HSC 2015 MX1 Marathon (archive) (3 Viewers)

[psyc1011]

Re: HSC 2015 3U Marathon

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

http://www.algebra.com/algebra/homework/real-numbers/Set-of-Real-Numbers.lesson

I don't think Dan is correct on using that font for the letter J, I think it should be Z for the set of integers (+ve and -ve)

 

[psyc1011]

Re: HSC 2015 3U Marathon

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

yeah, did you construct an isosceles triangle with base angles theta?

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

No you didnt understand what i was trying to say... You expanded the trig expression and the integrated it after instead you should first let u =sinx so the expansion is easier and the substitution is also easier.

I've been thinking more about this question since and you can do it your way by substituting u and integrating from there. Personally, like Kinney-Lewis method and I understood it step by step.

This is how he does one of his examples:

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

I think with this question you need to understand part (i) and understand how it is interlinked.

 

[dan964]

Re: HSC 2015 3U Marathon

http://www.algebra.com/algebra/homework/real-numbers/Set-of-Real-Numbers.lesson

I don't think Dan is correct on using that font for the letter J, I think it should be Z for the set of integers (+ve and -ve)

Its either, although I think J is the actual notation, but yes, double-stroked Z would be better. I have just seen J used a lot. (latex is playing up)

I would still advise against using S(k) for non-series questions, because that is what the notation implies.
(and I don't speak highly of the worked examples in Fitzpatrick, especially the new version)

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

Its either, although I think J is the proper notation, but yes, double-stroked Z would be better. I have just seen J used a lot.

Thanks for showing me that, Seen Z, Z+, Z- ....but never seen J set until this week.

 

[dan964]

Re: HSC 2015 3U Marathon

Thanks for showing me that, Seen Z, Z+, Z- ....but never seen J set until this week.

I suspect it is an older notation. But yeah Z is the best one to use.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

This question is from the Caringbah 2015 trials:



Their answer they have in their solution as A, which I understand but is it technically wrong in their solution as they do not have the '+C' constant there?

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

I've only heard of the name Caringbah, I am going to 'Google Map' where it is now.

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

Cool I didn't realise it was South East of Sydney (near Cronulla). You learn something new everyday.

 

[leehuan]

Re: HSC 2015 3U Marathon

It should have a +C. I've seen many faulty papers where they forget +C in multiple choice though.
---------------------------------------------------------------------

 

[Drsoccerball]

Re: HSC 2015 3U Marathon

It should have a +C. I've seen many faulty papers where they forget +C in multiple choice though.
---------------------------------------------------------------------

 

[braintic]

Re: HSC 2015 3U Marathon

It should have a +C. I've seen many faulty papers where they forget +C in multiple choice though.

If not having a +c is "faulty", then the table of standard integrals on the back of every HSC exam is also "faulty".

 

[asdfghjklqwerty]

Re: HSC 2015 3U Marathon

i need help with part b please. thanks

A stone is projected with a velocity of 30m/s from a point at the foot of an inclined plane making an angle of 30 degrees to the horizontal. The path of the projectile can be assumed to be in the vertical plane containing the line of the greatest slope of the inclined plane. If the angle of projection alpha > 30 degreees, for what values of alpha will the stone strike the inclined plane:
a) horizontally (answer 49 degrees 6 mins)
b) at right angles (answer 70 degrees 54 mins)

g = 10m/s^2

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

Caringbah 2015 trials, I had no idea on how to kick start this one. Someone give me an idea on part (i).

 

[asdfghjklqwerty]

Re: HSC 2015 3U Marathon

is the answer 12pi cm?
if so then what i did was
AYB=rtheta
=r x pi/3
since BC=r=12cm
AYB=4pi
P=AYB X 3 =12pi cm

 

[dan964]

Re: HSC 2015 3U Marathon

Caringbah 2015 trials, I had no idea on how to kick start this one. Someone give me an idea on part (i).

Noting that Z, Y, X are identical lengths (equal arcs on equal angles of 60).

A is the centre of the circle which the arc BC lies on. Hence the radius of the circle is 12 cm
Similarly for the radius of the circle with centres B and C.
Hence:
X = 12 * pi/3
and similarly for Y and Z
thus P is
12 pi cm

so yes asdfghjkljqwerty (very original username) is right.

Do you need help with part ii?

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

I'll have a think about part (ii) but yes the answer was 12 pi for part (i)

 

[davidgoes4wce]

Re: HSC 2015 3U Marathon

Noting that Z, Y, X are identical lengths (equal arcs on equal angles of 60).

A is the centre of the circle which the arc BC lies on. Hence the radius of the circle is 12 cm
Similarly for the radius of the circle with centres B and C.
Hence:
X = 12 * pi/3
and similarly for Y and Z
thus P is
12 pi cm

so yes asdfghjkljqwerty (very original username) is right.

Do you need help with part ii?

I think I may have just been having a long day, and my head was not seeing things clearly. Yes, l=r x theta is the formula to use for this one.

 

[rand_althor]

Re: HSC 2015 3U Marathon

Using the Binomial Theorem, prove that 7ⁿ+2 is divisible by 3, where n is a positive integer.