HSC 2015 MX1 Marathon (archive) (3 Viewers)

[photastic]

Re: HSC 2015 3U Marathon

Hasn't been asked for a while but a pretty standard question.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon



Projectile Motion question confused by part (iii)

tried to use different coordinates
x=3, y=1.8
x=3, y=3.0
x=3, y=8.0

in order to solve this equation. Came out with different values to the one that must be between 50 degrees 41' and 76 degrees 39'

 

[thomasdo1]

Re: HSC 2015 3U Marathon

Projectile Motion question confused by part (iii)

tried to use different coordinates
x=3, y=1.8
x=3, y=3.0
x=3, y=8.0

in order to solve this equation. Came out with different values to the one that must be between 50 degrees 41' and 76 degrees 39'

Do the under the ceiling condition first, you found max height in part i], so let the max height = 8 solve for theta and you will get 76*39' because the angle has to be acute (in first quad), secondly you need it to be over y = 3 when x = 3, therefore let x = 3, y = 3, solve for theta and you will get 84' and 50'41' . 84'19' doesn't work because it will hit the ceiling , try sub it into the max height to check.

So it has to be from 50'41' to 76'39'

extra information: 50'41' hits (3,3) on the way up, 84 hits (3,3) on the way down but hits the ceiling, so getting above (3,3) would be between 50'41' and 84'19' if there wasn't a ceiling.

Hasn't been asked for a while but a pretty standard question.

the answer is n = 10 right?

 

[photastic]

Re: HSC 2015 3U Marathon

the answer is n = 10 right?

Yep, what I hate about these type of questions is using trial and error.

 

[rand_althor]

Re: HSC 2015 3U Marathon

 

[godofindolence]

Re: HSC 2015 3U Marathon

let roots= (a-x), a, (a+x)
sum of roots => 3a = 36/8
a = 3/2

product of roots=> a^3 - ax^2 = -21/8
but since a = 3/2 ; x=2/-2
roots are -1/2, 3/2, 7/2

 

[InteGrand]

Re: HSC 2015 3U Marathon

let roots= (a-x), a, (a+x)
sum of roots => 3a = 36/8
a = 3/2

product of roots=> a^3 - ax^2 = -21/8
but since a = 3/2 ; x=2/-2
roots are -1/2, 3/2, 7/2

Lol avoid the letter x for the difference between the roots (use d or something), since it's the variable in the equation too (it's not that big a deal but maybe some markers wouldn't like it).

 

[rand_althor]

Re: HSC 2015 3U Marathon

 

[godofindolence]

Re: HSC 2015 3U Marathon

http://puu.sh/kUxZc/9389879c8a.JPG

A particle is performing Simple Harmonic Motion in a straight line. In 1 minute of it's motion, it completes exactly 15 oscillations and travels exactly 120 metres. What is the amplitude of the motion?

 

[thomasdo1]

Re: HSC 2015 3U Marathon

EDIT: already been done above, I took too slow

http://puu.sh/kUxZc/9389879c8a.JPG

A particle is performing Simple Harmonic Motion in a straight line. In 1 minute of it's motion, it completes exactly 15 oscillations and travels exactly 120 metres. What is the amplitude of the motion?

Is it a = 2 metres? 120/15*4 = 2

 

[godofindolence]

Re: HSC 2015 3U Marathon

yes!

 

[thomasdo1]

Re: HSC 2015 3U Marathon

A stone is thrown so that it will hit a bird at the top of a pole. However, at the instant the stone is thrown, the bird flies away in a horizontal straight line at a speed of 10 m/s. The stone reaches double the height of the pole and, in its descent touches the bird. Find the horizontal component of the velocity of the stone.

good ol fitzy

 

[InteGrand]

Re: HSC 2015 3U Marathon

A stone is thrown so that it will hit a bird at the top of a pole. However, at the instant the stone is thrown, the bird flies away in a horizontal straight line at a speed of 10 m/s. The stone reaches double the height of the pole and, in its descent touches the bird. Find the horizontal component of the velocity of the stone.

good ol fitzy

Choose the coordinate axes so that the origin is at the vertex of the parabola, with the vertical axis being the axis of symmetry of the parabola (positive direction being downwards) and the horizontal axis being tangential to the parabola.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

This question was from the 1992 HSC Exam paper.


Two questions with this
Q1) Is there a mistake in the solutions? Should the integrated term in part (ii) show nC2 x^3/3?

Q2) Does it matter which side we add the 'C' constant?

 

[InteGrand]

Re: HSC 2015 3U Marathon

This question was from the 1992 HSC Exam paper.


Two questions with this
Q1) Is there a mistake in the solutions? Should the integrated term in part (ii) show nC2 x^3/3?

Q2) Does it matter which side we add the 'C' constant?

Q1) Yes – typo

Q2) No.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

I don't know what Binomial Expansions is used for in applications and real life scenarios but one thing I will say is , it is a process. The more questions you do the more beautiful you see mathematics is. It's like our version of poetry in motion.

 

[photastic]

Re: HSC 2015 3U Marathon

I don't know what Binomial Expansions is used for in applications and real life scenarios but one thing I will say is , it is a process. The more questions you do the more beautiful you see mathematics is. It's like our version of poetry in motion.

The binomial expansion is actually used when distributing IP addresses, economic predictions and infrastructure in engineering and theres many more applications.

 

[Drsoccerball]

Re: HSC 2015 3U Marathon

The binomial expansion is actually used when distributing IP addresses, economic predictions and infrastructure in engineering and theres many more applications.

I don't know what Binomial Expansions is used for in applications and real life scenarios but one thing I will say is , it is a process. The more questions you do the more beautiful you see mathematics is. It's like our version of poetry in motion.

Shouldn't you know this don't you do engineering ?

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

The binomial expansion is actually used when distributing IP addresses, economic predictions and infrastructure in engineering and theres many more applications.

Interesting I might have a look at other online sources. It seems to me that with HSC texts they don't relate it to applications that much. (I don't think i have seen a question so far)

I read this from a website: "Binomial Theorem has also been a great use in the architecture industry in design of infrastructure. It allows engineers, to calculate the magnitudes of the projects and thus delivering accurate estimates of not only the costs but also time required to construct them. For contractors, it is a very important tool to help ensuring the costing projects is competent enough to deliver profits."

I also see that it is used a lot in Physics.

Would be interested to see how numbers of IP addresses are formulated based on the binomial theorem.

 

[InteGrand]

Re: HSC 2015 3U Marathon

I also see that it is used a lot in Physics.

Pretty much everything in maths is used a lot in physics.