2012 Year 9 &10 Mathematics Marathon (2 Viewers)

[TerenceM]

Hey guys,
Thought it would be cool to start a mathematics marathon for Year 10's and such. Pretty much post up questions and answer it

Question:

Solve for a and b

(3√2+7)² = a +√b

After answering please fuel the thread by posting your own question!
Cheers

 

[Carrotsticks]

Re: 2012 Year 9 &10 Mathematics Marathon

Good idea! Here's a fun one to add on top of TerenceM's:

"An equilateral triangle with side length 1 is placed inside a circle such that all the vertices of the triangle touch the circumference of the circle (also known as 'circumscribing'). What is the radius of the circle?"

 

[russ3l]

Re: 2012 Year 9 &10 Mathematics Marathon

answer for terence's:

(3√2+7)2 = a +√b
=18+42√2+49
=67+42√2
=67+ √3528

therefore
a = 67 and b = 3528

2014/5 HSC'ers unite!

 

[TerenceM]

Re: 2012 Year 9 &10 Mathematics Marathon

Thanks Carrotsticks! and I shall leave that question for others but work it out myself

 

[TerenceM]

Re: 2012 Year 9 &10 Mathematics Marathon

answer for terence's:

(3√2+7)2 = a +√b
=18+42√2+49
=67+42√2
=67+ √3528

therefore
a = 67 and b = 3528

2014/5 HSC'ers unite!

Yep! That's correct.

 

[russ3l]

Re: 2012 Year 9 &10 Mathematics Marathon

Good idea! Here's a fun one to add on top of TerenceM's:

"An equilateral triangle with side length 1 is placed inside a circle such that all the vertices of the triangle touch the circumference of the circle (also known as 'circumscribing'). What is the radius of the circle?"

thats a tricky one :/

 

[Carrotsticks]

Re: 2012 Year 9 &10 Mathematics Marathon

thats a tricky one :/

Hint: Draw lines connecting the vertices to the centre of the circle/triangle.

 

[ymcaec]

Re: 2012 Year 9 &10 Mathematics Marathon

Good idea! Here's a fun one to add on top of TerenceM's:

"An equilateral triangle with side length 1 is placed inside a circle such that all the vertices of the triangle touch the circumference of the circle (also known as 'circumscribing'). What is the radius of the circle?"

0.577 to 3 dp ?

 

[qwerty44]

Re: 2012 Year 9 &10 Mathematics Marathon

0.577 to 3 dp ?

Correct

 

[russ3l]

Re: 2012 Year 9 &10 Mathematics Marathon

0.577 to 3 dp ?

i got that too!

 

[qwerty44]

Re: 2012 Year 9 &10 Mathematics Marathon

Another thing you should keep in mind is that the side length of an equilateral triangle inscribed in a circle of radius R is . This can be proved later with calculus. So in this case, R*sqrt3=1, therefore R=1/sqrt3 (0.577...)

Just an interesting relationship...

 

[russ3l]

Re: 2012 Year 9 &10 Mathematics Marathon

do you guys know how to post up numbers like what twinklegal19 did? like, is it an app or something :S year 10 student here

 

[TerenceM]

Re: 2012 Year 9 &10 Mathematics Marathon

Guys post more questions

Another : 5 sisters are born on 2 year successive intervals. The eldest sister is twice the age of the youngest sister. What is the age of the 3rd youngest sister?

 

[twinklegal19]

Re: 2012 Year 9 &10 Mathematics Marathon

do you guys know how to post up numbers like what twinklegal19 did? like, is it an app or something :S year 10 student here

Use Latex

http://community.boredofstudies.org/showthread.php?t=234259

http://www.codecogs.com/latex/eqneditor.php

 

[qwerty44]

Re: 2012 Year 9 &10 Mathematics Marathon

do you guys know how to post up numbers like what twinklegal19 did? like, is it an app or something :S year 10 student here

It's called LaTeX. http://www.codecogs.com/latex/eqneditor.php <you can try it out here

To post with it on here [ TEX ] *put code in here* [ / TEX ] without any spaces in the brackets.

 

[TerenceM]

Re: 2012 Year 9 &10 Mathematics Marathon

Use Latex

http://community.boredofstudies.org/showthread.php?t=234259

http://www.codecogs.com/latex/eqneditor.php

Cheers!

 

[Carrotsticks]

Re: 2012 Year 9 &10 Mathematics Marathon

Mind if I help post some questions if you have none?

 

[twinklegal19]

Re: 2012 Year 9 &10 Mathematics Marathon

Digging up my old year 9/10 maths books

A rectangular lawn, with length x m and width y m in the ratio 8:3, is surrounded on all sides by a path 80cm wide. The outer perimeter of the path is 50.4m. Find the area of the lawn.

 

[russ3l]

Re: 2012 Year 9 &10 Mathematics Marathon

might be stupid but

factorise:



year 9-10 only!

 

[TerenceM]

Re: 2012 Year 9 &10 Mathematics Marathon

Mind if I help post some questions if you have none?

Sure! The more, the merrier :L