2012 Year 9 &10 Mathematics Marathon (3 Viewers)

twinklegal19 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

$\\\\$i. Express$~x^2-6x+3 $ in the form $(x-h)^2+k\\\\$ii. Hence make $x$ the subject of $ y=x^2-6x+3\\\\$iii. Hence or otherwise, find the permissible values of $ y$

RivalryofTroll · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

TerenceM said:
LOL wait! the ^ is to the power right?

yes.

ymcaec · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

twinklegal19 said:
$\\\\$i. Express$~x^2-6x+3 $ in the form $(x-h)^2+k\\\\$ii. Hence make $x$ the subject of $ y=x^2-6x+3\\\\$iii. Hence or otherwise, find the permissible values of $ y$

$$i. $\left ( x-3 \right )^{2}-6$
$$ii. $x = \ 3\pm \sqrt{y+6}$
$iii. All real y except y $<$ -6$

ymcaec · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

RivalryofTroll said:
Here's a good question:

Find the minimum value for the term 3^(x^2-8x+14)

$\frac{1}{9}$?$$

Demento1 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Hmm what exactly have I missed? I can grab a few of my school papers from the past and give you the Qs I got wrong.

Carrotsticks · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Eliminate theta from the following expressions:

$x=a \sin \theta $ and $ y= b \cos \theta$

kazemagic · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Find da value of this

Demento1 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Carrotsticks said:
Eliminate theta from the following expressions:

$x=a \sin \theta $ and $ y= b \cos \theta$

Someone happy to do the question above for carrot? I'm afraid I'm on my ipod and I have table tennis soon so I will have to leave it for later. Nice simple q I might add.

kev- · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

TerenceM said:
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?

let the youngest sister be x
therefore oldest sister = x+2+2+2+2
2x=x+8
x+8
third youngest sister is 8+2+2 = 12 years old.

this question was in the Ngo and Sons Year 10 exit exam! O: where'd you find it?

ymcaec · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

kazemagic said:
Find da value of this

1

TerenceM · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

kev- said:
let the youngest sister be x
therefore oldest sister = x+2+2+2+2
2x=x+8
x+8
third youngest sister is 8+2+2 = 12 years old.

this question was in the Ngo and Sons Year 10 exit exam! O: where'd you find it?

Lol I did it myself. Failed it however cos I was sick and everything so barely studied and such LOL and silly mistakes TT

russ3l · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Carrotsticks said:
Eliminate theta from the following expressions:

$x=a \sin \theta $ and $ y= b \cos \theta$

$a^2y^2+b^2x^2=a^2b^2$ ?

ganji · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

so you let x = that massive equation.

square both sides so..

x^2 = 7 - 6[insert that massive equation]

the massive equation = x

hence: x^2 = 7 - 6x
x^2 + 6x - 7 = 0
(x+7)(x-1)=0
x = -7 or 1
but because x>=0 because its a square root
therefore x=1

twinklegal19 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

ymcaec said:
$$i. $\left ( x-3 \right )^{2}-6$
$$ii. $x = \ 3\pm \sqrt{y+6}$
$iii. All real y except y $<$ -6$

Correct! Or alternately for iii, just $y\geq-6$ would probably be faster to write in an exam

twinklegal19 · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Here's a question from my year 10 yearly exam

$\\$i. If $k$ is any integer, write an expression for odd number $n$ in terms of $k.\\\\$ii. If $n$ is an odd integer, show that $ n^2+4n-1$ is divisible by 4$$

Also, don't forget to show full working for all questions in this thread

bleakarcher · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

mwong said:
$a^2y^2+b^2x^2=a^2b^2$ ?

yep

simplifying leads to the general equation of an ellipse x^2/a^2 + y^2/b^2=1

RivalryofTroll · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

ymcaec said:
$\frac{1}{9}$?$$

Correct. 3^-2 = 1/9

russ3l · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

simplify

$\frac{1}{(a-b)(a-c)} + \frac{1}{(b-a)(b-c)} + \frac{1}{(c-a)(c-b)}$

RivalryofTroll · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

Here's another one for you smarties:

16^x - 18(4^x) + 32 = 0

Solve for x.

ymcaec · Jul 2, 2012

Re: 2012 Year 9 &10 Mathematics Marathon

twinklegal19 said:
Here's a question from my year 10 yearly exam

$\\$i. If $k$ is any integer, write an expression for odd number $n$ in terms of $k.\\\\$ii. If $n$ is an odd integer, show that $ n^2+4n-1$ is divisible by 4$$

Also, don't forget to show full working for all questions in this thread

$i. $ n = 2k + 1 $ or $ n = 2k - 1\\\\$ii. Substituting $n = 2k + 1$ into the equation $ n^2+4n-1 \\(2k + 1)^2 + 4 (2k+1) - 1\\= 4k^2 + 4k + 1 + 8k + 4 - 1\\= 4k^2 + 12k + 4\\$Since everything are multiples of 4$\\\therefore n^2 + 4n - 1 $ is divisible by 4 if n is an odd integer$

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