Thursday 30 September 2010

Random Math Question

Find the shaded area.
Let the midpoint of line AD be E. (Centre of semi-circle). Let the arc of AC and AD cut at point F.
AE = EF = 3.5 (radius of circle)
BA = BF = 7 (radius of circle)
EB is common. Then,
Triangle ABE is congruent to Triangle FBE. Hence,
angle ABE = angle FBE = tan-1(AE/AB) = tan-1(1/2) (Note: tan-1 means tangent inverse)
angle ABF = angle ABE + angle FBE = 2 tan-1(1/2) (get this angle in degree)
Area of sector ABF = (2 tan-1 (1/2))/360 x 7 x 7 x pi = (49 pi tan-1(1/2))/180

angle AEB = angle FEB = tan-1(AB/AE) = tan-1(2)
angle AEF = angle AEB + angle FEB = 2 tan-1(2) (get this angle in degree too)
Area of sector AEF = (2 tan-1(2))/360 x 3.5 x 3.5 x pi = (49 pi tan-1(2))/720

Area of quadrilateral ABFE = 3.5x7 = 24.5

Area of shaded region = Area of sector ABF + Area of sector AEF - Area of quadrilateral ABFE
= (49 pi tan-1(1/2))/180 + (49 pi tan-1(2))/720 - 24.5
= 11.8cm2 (round off to 1 decimal point)
(exact pi is used, not 22/7)

Friday 24 September 2010

Games on iPad

This is posted by Lim Li.
In Angry Birds, you are supposed to kill the green thingy by shooting the birds using a catapult. I do not play it often as I am stuck on level 3-12.

In Plants VS Zombies, you are supposed to kill the zombies by planting plants to attack the zombies and to prevent them from eating your brains. Sometimes, I play this game with my cousin, Liu Qin, who just completed the game like me and my sister and brother (we completed the game long ago).

My mother keeps saying that this is our favourite game because she always sees us playing it. However, we play it everyday because we need to get the gems (one gem can be obtained per day from the word game) to buy stuff which help you play the game better. My high score is 278686, but the highest in the world is 30 something millions!

In Farm Story, we are given a plot of land to plant and harvest crops to earn money. If we don't harvest the plants, they will die. This game is rather repetitive and boring, but we play it every day. We are now at level 42.

Thursday 16 September 2010

A Great Educational Toy

This is posted by LJ's mum.
My kids practically grow up with Tomy Megasketcher, a magnetic drawing board. It is their favourite toy. It has a unique screen that allows one to draw clear and crisp pictures, unlike the rough pictures drawn on honeycomb type magnetic board made by Fisher. I bought the first one when Lim Min was 4 or 5 years old and to-date I must have bought over 10 of them (about 1 every year) as the impression left on the drawing surface become quite faint after some months of heavy usage.

When my kids were young (before schooling age), they loved to to draw random pictures and complicated mazes (Lim Jeck's favourite), and now they use it to practise spelling/ tingxie, solve maths problems or just doodle and scribble.

It is a great learning companion for them all these years!

Lim Jeck solving a question that someone posted on Mathlinks.

Lim Li creating different ways of writing the word 'BAD'.

Sunday 12 September 2010

Math Qn

Someone posted the following question on the cbox:
Let AG be x cm.
Then GB = 12-x
Triangle AGF is similar to Triangle ABC, hence AG = GF = x
Tiangle BGF is similar to Triangle BAE, hence
=> (12-x)/x = 12/6 (since AB = 12, AE = 6)
=> 12-x = 2x
=> x=4
Area of Triangle DEF = 1/2 x ED x AG = 1/2 x 6 x 4 = 12
Area of Triangle DFC = 1/2 x DC x (BC - GF) = 1/2 x 12 x (12-4) = 48
Hence, Area of shaded region = 12 + 48 = 60 cm2.

Sunday 5 September 2010


SMO (Senior) - Individual 8th 120
SMO (Senior) - Team 3rd 88 (I think, 350/4)
SMO (Open) - Individual 8th 120
SMO (Open) - Team 4th 83 (250/3)
IMO Silver - 500
Total - 911 :)