HSC 2017-2018 Maths Marathon (1 Viewer)

dan964

what
Joined
Jun 3, 2014
Messages
3,473
Location
South of here
Gender
Male
HSC
2014
Uni Grad
2019
Welcome to the 2017 HSC 2U Marathon,

1. Only post questions within the level and scope of 2U HSC Mathematics.

2. Provide neat working out when possible

3. Don't flood the thread with multiple unanswered questions/spam.

4. Challenging questions that a 2U student can pick up easily are okay, but try to stay within the 2U syllabus content.


Here is a question I've pulled for you (modified from Ascham 2011 2U trial HSC)

For the curve
1. Find the stationary points and determine their nature
2. Find any points of inflexion
3. Sketch the graphs showing info from (1) & (2)
4. When is the curve decreasing with downward concavity?
 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,805
Gender
Male
HSC
2015
Re: HSC 2017 Maths (Advanced) Marathon

 

frog1944

Member
Joined
Apr 9, 2016
Messages
210
Gender
Undisclosed
HSC
2017
Re: HSC 2017 Maths (Advanced) Marathon

How would you find all the functions that are both odd and even?
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Re: HSC 2017 Maths (Advanced) Marathon

How would you find all the functions that are both odd and even?
Any (real-valued) function (of a real variable) defined on a symmetric interval (about 0) that is both odd and even must satisfy f(x) = f(-x) = -f(-x) for all x in the domain, which implies f(-x) = 0 for all x in the domain, whence f(x) = 0 for all x in the domain (as the domain is a symmetric interval).

So the only functions with domain and codomain being subsets of R that are both odd and even are those that are identically 0 on a symmetric domain about 0. (If the domain is not symmetric about 0, we can't really talk about f(x) being equal to f(-x) for all x, which is something we need to do for the function to be even. I guess though you still could by saying that it only matters for x such that x and -x are in the domain. But for HSC purposes, the domain is usually symmetric.)
 
Last edited:

dan964

what
Joined
Jun 3, 2014
Messages
3,473
Location
South of here
Gender
Male
HSC
2014
Uni Grad
2019
Re: HSC 2017 Maths (Advanced) Marathon

For the curve
1. Find the stationary points and determine their nature
2. Find any points of inflexion
3. Sketch the graphs showing info from (1) & (2)
4. When is the curve decreasing with downward concavity?
The current question...
 

JackPatel

New Member
Joined
Aug 22, 2016
Messages
14
Gender
Male
HSC
2017
Re: HSC 2017 Maths (Advanced) Marathon

y = 3x³-6x²+4x+7
y’ = 9x²-12x+4

For S.P.
y’=0
9x²-12x+4=0
x= 2/3 y=71/9
Therefore S.P. at (2/3 , 71/9)


For I.P
y′′=0
y′′=18x-12
18x-12=0
x=2/3 y= 71/9
Therefore I.P. at (2/3 , 71/9)

Soz don't have time
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
Re: HSC 2017 Maths (Advanced) Marathon

A cube is inscribed in a right circular cone of height h and radius r so that one side is coplanar with the base and all four opposite vertices are in contact with the curved surface of the cone.

Find the side length of the cube in terms of h and r.
 
Last edited:

dragon658

Member
Joined
Oct 20, 2015
Messages
55
Gender
Male
HSC
2017
Re: HSC 2017 Maths (Advanced) Marathon

Hey guys, how do I go about doing this: find the values of l that will make the quadratic y=(l+6)x^2-2lx+3 a perfect square. And can someone explain what 1/alpha + 1/beta is when doing the roots of a quadratic.
 

Green Yoda

Hi Φ
Joined
Mar 28, 2015
Messages
2,859
Gender
Male
HSC
2017
Re: HSC 2017 Maths (Advanced) Marathon

Hey guys, how do I go about doing this: find the values of l that will make the quadratic y=(l+6)x^2-2lx+3 a perfect square. And can someone explain what 1/alpha + 1/beta is when doing the roots of a quadratic.
The expression is a perfect when the discriminant is rational.

1/alpha +1/beta = alpha+beta/alpha*beta which is sum of roots/product of roots
 

Green Yoda

Hi Φ
Joined
Mar 28, 2015
Messages
2,859
Gender
Male
HSC
2017
Re: HSC 2017 Maths (Advanced) Marathon

Insert three geometric means between 8 and 1/32.
 

Lugia101101

New Member
Joined
Sep 4, 2016
Messages
19
Gender
Undisclosed
HSC
2016
Re: HSC 2017 Maths (Advanced) Marathon

If I'm interpreting your question correctly:






 

boredofstudiesuser1

Active Member
Joined
Aug 1, 2016
Messages
570
Gender
Undisclosed
HSC
2018
Re: HSC 2017 Maths (Advanced) Marathon

Welcome to the 2017 HSC 2U Marathon,

1. Only post questions within the level and scope of 2U HSC Mathematics.

2. Provide neat working out when possible

3. Don't flood the thread with multiple unanswered questions/spam.

4. Challenging questions that a 2U student can pick up easily are okay, but try to stay within the 2U syllabus content.


Here is a question I've pulled for you (modified from Ascham 2011 2U trial HSC)

For the curve
1. Find the stationary points and determine their nature
2. Find any points of inflexion
3. Sketch the graphs showing info from (1) & (2)
4. When is the curve decreasing with downward concavity?
I took a photo but apparently it exceeds the size allowed :(
 

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

Top