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HSC 2017-2018 Maths Marathon (1 Viewer)

dan964

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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

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Re: HSC 2017 Maths (Advanced) Marathon

 

frog1944

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Re: HSC 2017 Maths (Advanced) Marathon

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

InteGrand

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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.)
 
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dan964

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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

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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

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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.
 
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dragon658

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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

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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

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Re: HSC 2017 Maths (Advanced) Marathon

Insert three geometric means between 8 and 1/32.
 

Lugia101101

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Re: HSC 2017 Maths (Advanced) Marathon

If I'm interpreting your question correctly:






 

boredofstudiesuser1

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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 :(
 

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