2012 Year 9 &10 Mathematics Marathon (4 Viewers)

TerenceM

New Member
Joined
Apr 24, 2012
Messages
24
Gender
Male
HSC
2014
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
 
Last edited:

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
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?"
 
  • Like
Reactions: x1

russ3l

Member
Joined
Dec 12, 2011
Messages
258
Location
Sydney
Gender
Male
HSC
2014
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!
 
  • Like
Reactions: x1

TerenceM

New Member
Joined
Apr 24, 2012
Messages
24
Gender
Male
HSC
2014
Re: 2012 Year 9 &10 Mathematics Marathon

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

TerenceM

New Member
Joined
Apr 24, 2012
Messages
24
Gender
Male
HSC
2014
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

Member
Joined
Dec 12, 2011
Messages
258
Location
Sydney
Gender
Male
HSC
2014
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 :/
 

ymcaec

Member
Joined
Apr 25, 2012
Messages
77
Gender
Undisclosed
HSC
N/A
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

Member
Joined
Oct 12, 2011
Messages
557
Gender
Male
HSC
2013
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

Member
Joined
Dec 12, 2011
Messages
258
Location
Sydney
Gender
Male
HSC
2014
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

New Member
Joined
Apr 24, 2012
Messages
24
Gender
Male
HSC
2014
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

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
Re: 2012 Year 9 &10 Mathematics Marathon

Mind if I help post some questions if you have none?
 
Joined
Apr 1, 2011
Messages
1,012
Location
District 12
Gender
Male
HSC
2013
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

Member
Joined
Dec 12, 2011
Messages
258
Location
Sydney
Gender
Male
HSC
2014
Re: 2012 Year 9 &10 Mathematics Marathon

might be stupid but

factorise:



year 9-10 only! :p
 

Users Who Are Viewing This Thread (Users: 0, Guests: 4)

Top