Login

Welcome, Guest. Please login or register.

March 29, 2024, 05:31:25 am

Author Topic: Mathematics Question Thread  (Read 1296828 times)  Share 

0 Members and 1 Guest are viewing this topic.

Happy Physics Land

  • ATAR Notes Legend
  • Forum Obsessive
  • ***
  • Posts: 335
  • MAXIMISE your marks by MINIMISING your errors
  • Respect: +38
Re: Mathematics Question Thread
« Reply #975 on: November 26, 2016, 10:52:10 pm »
0
Bit misleading aye :^)

That aside... Don't ever want to see First Principals again :(  As Rui Said, building blocks

First Principal is Duncan.
True, dont want to see First Principal again :) .
Mathematics: 96
Maths Extension 2: 93
Maths Extension 1: 97
English Advanced: 92
Physics: 95
Chemistry: 92
Engineering Studies: 90
Studies of Religion I: 98

2017 ATAR: 99.70
University of Sydney Civil Engineering and Commerce
University of Sydney Faculty of Civil Engineering Scholar
Student Representatives Council Student Housing Officer
City of Sydney Council Sydney Ambassador
University of Sydney Business School Student Mentor
Entrepreneur, Company of Year Junior Achievements Australia

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #976 on: November 26, 2016, 11:10:01 pm »
+1
dont want to see First Principal again :) .

Differentiation by first principles is revisited in first year math courses  8)

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #977 on: November 26, 2016, 11:19:12 pm »
0
Differentiation by first principles is revisited in first year math courses  8)
It's one of the easier things there though :P

Screw epsilon-delta stuff

Wales

  • MOTM: JUN 2017
  • Forum Leader
  • ****
  • Posts: 516
  • Respect: +91
Re: Mathematics Question Thread
« Reply #978 on: November 26, 2016, 11:29:54 pm »
0

 epsilon-delta stuff

That sounds scary...
Heavy Things :(

feeah

  • Adventurer
  • *
  • Posts: 14
  • Respect: 0
Re: Mathematics Question Thread
« Reply #979 on: November 30, 2016, 03:33:15 pm »
+1
Hi there,
I'm not sure if this the right thread to take this question to, but I'm looking for some advice. I currently do 14 units, including 2 unit mathematics. Math has always come really easily to me, so I'm doing relatively fine in the subject, but I have no motivation to study at all. Math was my second highest-scoring subject last but, but this year I've already messed up my first exam (which weighed 20% of the internal assessments) because I didn't study at all-- I estimate perhaps a 60-75% mark from it. I've been considering dropping math, primarily because I have no motivation to study, but also because of my low mark for the first exam.However, I'm hesitant to do so because I'm certain that if I do put the effort in, I could get really high marks. Additionally, I'm worried about only having 2 extension subjects as my back-ups, as I'm not doing really well in them, and I'm not sure if I'll even want to keep them throughout the year.

Do you think I should drop math right now, which gives me more time to study for my assignments that are due in the next few weeks, or should I wait a while until I'm sure dropping is the best decision?

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #980 on: November 30, 2016, 04:20:17 pm »
+2
Hi there,
I'm not sure if this the right thread to take this question to, but I'm looking for some advice. I currently do 14 units, including 2 unit mathematics. Math has always come really easily to me, so I'm doing relatively fine in the subject, but I have no motivation to study at all. Math was my second highest-scoring subject last but, but this year I've already messed up my first exam (which weighed 20% of the internal assessments) because I didn't study at all-- I estimate perhaps a 60-75% mark from it. I've been considering dropping math, primarily because I have no motivation to study, but also because of my low mark for the first exam.However, I'm hesitant to do so because I'm certain that if I do put the effort in, I could get really high marks. Additionally, I'm worried about only having 2 extension subjects as my back-ups, as I'm not doing really well in them, and I'm not sure if I'll even want to keep them throughout the year.

Do you think I should drop math right now, which gives me more time to study for my assignments that are due in the next few weeks, or should I wait a while until I'm sure dropping is the best decision?

Hey feeah! Definitely the right spot ;D

Normally I would say that if you are lacking motivation for a subject early in the game, and you have the units to spare, then drop. Motivation only becomes harder to find the further through Year 12 you get, and so starting with none might be an indicator that you aren't in a subject that you are passionate about. That said, it doesn't sound like you dislike the subject, more just that you are in a bit of a rut?

My question to you is this; is Math something you enjoy? Is it something that realistically you will work hard to improve in? Yes, it's nice to say you can, but will you with that many units and that much on your plate?

Don't stress too much about results at the end, stress more about whether you have the time to put work into the subject or not I think ;D

If you think you can put the work in, then hang around in my opinion. Especially if you are iffy on your Extension subjects too ;D just try really hard to put some work into it over the holidays!

Thebarman

  • Trendsetter
  • **
  • Posts: 103
  • Gone fishing
  • Respect: +6
Re: Mathematics Question Thread
« Reply #981 on: December 02, 2016, 12:47:19 am »
0
Thank you so much for answering my math questions. You guys have been lifesavers! Would you mind helping me out with another question?
The normal of the parabola x^2 = 18y at (-6,2) cuts the parabola again at Q. Find the coordinates of Q.

Thanks again!

“Before you judge a man, walk a mile in his shoes. After that who cares? He's a mile away and you've got his shoes!”
2017 HSC: Advance English, Mathematics, SORII, Biology, Business Studies, Modern History.
Atar: 92.05

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #982 on: December 02, 2016, 01:45:50 am »
+1
Thank you so much for answering my math questions. You guys have been lifesavers! Would you mind helping me out with another question?
The normal of the parabola x^2 = 18y at (-6,2) cuts the parabola again at Q. Find the coordinates of Q.

Thanks again!

Sure! Let's find the equation of that normal. First we'll differentiate to find the gradient:



So that's the gradient of the tangent though, we want the normal!



So we now have a gradient of the normal, and a point it passes through, we use point-gradient form to find the equation:



So now we have the equation of the normal; that normal meets the parabola again at the point Q. How do we find Q? Well, we find it the same as any other point of intersection, by solving \(2x-3y+18=0\) and \(y=\frac{x^2}{18}\) simultaneously. I'll let you take that, but note it will have two solutions. One of them will be \(x=-6,y=2\), but this is the point we already have for the normal. We want the other solution ;D

I hope that helps! :)

julzzz

  • Adventurer
  • *
  • Posts: 15
  • Respect: 0
Re: Mathematics Question Thread
« Reply #983 on: December 02, 2016, 06:49:50 pm »
+1
hey doing a few questions... any help would be much apreciated!
1. find the volume of the solid formed when the curve y=(x+5)^2 is rotated about the y-axis from y=1 to y=4

2a. differentiate (2x^2+1)/(3x^2-4)
b. hence evaluate (integral from 0 to 1) of x/(3x^2-4)^2 dx
P.s. for question 2 i can do part a but dont know how to do part b.

3. find the exact area bounded by the parabola y=x^2 and the line y=4-x

4. find the area enclosed between the curves y=(root)x and y=x^3

5. for the shaded region find the area and the volume around the x-axis. The region is of x^2=4ay coloured to (0,a)

These are from maths in focus. cheers for ANY help

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #984 on: December 02, 2016, 07:06:19 pm »
0
hey doing a few questions... any help would be much apreciated!
1. find the volume of the solid formed when the curve y=(x+5)^2 is rotated about the y-axis from y=1 to y=4

2a. differentiate (2x^2+1)/(3x^2-4)
b. hence evaluate (integral from 0 to 1) of x/(3x^2-4)^2 dx
P.s. for question 2 i can do part a but dont know how to do part b.

3. find the exact area bounded by the parabola y=x^2 and the line y=4-x

4. find the area enclosed between the curves y=(root)x and y=x^3

5. for the shaded region find the area and the volume around the x-axis. The region is of x^2=4ay coloured to (0,a)

These are from maths in focus. cheers for ANY help
Hints.

1. You're trying to find a volume with respect to the y axis. Hence you need to make x2 the subject, which takes quite a fair bit of rearranging.

2. What is the answer to 2a? Cause it's bound to be necessary for 2b

3. This is a classic area between the curves question. Sketch the curves, figure out which is the upper and lower curve, and integrate (upper - lower)

4. Same as above, but you need to work out the point of intersections first, which are 0 and 1

5. The region is bounded between x^2=4ay and y=a.
So figure out whether you want to integrate with respect to dx, or dy. Then show your progress.
(Note that if you integrate with respect to x you have to consider the area of a rectangle. If you do it w.r.t. y then you don't)
« Last Edit: December 02, 2016, 07:08:51 pm by RuiAce »

J.B

  • Trendsetter
  • **
  • Posts: 123
  • Respect: 0
Re: Mathematics Question Thread
« Reply #985 on: December 03, 2016, 10:33:25 am »
0
Hi, I was wondering if anyone could help me with this question?

The start of the question:

The speed of a train was recorded at intervals of one minute. The times, in minutes, and the corresponding speeds v, in kilometres per hour, are listed in the following table.

And i have attached the second part as a photo.

Thank you.

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #986 on: December 03, 2016, 10:52:33 am »
0
Hi, I was wondering if anyone could help me with this question?

The start of the question:

The speed of a train was recorded at intervals of one minute. The times, in minutes, and the corresponding speeds v, in kilometres per hour, are listed in the following table.

And i have attached the second part as a photo.

Thank you.


It would make sense as to if part (ii) (or later) is a Simpson's rule or Trapezoidal rule computation. Because that table is only barely useful for part (i) but would be very very useful for a part (ii)



_____________________________


Consider this analogy: Suppose the particle starts at x=1. It travels at a constant speed of 15km/hr. Then 1 hour later, it will be at x=16
Hence, the distance travelled is 15.

Now suppose the particle starts at x=-1. It travels at a constant speed of 15km/hr. Then 1 hour later, it will be at x=14
Hence, the distance travelled is STILL 15.

Which is the point. The definite integral allows us to IGNORE any initial conditions, provided we have enough information on the velocity of the particle.

Essentially, what we are doing is integrating the velocity, AND working our way around the initial conditions.

The explanation is hard to juggle without a concrete example (this is just a table of values). I've tried my best but do voice any confusion

J.B

  • Trendsetter
  • **
  • Posts: 123
  • Respect: 0
Re: Mathematics Question Thread
« Reply #987 on: December 03, 2016, 11:32:56 am »
0


It would make sense as to if part (ii) (or later) is a Simpson's rule or Trapezoidal rule computation. Because that table is only barely useful for part (i) but would be very very useful for a part (ii)



_____________________________


Consider this analogy: Suppose the particle starts at x=1. It travels at a constant speed of 15km/hr. Then 1 hour later, it will be at x=16
Hence, the distance travelled is 15.

Now suppose the particle starts at x=-1. It travels at a constant speed of 15km/hr. Then 1 hour later, it will be at x=14
Hence, the distance travelled is STILL 15.

Which is the point. The definite integral allows us to IGNORE any initial conditions, provided we have enough information on the velocity of the particle.

Essentially, what we are doing is integrating the velocity, AND working our way around the initial conditions.

The explanation is hard to juggle without a concrete example (this is just a table of values). I've tried my best but do voice any confusion

Thank you.
I'm still a bit confused. It's probably really stupid, but I don't understand why v=dx/dt. Like I understand that velocity = distance/time. Is this just the same thing? And then I don't understand how you bring the x to the other side.
Sorry this is probably really stupid!

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #988 on: December 03, 2016, 11:35:01 am »
0
Thank you.
I'm still a bit confused. It's probably really stupid, but I don't understand why v=dx/dt. Like I understand that velocity = distance/time. Is this just the same thing? And then I don't understand how you bring the x to the other side.
Sorry this is probably really stupid!
Speed = distance/time, also the absolute value of the velocity

Not sure what you mean by bring x to the other side

J.B

  • Trendsetter
  • **
  • Posts: 123
  • Respect: 0
Re: Mathematics Question Thread
« Reply #989 on: December 03, 2016, 11:37:34 am »
0
Speed = distance/time, also the absolute value of the velocity

Not sure what you mean by bring x to the other side


What topic is it taught in? As I have only done Integration, Exp and Logs, Geometry 2, and Trig Functions?