All About Math Olympiad Training & Questions

[MathIzzzFun]

CoffeeCat:

FrekiWang:

[quote=\"MathIzzzFun\"]
4. Let the area of a 1 cm x 1 cm x 1 cm triangle be A. Find the area of a 2 cm x 2 cm x 2 cm x 1 cm x 1 cm x 1 cm hexagon that is inscribed in a circle in terms of A.

(This was the problem on the banner, but the banner was taken down. Is it because the problem was too difficult?)

Ans: \t13 A

Visualize the figure as a hexagon with alternate 2cm and 1 cm sides... suppose the hexagon is ABCDEF
AB=2cm
BC=1cm
CD=2cm
DE=1cm
EF=2cm
FA=1cm

Extend AB, DC to meet at X
Extend BA, EF to meet at Y
Extend FE CD to meet at Z

Now XYZ is an equilateral triangle with sides 4 cm. If you divide each side into 4 x 1cm sections. Subdivide this triangle into 16 x 1 cm side equilateral triangle.

The hexagon will consist of 13 such triangles.

http://i50.tinypic.com/2a6ui2w.png\">



cheers.

First of all, 1cm x 1cm x 1cm is a wrong description of a triangle, it should be 1cm by 1cm by 1cm, but not 1cm times 1cm times 1cm. The same applies to a hexagon.

Assuming the description is valid, a 2x2x2x1x1x1 hexagon is different from a 2x1x2x1x2x1 hexagon (shown in that diagram).

The correct diagram is the one below:

http://i45.tinypic.com/1zdtzdv.jpg\">

So maybe the real reason why the problem/banner was taken down is due to the typo xD Since the ans is 13A and supposed to be do-able by primary maths, the setter probably intends it to be the description by MathIzzzFun.[/quote]I am not too concerned with whether the hexagon should be described as 1cm by 1 cm by 1 cm by 2 cm by 2 cm by 2cm or 1 cm x 1 cm x 1cm x 2cm x 2cm x 2cm.

I think all will understand described hexagon is the one drawn by FrekiWang. This is why I said in my post to \"visualize\" the hexagon as 1 cm by 2 cm by 1 cm by 2 cm by 1 cm by 2 cm, because in terms of area, these two hexagons have the same area.... this is how to visualize it to be the same....

Using FrekiWang's diagram, locate the centre of the circle, and connect the centre of the circle to all the vertices of the hexagon to get 3 identical isosceles triangles of base 2 cm and 3 identical isosceles triangles of base 1 cm. Now all these 6 triangles will have same slant side which is equal to the radius of the circle.

Cut out these triangles and rearranged them in the final configuration ie the one that I drew in my posting - alternate 1 cm base triangle with 2 cm base triangle. Sum of all interior angles in the hexagon is 720 deg, and by symmetry, every interior is 120 deg, and one will be able to get the \"13A\" by dividing this hexagon as shown in my posting.

In essence, the approach is similar to the one adopted for Q1 (rearrange the square into a cross) - reshuffling the areas to one that will easily yield the required result.

cheers.

[Absolutely Bo Chap]

Thanks. Nice solution by MathIzzzFun.


Anyway, the trainer is also apparently an instructor with the Singapore National Teams and Problem 4 has been used.

Also, apparently there was some vandalism near Keban Baru CC where somebody slashed all the banners. So all banners were taken down during that period of time LOL.

[Absolutely Bo Chap]

Keban Baru CC will conduct another Maths Olympiad workshop either in March or June, in case anybody is interested. No details available yet.

[ahxuan.031873ymail.031873com]

Hi,

Can anyone share what are the benefits of joining the P6 Math Olympiad Training in school? Not so much on the competition. More on what they have learn from the training. Am deciding if I should let my child participate. Thanks.

[HyperKiasu]

May I know when the NMOS (by NUS High) will be? which month?


thanks

[dagong99]

HyperKiasu:

May I know when the NMOS (by NUS High) will be? which month?


thanks

Dates for NMOS not out yet, most likely end Jun/mid Jul but SPSO is on 13 Jul (Theory) & 25 Jul (Practical).

[HyperKiasu]

dagong99:

HyperKiasu:

May I know when the NMOS (by NUS High) will be? which month?


thanks

Dates for NMOS not out yet, most likely end Jun/mid Jul but SPSO is on 13 Jul (Theory) & 25 Jul (Practical).

thanks.

Pardon my ignorance, what the practical SPSO is?

[dagong99]

HyperKiasu:

dagong99:

[quote=\"HyperKiasu\"]May I know when the NMOS (by NUS High) will be? which month?


thanks

Dates for NMOS not out yet, most likely end Jun/mid Jul but SPSO is on 13 Jul (Theory) & 25 Jul (Practical).

thanks.

Pardon my ignorance, what the practical SPSO is?[/quote]Oh, Singapore Primary Science Olympiad (SPSO) has 2 rounds, theory & practical, it's for P5 students, those 'survived' theory will be invited for practical.

The top students from these rounds of SPSO will be shortlisted for a training programme conducted by NUS High School in preparation for International Mathematics & Science Olympiad (IMSO). The final squad, which consists of six official participants and two reserves, will be selected to form the Science team to represent Singapore in IMSO 2013.

[ahxuan.031873ymail.031873com]

quekcc:

Firstly, the training in school will be very intensive. For the training that I had conducted, it will cover 80-90% of the P6 topics within the 15-20 hrs, and will probably before March holidays!


So, ideally, these are for better students who like solving challenging problems.

Thanks for information.

[HyperKiasu]

dagong99:

Oh, Singapore Primary Science Olympiad (SPSO) has 2 rounds, theory & practical, it's for P5 students, those 'survived' theory will be invited for practical.

The top students from these rounds of SPSO will be shortlisted for a training programme conducted by NUS High School in preparation for International Mathematics & Science Olympiad (IMSO). The final squad, which consists of six official participants and two reserves, will be selected to form the Science team to represent Singapore in IMSO 2013.

Hi, thanks for d info.
IMSO means the participants need to take both math and science?
so how are they selected? SPSO is not the only contest as a basis for selection?. :roll:

tnx