HSC 2012 Maths Marathon (archive) (1 Viewer)

SpiralFlex · Mar 5, 2012

Re: 2012 HSC Mathematics Marathon!

Dweary me....

Timske · Mar 5, 2012

Re: 2012 HSC Mathematics Marathon!

ooh?

ademb13 · Mar 6, 2012

Re: 2012 HSC Mathematics Marathon!

pretty simple dont you think

SpiralFlex · Mar 6, 2012

Re: 2012 HSC Mathematics Marathon!

Spiral's girlfriend is still burning. There is still time to save her!

Examine · Mar 8, 2012

Re: 2012 HSC Mathematics Marathon!

1. Solve |x-3|+|x+4|=|x-2|
2. Solve x^3/2=1/8
3. Solve 6y^2/3y-2<-3

zeebobDD · Mar 8, 2012

Re: 2012 HSC Mathematics Marathon!

Examine said:
1. Solve |x-3|+|x+4|=|x-2|
2. Solve x^3/2=1/8
3. Solve 6y^2/3y-2<-3

no.

aahhhhhaaaaaaa

2) x^3 =1/4 x=cuberoot of 1/4
3) after all the simplification you will get an expression:

(3x-2)(2x^2+1)<0 then draw the graph n interpret where its <0

CrackerMo · Mar 8, 2012

Re: 2012 HSC Mathematics Marathon!

SpiralFlex said:
Of course the general rule of the 2U thread is that 4U students cannot answer any of the questions. Only provide them.

$Spiral's girlfriend is trapped inside a burning house and wants to rescue her! He is currently situated at his place of living. At the lighthouse directly north of A. The path he wants to take runs diagonally downwards and across. This mystical path is highlighted in blue as he waves his wand to find the shortest distance. To get there as quick as possible, Spiral must row across the destructive ocean from his lighthouse to point B,$\; x \;\textup{km} \;$ from A and then use his tiny feet to run towards the burning building. If Spiral's rowing speed is$\; 6 \textup{km/h}\;$ and his jogging speed is$\; 10 \textup{km/h}. $[Assume burning building is 10 km east from A.]$

$i. Find an expression in hours for Spiral to row from the lighthouse to B.$

$ii. Hence find the total time taken for Spiral to travel across the glowing path to rescue his girlfriend.$

$iii. Hence show that when$\; x= 4.5 \textup{km/h},$\; the time it takes for Spiral to travel from the lighthouse to rescue his girlfriend is a minmum.$

$iv. Hence find the quickest time it takes Spiral to go to the rescue his girlfriend from the lighthouse and live happily ever after. Give your answer correct to the nearest minute.$

Haha Spiral, did you get this from Cambridge? I swear I did this question before in max/min problems :O

EDIT:

I don't get Q 4...

zeebobDD · Mar 8, 2012

Re: 2012 HSC Mathematics Marathon!

CrackerMo said:
Haha Spiral, did you get this from Cambridge? I swear I did this question before in max/min problems :O

I don't get Q 4...

u sub the value of x, you jus found back into your equations to get the shortest time

SpiralFlex · Mar 8, 2012

Re: 2012 HSC Mathematics Marathon!

CrackerMo said:
Haha Spiral, did you get this from Cambridge? I swear I did this question before in max/min problems :O

EDIT: View attachment 24545

I don't get Q 4...

This max/min problem is common haha and no it shouldn't be from Cambridge unless by coincidence.

CrackerMo · Mar 9, 2012

Re: 2012 HSC Mathematics Marathon!

But isn't the x value I already found, the minimum Time?

SpiralFlex · Mar 9, 2012

Re: 2012 HSC Mathematics Marathon!

The x value is not the time.

zeebobDD · Mar 10, 2012

Re: 2012 HSC Mathematics Marathon!

CrackerMo said:
But isn't the x value I already found, the minimum Time?

nope, but you should have an equation for the minimum time with x as a subject

twinklegal19 · Jul 31, 2012

Re: 2012 HSC Mathematics Marathon!

Time to revive this thread, don't you think?

$$Show that $\frac{d}{dx}(xe^x)=e^x+xe^x$ and hence evaluate $\int_{0}^{2}xe^xdx$

Sy123 · Jul 31, 2012

Re: 2012 HSC Mathematics Marathon!

$\frac{d}{dx} x e^x \\ u=x \ \ u'=1 \\ v=e^x \ \ v'=e^x \\ \\ \therefore \frac{d}{dx} x e^x=u'v+v'u=e^x+x e^x \\ \\ \therefore \int_0^2 x e^x \ dx + \int_0^2 e^x \ dx = 2e^2-0 \\ \\ \int_0^2 x e^x \ dx + e^2-1=2e^2-0 \\ \\ \therefore \int_0^2 x e^x \ dx = e^2+1$

Heh can we continue this in the 3U marathon or something? Id rather have both 2U and 3U in the 3U marathon rather than seperate ones for each.
If you agree I can post the next question over there or I can post it here.

barbernator · Jul 31, 2012

Re: 2012 HSC Mathematics Marathon!

Sy123 said:
$\frac{d}{dx} x e^x \\ u=x \ \ u'=1 \\ v=e^x \ \ v'=e^x \\ \\ \therefore \frac{d}{dx} x e^x=u'v+v'u=e^x+x e^x \\ \\ \therefore \int_0^2 x e^x \ dx + \int_0^2 e^x \ dx = 2e^2-0 \\ \\ \int_0^2 x e^x \ dx + e^2-1=2e^2-0 \\ \\ \therefore \int_0^2 x e^x \ dx = e^2+1$

Heh can we continue this in the 3U marathon or something? Id rather have both 2U and 3U in the 3U marathon rather than seperate ones for each.
If you agree I can post the next question over there or I can post it here.

do eeeeet

twinklegal19 · Jul 31, 2012

Re: 2012 HSC Mathematics Marathon!

Sy123 said:
$\frac{d}{dx} x e^x \\ u=x \ \ u'=1 \\ v=e^x \ \ v'=e^x \\ \\ \therefore \frac{d}{dx} x e^x=u'v+v'u=e^x+x e^x \\ \\ \therefore \int_0^2 x e^x \ dx + \int_0^2 e^x \ dx = 2e^2-0 \\ \\ \int_0^2 x e^x \ dx + e^2-1=2e^2-0 \\ \\ \therefore \int_0^2 x e^x \ dx = e^2+1$

Heh can we continue this in the 3U marathon or something? Id rather have both 2U and 3U in the 3U marathon rather than seperate ones for each.
If you agree I can post the next question over there or I can post it here.

k

at this stage, I'm a lot more knowledgeable in 2U than 3U stuff but that's fine by me

SpiralFlex · Jul 31, 2012

Re: 2012 HSC Mathematics Marathon!

Oh dear. ^^^^^ Was that me? Haha I can't believe I posted that question.

fatima96 · Sep 23, 2012

2U Maths marathon

Showing full working, simplify.

$\frac{2tan}{1+tan^2}$

Shadowdude · Sep 23, 2012

Re: 2U Maths marathon

$1 + \tan^{2}{x} = \sec^{2}{x}$

Use $tan(x) = \frac{sin(x)}{cos(x)}$

That should make you be able to do it yourself.

Timothy6340 · Sep 23, 2012

Re: 2U Maths marathon

sin2x

HSC 2012 Maths Marathon (archive) (1 Viewer)

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