach you in my verse
Sounds like corpse, corps, horse, and worse.
I will keep you, Suzy, busy,
Make your head with heat grow dizzy.
Tear in eye, your dress will tear.
So shall I! Oh hear my prayer.
Just compare heart, beard, and heard,
Dies and diet, lord and word,
Sword and sward, retain and Britain.
(Mind the latter, how it's written.)
Now I surely will not plague you
With such words as plaque and ague.
But be careful how you speak:
Say break and steak, but bleak and streak;
Cloven, oven, how and low,
Script, receipt, show, poem, and toe.
Hear me say, devoid of trickery,
Daughter, laughter, and Terpsichore,
Typhoid, measles, topsails, aisles,
Exiles, similes, and reviles;
Scholar, vicar, and cigar,
Solar, mica, war and far;
One, anemone, Balmoral,
Kitchen, lichen, laundry, laurel;
Gertrude, German, wind and mind,
Scene, Melpomene, mankind.
Billet does not rhyme with ballet,
Bouquet, wallet, mallet, chalet.
Blood and flood are not like food,
Nor is mould like should and would.
Viscous, viscount, load and broad,
Toward, to forward, to reward.
And your pronunciation's OK
When you correctly say croquet,
Rounded, wounded, grieve and sieve,
Friend and fiend, alive and live.
Ivy, privy, famous; clamour
And enamour rhyme with hammer.
River, rival, tomb, bomb, comb,
Doll and roll and some and home.
Stranger does not rhyme with anger,
Neither does devour with clangour.
Souls but foul, haunt but aunt,
Font, front, wont, want, grand, and grant,
Shoes, goes, does. Now first say finger,
And then singer, ginger, linger,
Real, zeal, mauve, gauze, gouge and gauge,
Marriage, foliage, mirage, and age.
Query does not rhyme with very,
Nor does fury sound like bury.
Dost, lost, post and doth, cloth, loth.
Job, nob, bosom, transom, oath.
Though the differences seem little,
We say actual but victual.
Refer does not rhyme with deafer.
Foeffer does, and zephyr, heifer.
Mint, pint, senate and sedate;
Dull, bull, and George ate late.
Scenic, Arabic, Pacific,
Science, conscience, scientific.
Liberty, library, heave and heaven,
Rachel, ache, moustache, eleven.
We say hallowed, but allowed,
People, leopard, towed, but vowed.
Mark the differences, moreover,
Between mover, cover, clover;
Leeches, breeches, wise, precise,
Chalice, but police and lice;
Camel, constable, unstable,
Principle, disciple, label.
Petal, panel, and canal,
Wait, surprise, plait, promise, pal.
Worm and storm, chaise, chaos, chair,
Senator, spectator, mayor.
Tour, but our and succour, four.
Gas, alas, and Arkansas.
Sea, idea, Korea, area,
Psalm, Maria, but malaria.
Youth, south, southern, cleanse and clean.
Doctrine, turpentine, marine.
Compare alien with Italian,
Dandelion and battalion.
Sally with ally, yea, ye,
Eye, I, ay, aye, whey, and key.
Say aver, but ever, fever,
Neither, leisure, skein, deceiver.
Heron, granary, canary.
Crevice and device and aerie.
Face, but preface, not efface.
Phlegm, phlegmatic, ass, glass, bass.
Large, but target, gin, give, verging,
Ought, out, joust and scour, scourging.
Ear, but earn and wear and tear
Do not rhyme with here but ere.
Seven is right, but so is even,
Hyphen, roughen, nephew Stephen,
Monkey, donkey, Turk and jerk,
Ask, grasp, wasp, and cork and work.
Pronunciation (think of Psyche!)
Is a paling stout and spikey?
Won't it make you lose your wits,
Writing groats and saying grits?
It's a dark abyss or tunnel:
Strewn with stones, stowed, solace, gunwale,
Islington and Isle of Wight,
Housewife, verdict and indict.
Finally, which rhymes with enough,
Though, through, plough, or dough, or cough?
Hiccough has the sound of cup.
My advice is to give up!!!

Please kill 1337 speak, chat, lols and other nonsensical internet jargon!!

Error in TYS notes

Thanks to Leslie for this. Can you spot the error?

Probability in DotA?!?!

Yes, you may have known that Mr Guay is currently a little into the game of DotA. And here are some interesting items in DotA that poses some mathematical questions!

There is an item in the game called Vanguard. Here are the details, taken from DotaPortal:

Vanguard

Description:+5 HP regen/second
+250 Hit Points
65% to block 40 damage

What's interesting is that the amount of damage it blocks is actually a probability! Now...what if you have 2 Vanguards? What is the effect? Some choices:

a) 65% chance to block 80 damage
b) No additional effect i.e. same as having one Vanguard. Which means you just wasted valuable gold!
c) 65%+65%=125% (or rather 100%, since probability can not exceed 100%) to block 40 damage. This means that you get a permanent block of 40 damage.
d) The 2 Vanguards are mutally independent, and hence we need to recalculate the probability.
e) I don't care cos games and maths don't mix! Stop spoiling it!

use your mouse and highlight the space below for answer....

Although Mr Guay can't be 100% sure as he is not the games programmer, it will most likely be (d). So to calculate the probabilty, we can do the direct method, i.e.

P(both Vanguard activating) + P(1 Vanguard activating and the other not)
= (0.65 x 0.65)+[(0.65x0.35)+(0.35x0.65)]
= 0.8775
= 87.75%

Or indirectly,
1 - P(both Vanguards not activating)
= 1 - (0.35x0.35)
= 0.8775
= 87.75%

So, when we buy 2 Vanguards, we increase the probability from 65% to 87.75% of blocking 40 damage. Pls note that Mr Guay is not sure how much damage 2 Vanguards will block when both activate but my guess is only a block of 40 damage instead of 80 damage.

That's all well and good but in the game, the amt of gold is quite limited. There is another item which is one of the material used to make a Vanguard and has similiar properties. Let's compare them and their price:

Vanguard ($2275) 65% to block 40 damage

Stout Shield ($300) 30% to block 30 damage

So which is more worthwhile? How many Stout Shields do we need to buy to obtain the same probability of damage reduction of 1 Vanguard? I know the amt of damage reduction is lesser but disregard that for now. Also disregard the additional porperties Vanguard gives you such as HP regeneration, as we're only concern about blocking damages.

use your mouse and highlight the space below for answer....

Probability of shield NOT activating = 1 - 0.3 = 0.7 (or 70%)

P(2 stout shields)
= 1 - P(both shields do not activate)
= 1 - (0.7 x 0.7)
= 0.51
= 51%

P(3 stout shields)
= 1 - P(3 shields all do not activate)
= 1 - P(0.7 x 0.7 x 0.7)
= 0.657
=65.7%

Hence, with 3 Stout Shields we can have the same blocking probability as a Vanguard, but 3 Shields only cost $900! Something to think about....

There are some other items in DotA that deals with probability, such as Butterfly, Basher, Buriza etc. Have fun!

Status update

Currently doing practicum in Kranji Secondary.

And there's a high chance I'll be posted back to Shuqun!

ITE = It's The End?

Old news but just wanna share it nonetheless.

http://theonlinecitizen.com/2008/01/20/principals-who-put-down-students-have-no-place-in-educating-our-young/#more-643

Are the impressions of ITE really that bad? I personally don't think so.

Did you know?

Quite an interesting video clip I chanced upon.



So is it still relevant to teach the subjects in schools today? Or should we teach them about Internet, computers and connectivity in this fast changing world rather than Maths, Science and History? Since after all, they can locate these information easily if they have mastery of the Net and IT.