3 Unit Maths HSC Exam Revision (1 Viewer)

[random-1005]

Title is self explainatory, got any interesting/good questions (3 unit and harder 2unit) post them up here. When you answer a question put another one back up.

FIRST QUESTION:

Find the exact value of tan ( arcsin(5/13) -arccos ( 3/5) )

 

[Pwnage101]

[Although i haven't answered any question, i thought i might add a question before i forget. It is technically MX1, but i'd classify it as 'Harder MX1' under MX2. It is a challenging question. Work at it and have a go!]

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

I'll give you the numerical approximate answer: 12.1 metres per second. Now can anyone provide a full set of solutions, with the exact answer? Remember to define notation, etc.

 

[random-1005]

[Although i haven't answered any question, i thought i might add a question before i forget. It is technically MX1, but i'd classify it as 'Harder MX1' under MX2. It is a challenging question. Work at it and have a go!]

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

I'll give you the numerical approximate answer: 12.1 metres per second. Now can anyone provide a full set of solutions, with the exact answer? Remember to define notation, etc.

that is hard, i give up lol

 

[kcqn93]

[Although i haven't answered any question, i thought i might add a question before i forget. It is technically MX1, but i'd classify it as 'Harder MX1' under MX2. It is a challenging question. Work at it and have a go!]

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

I'll give you the numerical approximate answer: 12.1 metres per second. Now can anyone provide a full set of solutions, with the exact answer? Remember to define notation, etc.

LOL fitzpatrick, projectile motion chapter, question 17, i believe there are answers lying around on BoS somewhere

 

[hscishard]

Hey quick question.
Do you guys do all the questions in fitz? Or do you leave some out, because it's too easy/hard.

 

[bouncing]

LOL fitzpatrick, projectile motion chapter, question 17, i believe there are answers lying around on BoS somewhere

yeah :L i was about to say haha

lets not do that question - waste of time

How many arrangements of the letters of the word PARRAMATTA are possible?
(i just opened fitz 3u to a random page haha)

 

[hscishard]

37800

 

[random-1005]

yeah :L i was about to say haha

lets not do that question - waste of time

How many arrangements of the letters of the word PARRAMATTA are possible?
(i just opened fitz 3u to a random page haha)

lol, hope you get that kind of question in your exam, they are about the only perm/combs questions i got right

10! / (4!2!2!)

 

[bouncing]

lol, hope you get that kind of question in your exam, they are about the only perm/combs questions i got right

10! / (4!2!2!)

haha yeah

post a question?

@ hscishard are you learning ahead or has your school just taught it? :\



A particle is projected to just clear 2 walls of height 7m and distant 7m and 14m from the point of projection. Prove that if alpha is the angle of projection, then tan alpha = 3/2

Prove that if the walls are h metres high and distance b metres and c metres from the point of projection, then tan alpha = h(b+c)/bc

* i actually need help with that question haha

 

[Carrotsticks]

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

Why would you say that it just 'touches' the bird?

Why can't you just say that it smashes the absolute crap out of it?

Just sayin'.

 

[hscishard]

haha yeah

post a question?

@ hscishard are you learning ahead or has your school just taught it? :\



A particle is projected to just clear 2 walls of height 7m and distant 7m and 14m from the point of projection. Prove that if alpha is the angle of projection, then tan alpha = 3/2

Prove that if the walls are h metres high and distance b metres and c metres from the point of projection, then tan alpha = h(b+c)/bc

* i actually need help with that question haha

Interesting question.

Drawing this gives a parabola.
when x =7, y = 7
when x = 14, y =7
when x = 0, y=0

Simulatenous equations of y=ax^2+bx+c
c=0
49a+7b=7
194a+14b=7

Simulatenously solve, you will get a = -1/14 and b = 21/14 = 3/2
y=-1/14x^2 + 3/2x
Differentiating, y' -1/7x + 3/2
When x = 0, y' = 3/2

Tan(alpha) = 3/2. Which is the angle of projection, I think it's a tangent to the parabola at 0,0. If that is true, this proof should be correct.

 

[hscishard]

Yea I went ahead.

 

[random-1005]

Prove by induction that 9^(n+2) -4^(n) is divisable by 5 for all positive integers n .
​

 

[random-1005]

ANOTHER QUESTION : In a few short sentences explain the theory behind newton's method, derive the newton's method formula and give the cases where the method will fail to produce a better approximation. (im not sure if derivation of newtons method is in sylabbus (i know i spelt it wrong ), who knows whats in the sylabbus, ah its good fun anyway).



Also note that the inverse trig question at the start hasnt been answered yet !!

Another thing to consider, practically every question i am putting up i am making up on the spot, you would probably never see a question worded like this in the hsc, i just make them this way to do short tests of knowledge, i will like never put up really lengthy Q6 or Q7 questions.

 

[undalay]

[Although i haven't answered any question, i thought i might add a question before i forget. It is technically MX1, but i'd classify it as 'Harder MX1' under MX2. It is a challenging question. Work at it and have a go!]

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

I'll give you the numerical approximate answer: 12.1 metres per second. Now can anyone provide a full set of solutions, with the exact answer? Remember to define notation, etc.

Displacement of stone = Displacement of bird
Vt = 10t + X, where X = initial displacement of bird.

V = 10 + X/t

t is a function of max height (which is 2x pole height).

Thus velocity is a function of pole height, and initial displacement.

E.g. If you have initial distance of pole from thrower to be 1000 km, and pole height to be 1m, you'll need a REALLY high x-velocity to hit that bird. (much more than 12.1 m /s)

TLR;
There is no unique solution

 

[bouncing]

Title is self explainatory, got any interesting/good questions (3 unit and harder 2unit) post them up here. When you answer a question put another one back up.

FIRST QUESTION:

Find the exact value of tan ( arcsin(5/13) -arccos ( 3/5) )

what does arc mean?

 

[random-1005]

what does arc mean?

inverse ( to minus one), common notation on the net

 

[hscishard]

-33/56?

 

[random-1005]

-33/56?

nup, did u make a typo ??

 

[hscishard]

-16/63