Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

2012 Interview/MAT preparation

We were talking about this on the applicants page and I have seen this done in previous years so I figured it would healthy to do one this year.
The purpose of this thread is basically to test each other with Qs and to get help.
Two things:
-Please spoiler any solutions you may post. It really sucks when a question is spoiled for you by accidentally glancing at a solution.
-Can people please use their common sense when it comes to posing questions. Let's not have questions like: prove Maxwell's equations or some crazy contour integral.

Here are some I thought of that could work, apologies if they are too easy:
-Is

\pi^{e}<e^{\pi}

-Prove that if the digital sum of a number is a multiple of 9 then it is divisible by 9.
-A sphere of unit radius is cut into two portions by a plane distance h from the centre. If the ratio of the bigger portion to the smaller portion is 2:1, show that h is a root of the equation

3h^3-9h+2=0

. Find h to two decimal places.

Scroll to see replies

For question 2 what is the digital sum of a number? I've never come across that before

And for question 3 I have a pretty good idea about how to go about it, I will attempt it then hopefully post a solution.

(edited 12 years ago)

The digital sum of 456 = 4+5+6 = 15

OP

Original post by TheJ0ker

Question 1

Spoiler

Just lol

Original post by TenOfThem

The digital sum of 456 = 4+5+6 = 15

Thanks

Just testing

Spoiler

Original post by TenOfThem

The digital sum of 456 = 4+5+6 = 15

Re-read his question. He said if the digital sum of a number is 9, then the number itself is divisible by 9.

EDIT: Misunderstood your post, sorry about that.

(edited 12 years ago)

Original post by ben-smith

Just lol

What?

OP

Original post by TheJ0ker

What?

Nothing, I just thought it was funny that someone aspiring to study maths at university uses that as a justification :tongue:

:tongue:

OP

Original post by Farhan.Hanif93

Re-read his question. He said if the digital sum of a number is 9, then the number itself is divisible by 9.

She's explaining what the digital sum is.
EDIT: Just realised TenofThem is not a guy...

(edited 12 years ago)

So for example

For Q2

Spoiler

and extrapolate :smile:

:smile:

(edited 12 years ago)

Original post by Farhan.Hanif93

Re-read his question. He said if the digital sum of a number is 9, then the number itself is divisible by 9.

yes I know ... not sure what your point is

that was a general e.g. explaining "digital sum" to Joker

Original post by TheJ0ker

Question 1

Spoiler

If you're looking for a hint, notice that

\pi ^e = e^{e\ln \pi}

.

It will come in handy at some point to consider the maximum value of

\dfrac{\ln x}{x}

.

Original post by TenOfThem

yes I know ... not sure what your point is

that was a general e.g. explaining "digital sum" to Joker

Oh my apologies, I thought you were trying to state that his proposition was false. My bad. :p:

:p:

Original post by Farhan.Hanif93

Oh my apologies, I thought you were trying to state that his proposition was false. My bad. :p:

:p:

ahhhhh

np :smile:

:smile:

OP

Original post by Farhan.Hanif93

If you're looking for a hint, notice that

\pi ^e = e^{e\ln \pi}

.

It will come in handy at some point to consider the maximum value of

\dfrac{\ln x}{x}

.

Hmmm, not quite what I had in mind.

Original post by ben-smith

She's explaining what the digital sum is.
EDIT: Just realised TenofThem is not a guy...

Looks down

Checks

agrees

:biggrin:

:biggrin:

OP

Original post by TenOfThem

Looks down

Checks

agrees

:biggrin:

:biggrin:

Would it be out of line to ask for pics? :tongue:

:tongue:

Original post by ben-smith

Hmmm, not quite what I had in mind.

Comes out quite nicely that way.

OP

Original post by Farhan.Hanif93

Comes out quite nicely that way.

I'm sure it does, I like my way :colone:

:colone:

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