• Best of luck to the class of 2024 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • YOU can help the next generation of students in the community!
    Share your trial papers and notes on our Notes & Resources page
MedVision ad

1st Year University Mathematics Thread (1 Viewer)

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
Hey all!

We have a 3U and 4U Maths Marathon, but I noticed that we don't have such a thing for University students!

I'll start with the basic calculations (just to ease everybody in) before throwing in some harder problems.

 

Amleops

Perpetual Student
Joined
Aug 23, 2011
Messages
811
Gender
Male
HSC
2012
Shame this thread hasn't taken off yet. I'm doing Calculus and Linear Algebra at Summer School this year so I could do with some extra practice if we can start this thread up again :).

As for now, haven't really learnt a lot of the content yet, but from cursory readings I think I can do one of the questions:



And yes, one of my aims this Summer is to learn how to properly use LaTeX haha.
 

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
Shame this thread hasn't taken off yet. I'm doing Calculus and Linear Algebra at Summer School this year so I could do with some extra practice if we can start this thread up again :).

As for now, haven't really learnt a lot of the content yet, but from cursory readings I think I can do one of the questions:





And yes, one of my aims this Summer is to learn how to properly use LaTeX haha.
Good luck with that! If you have any questions please feel free to ask in our Mathematics section, or perhaps in this thread.

Yep, your proof looks good =)

Also, learning TeX is great, can be quite slow to begin with but it'll become second nature in no time.
 

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
This one is just simple straight forward partial derivatives.

Try this:

If is differentiable, find the limit

Frank, this thread is to encourage people to answer ie: start off with the 'straight forward' questions, and then move on to the more difficult ones.

We're not here to flex our Maths muscles.
 

HeroicPandas

Heroic!
Joined
Mar 8, 2012
Messages
1,547
Gender
Male
HSC
2013
there is just a small mistake on the fourth line of your working out haha (should be partial y)
 

RenegadeMx

Kosovo is Serbian
Joined
May 6, 2014
Messages
1,302
Gender
Male
HSC
2011
Uni Grad
2016
let x be a real number. prove x=floor(x/2)+ceiling(x/2) iff x is an integer
 

HeroicPandas

Heroic!
Joined
Mar 8, 2012
Messages
1,547
Gender
Male
HSC
2013
let x be a real number. prove x=floor(x/2)+ceiling(x/2) iff x is an integer
IF x is an integer, then it can be odd or even

Suppose x is odd, then there exists an integer M such that x = 2M + 1











Suppose x is even, then there exists an integer M such that x = 2M

So


ONLY IF, not sure atm, thinking about the contrapositive

I have this:

Let x be p/q such that p and q are integers and q is not 0 or 1

LHS = x = p/q

RHS = floor(x/2) + ceil(x/2)
= floor(p/2q) + ceil(p/2q)
 
Last edited:

sirable1

Active Member
Joined
Jan 9, 2012
Messages
709
Location
Sydney, Australia
Gender
Male
HSC
2012
Uni Grad
2016
Note: Sorry, I'm not sure how to use Latex at the moment!

Suppose that two vectors A and B are the following A(0,1,-1), B(2,1,M)

Find the value of 'M' if the angle between A and B is Pi/4

I know the formula for computing angles between vectors is (Cos(theta) = a . b/|a||b|) but I am unsure how to compute the inverse (like finding the value of 'M' here).

This appeared in the one of the past papers for MATH1131, S1 2014 and was quite clueless how to approach this question. Any thoughts?
 
Last edited:

nightweaver066

Well-Known Member
Joined
Jul 7, 2010
Messages
1,585
Gender
Male
HSC
2012
Note: Sorry, I'm not sure how to use Latex at the moment!

Suppose that two vectors A and B are the following A(0,1,-1), B(2,1,M)

Find the value of 'M' if the angle between A and B is Pi/4

I know the angle formula for computing angles between vectors is (Cos(theta) = a . b/|a||b|) but I am unsure how to compute the inverse (like finding the value of 'M' here).

This appeared in the one of the past papers for MATH1131, S1 2014 and was quite clueless how to approach this question. Any thoughts?
Lets hope this is right after having not touched first year maths for so long haha











 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top