HSC 2015 MX1 Marathon (archive) (2 Viewers)

[davidgoes4wce]

Re: HSC 2015 3U Marathon

A particle is moving in a straight line. At time t seconds it has displacement x metres from a fixed point O on the line, velocity ms^-1 and acceleration a ms^-2 given by a=x+1.5. Initially the particle is 5 m to the right of O and moving towards O with a speed of 6ms^-1.

Explain whether the particle is initially speeding up or slowing down.


The answer they have is: slowing down, since acceleration > 0 and velocity <0

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

OK I re-read the solutions, the particle initially has an x=5 and v=-6. Drawing the graph




I thought x=5, and v=6 (positive ). Maybe someone could break it down for me a bit more clearly.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

This question was part of the North Sydney Boys High School 2015 Trials but I'm still a bit stumped on it. My thinking is if the question says '5 m to the right of the Origin , O' it has to be obviously to be at x=5 , but I couldn't 100% sure determine whether to start off with v=-6 or v=6. Using either v=-6 or v=6 I was still able to get the same equation for v^2, which in this case was v^2=x^2+3x-4

 

[InteGrand]

Re: HSC 2015 3U Marathon

This question was part of the North Sydney Boys High School 2015 Trials but I'm still a bit stumped on it. My thinking is if the question says '5 m to the right of the Origin , O' it has to be obviously to be at x=5 , but I couldn't 100% sure determine whether to start off with v=-6 or v=6. Using either v=-6 or v=6 I was still able to get the same equation for v^2, which in this case was v^2=x^2+3x-4

It says the particle was initially moving towards the origin, so initially v would be -6, as it started to the right of the origin.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

This might be another silly question but I think of it in terms of Simple harmonic motion formula (from Marlin's formulae book), except with this one, the acceleration keeps increasing since its a straight line. If I treat x=5m, and velocity starting as a negative value, it will eventually approach the Origin, O then increase in velocity and continue increasing after passing the origin (positive v)

 

[rand_althor]

Re: HSC 2015 3U Marathon

Here is a projectile motion question I saw in another forum:



Here's a picture if you're having trouble visualising the scenario:

Edit: I've changed the wording of the question to make it clearer.

 

[braintic]

Re: HSC 2015 3U Marathon

Here is a projectile motion question I saw in another forum:



Here's a picture if you're having trouble visualising the scenario:

Edit: I've changed the wording of the question to make it clearer.

Since alpha MUST equal beta, why not write tan theta = 2 tan alpha ?

 

[Drsoccerball]

Re: HSC 2015 3U Marathon

Since alpha MUST equal beta, why not write tan theta = 2 tan alpha ?

Are you saying that the parabolic path has to intercept at a maximum ?

 

[braintic]

Re: HSC 2015 3U Marathon

Are you saying that the parabolic path has to intercept at a maximum ?

As you said, it's a PARABOLA.
The axis of symmetry is half way between the roots.
That makes the triangle isosceles.

 

[Drsoccerball]

Re: HSC 2015 3U Marathon

As you said, it's a PARABOLA.
The axis of symmetry is half way between the roots.
That makes the triangle isosceles.

Youre assuming that the triangle intersects at a maximum which it doesnt necessarily have to... I proved the result for all values and if you say it intersects at a max you only prove for one value

 

[rand_althor]

Re: HSC 2015 3U Marathon

Since alpha MUST equal beta, why not write tan theta = 2 tan alpha ?

Didn't really consider it as I copied the question.

Youre assuming that the triangle intersects at a maximum which it doesnt necessarily have to... I proved the result for all values and if you say it intersects at a max you only prove for one value

I changed the question so that the triangle does intersect at a maximum.

 

[braintic]

Re: HSC 2015 3U Marathon

Youre assuming that the triangle intersects at a maximum which it doesnt necessarily have to... I proved the result for all values and if you say it intersects at a max you only prove for one value

The question says "AT THE TOP OF ITS MOTION it touches the top vertex of the triangle."

 

[Drsoccerball]

Re: HSC 2015 3U Marathon

The question says "AT THE TOP OF ITS MOTION it touches the top vertex of the triangle."

My bad didn't see that part calculated all of it as if it could be any point waste of a page

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

Induction question, prove the following is a multiple of 10 for all positive integers 'n'.





My question is it important to mention that 'k' is an integer in this question at any stage. Reading alot of other examples I can understand why 'M' is mentioned as an integer in this step.

 

[dan964]

Re: HSC 2015 3U Marathon

Induction question, prove the following is a multiple of 10 for all positive integers 'n'.





My question is it important to mention that 'k' is an integer in this question at any stage. Reading alot of other examples I can understand why 'M' is mentioned as an integer in this step.

1. Firstly David, I wouldn't use the notation, even for 3u, (especially) of S(k+1) or S(k); because that implies a series which this is not. Use "For n=1*" (*or 2 depending on what the first case is), "Assume the formula is true for n=k", "For n=k+1*" (*the next term, not necessary n=k+1)
2. I am not sure if you need to because it is implicit in the initial conditions, that said it wouldn't be wrong.
would be sufficient if you needed to, and really stating in the required to prove statement and/or at the very beginning would be better.

 

[InteGrand]

Re: HSC 2015 3U Marathon

Here is a projectile motion question I saw in another forum:



Here's a picture if you're having trouble visualising the scenario:

Edit: I've changed the wording of the question to make it clearer.

Isn't this just basically a geometry problem? Don't need projectile motion.

 

[Drsoccerball]

Re: HSC 2015 3U Marathon

Isn't this just basically a geometry problem? Don't need projectile motion.

How would you get the "tan's"

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

1. Firstly David, I wouldn't use the notation, even for 3u, (especially) of S(k+1) or S(k); because that implies a series which this is not. Use "For n=1*" (*or 2 depending on what the first case is), "Assume the formula is true for n=k", "For n=k+1*" (*the next term, not necessary n=k+1)
2. I am not sure if you need to because it is implicit in the initial conditions, that said it wouldn't be wrong.
would be sufficient if you needed to, and really stating in the required to prove statement and/or at the very beginning would be better.

1. I've been following the S(k+1), S(k) method from the textbook 'New Senior Mathematics' from Fitzpatrick , Aus and Curran. Here is an example from their text:




2. Secondly, I have never heard of the J set, is there a more specific name for this set of numbers?

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

Here is another one from Fitzpatrick et al text book, which more specifically looks at S(K+1):

 

[Drsoccerball]

Re: HSC 2015 3U Marathon

Cssa 2014 was like that thers nothing wrong