# Thread: 2012 Year 9 &10 Mathematics Marathon

1. ## 2012 Year 9 &10 Mathematics Marathon

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

Cheers

2. ## 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?"

3. ## Re: 2012 Year 9 &10 Mathematics Marathon

(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!

4. ## Re: 2012 Year 9 &10 Mathematics Marathon

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

5. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by mwong

(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.

6. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by Carrotsticks
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 :/

7. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by mwong
thats a tricky one :/
Hint: Draw lines connecting the vertices to the centre of the circle/triangle.

8. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by Carrotsticks
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 ?

9. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by ymcaec
0.577 to 3 dp ?
Correct

10. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by ymcaec
0.577 to 3 dp ?
i got that too!

11. ## 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 $R\sqrt3$. This can be proved later with calculus. So in this case, R*sqrt3=1, therefore R=1/sqrt3 (0.577...)

Just an interesting relationship...

12. ## 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

13. ## 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?

14. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by mwong
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/...d.php?t=234259

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

15. ## Re: 2012 Year 9 &10 Mathematics Marathon

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

$You'll~get~used~to~it$

16. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by twinklegal19
Cheers!

17. ## Re: 2012 Year 9 &10 Mathematics Marathon

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

18. ## 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.

19. ## Re: 2012 Year 9 &10 Mathematics Marathon

might be stupid but

factorise:

$x - 6$

year 9-10 only! :P

20. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by Carrotsticks
Mind if I help post some questions if you have none?
Sure! The more, the merrier :L

21. ## Re: 2012 Year 9 &10 Mathematics Marathon

A mushroom farmer has sent an order of 70 kg of mushrooms to the markets in standard cases. If he had used larger cases, each capable of holding 2 kg more, he would have used 4 fewer cases.

What is the capacity (in kg) of the standard case?

22. ## Re: 2012 Year 9 &10 Mathematics Marathon

Well if you're in the older years, posting questions you have done in the past would be great! xD

23. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by qwerty44
A mushroom farmer has sent an order of 70 kg of mushrooms to the markets in standard cases. If he had used larger cases, each capable of holding 2 kg more, he would have used 4 fewer cases.

What is the capacity (in kg) of the standard case?
i havent done capacity D:

24. ## Re: 2012 Year 9 &10 Mathematics Marathon

I still have my maths exam papers that I did last year, I will post up the question that I got wrong hehe (once the last few questions have been answered)

Anyone who wants past year 10 papers from my school, feel free to PM me

25. ## Re: 2012 Year 9 &10 Mathematics Marathon

Originally Posted by mwong
might be stupid but

factorise:

$x - 6$

year 9-10 only! :P
$\left ( \sqrt{x}+\sqrt{6} \right )\left ( \sqrt{x}-\sqrt{6} \right )$

Latex thing is weird lol took me a while to do this TT

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