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2012 Year 9 &10 Mathematics Marathon (4 Viewers)

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TerenceM

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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 :D

Question:

Solve for a and b

(3√2+7)2 = a +√b

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

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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?"
 
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russ3l

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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!
 
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TerenceM

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Re: 2012 Year 9 &10 Mathematics Marathon

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

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Re: 2012 Year 9 &10 Mathematics Marathon

mwong said:
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!
Click to expand...
Yep! That's correct.
 
russ3l

russ3l

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Re: 2012 Year 9 &10 Mathematics Marathon

Carrotsticks said:
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?"
Click to expand...
thats a tricky one :/
 
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ymcaec

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Re: 2012 Year 9 &10 Mathematics Marathon

Carrotsticks said:
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?"
Click to expand...
0.577 to 3 dp ?
 
qwerty44

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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

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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
 
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TerenceM

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Re: 2012 Year 9 &10 Mathematics Marathon

Guys post more questions :D

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?
 
Carrotsticks

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Re: 2012 Year 9 &10 Mathematics Marathon

Mind if I help post some questions if you have none?
 
twinklegal19

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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

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Re: 2012 Year 9 &10 Mathematics Marathon

might be stupid but

factorise:



year 9-10 only! :p
 
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