Login

Welcome, Guest. Please login or register.

March 29, 2024, 05:35:05 am

Author Topic: 3U Maths Question Thread  (Read 1230348 times)  Share 

0 Members and 1 Guest are viewing this topic.

jakesilove

  • HSC Lecturer
  • Honorary Moderator
  • Part of the furniture
  • *******
  • Posts: 1941
  • "Synergising your ATAR potential"
  • Respect: +196
Re: 3U Maths Question Thread
« Reply #285 on: July 09, 2016, 07:52:11 pm »
+1
A friend of mine needed help with this question:

1. a. Consider the function f(x)=e^x/(1+e^x). Find f'(x) and deduce that f(x) is increasing for all x
b. State the range of f(x)
c. Find the inverse function f^-1(x)
d. Draw y-f(x) and y=f^-1(x) on the same diagram

Hey!

My solution is below




Jake
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #286 on: July 09, 2016, 08:15:51 pm »
0

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #287 on: July 09, 2016, 09:23:09 pm »
+1
A friend of mine needed help with this question:

1. a. Consider the function f(x)=e^x/(1+e^x). Find f'(x) and deduce that f(x) is increasing for all x
b. State the range of f(x)
c. Find the inverse function f^-1(x)
d. Draw y-f(x) and y=f^-1(x) on the same diagram


________________________





________________________
I have no further input for part c) - it could not be any simpler :)
________________________

« Last Edit: July 09, 2016, 09:46:03 pm by RuiAce »

IkeaandOfficeworks

  • Adventurer
  • *
  • Posts: 22
  • Respect: 0
  • School: All Saints Senior College
  • School Grad Year: 2016
Re: 3U Maths Question Thread
« Reply #288 on: July 09, 2016, 09:30:48 pm »
0
Hi Guys! Im having problems with this question:

The perimeter of a circular sector is 20 cm. The radius is increasing at the rate of 5cm/s . At what rate is the angle of the sector changing when the radius length is 10 cm? Also at what rate is the area changing when the radius length is 10 cm.

Thanks guys!

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #289 on: July 09, 2016, 09:36:28 pm »
+1
Hi Guys! Im having problems with this question:

The perimeter of a circular sector is 20 cm. The radius is increasing at the rate of 5cm/s . At what rate is the angle of the sector changing when the radius length is 10 cm? Also at what rate is the area changing when the radius length is 10 cm.

Thanks guys!





_________________________

« Last Edit: July 09, 2016, 09:39:29 pm by RuiAce »

jakesilove

  • HSC Lecturer
  • Honorary Moderator
  • Part of the furniture
  • *******
  • Posts: 1941
  • "Synergising your ATAR potential"
  • Respect: +196
Re: 3U Maths Question Thread
« Reply #290 on: July 10, 2016, 10:39:31 am »
+1
Just in case anyone's interested feel free  to try out this question

1. a. SKetch f(x)=(e^x)-4, showing clearly the points of intersection with the axes and the equations of any asymptotes
b. On the same diagram, sketch the graph of the inverse function f^-1(x), showing clearly any important features
c. Explain why the x-coordinate of any points of the intersection y=f(x) and y=f^-1(x) satisfies e^x - x - 4=0
d. Show the equation e^x - x - 4 =0 between x=0 and x=2 and use the method of 'halving by intervals' to find this root correct to the nearest whole number

Also anyone here wishing to try a few challenge circle geometry questions feel free to

If you're looking to post challenge questions, just for your own and our edification, you can find the challenge question thread here. If you actually need help with these questions, because you're not sure how to do them, then this is the place to post them; but no point posting them here just because they are 'hard'.

Happy to write up a solution, if you want one :)

Jake

EDIT BY JAMON: Moved these quoted questions to a more appropriate location  ;D
« Last Edit: July 10, 2016, 04:43:06 pm by jamonwindeyer »
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #291 on: July 10, 2016, 10:42:59 am »
0
If you're looking to post challenge questions, just for your own and our edification, you can find the challenge question thread here. If you actually need help with these questions, because you're not sure how to do them, then this is the place to post them; but no point posting them here just because they are 'hard'.

Happy to write up a solution, if you want one :)

Jake

Oh whoops, my bad ahaha but what if they're not "hard" in that sense but you still want to test someone?

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #292 on: July 10, 2016, 10:44:12 am »
+1
Oh whoops, my bad ahaha but what if they're not "hard" in that sense but you still want to test someone?
Please reserve this thread for SOS pleas, not for tests.

Not sure how obvious it actually was but to me it was very clear that you just took the circle geometry questions straight out of maths in focus.
« Last Edit: July 10, 2016, 10:47:24 am by RuiAce »

jakesilove

  • HSC Lecturer
  • Honorary Moderator
  • Part of the furniture
  • *******
  • Posts: 1941
  • "Synergising your ATAR potential"
  • Respect: +196
Re: 3U Maths Question Thread
« Reply #293 on: July 10, 2016, 10:45:14 am »
+1
Oh whoops, my bad ahaha but what if they're not "hard" in that sense but you still want to test someone?

If you want us to answer a question that you can't, because you need help, post them here. This thread is to help you feel more comfortable with Extension 1, to be better equipped walking into your exam. We have a lot of questions we need to answer. If there are questions you're just interested in, rather than actually need help with, then that's great! We just need to prioritize questions people are struggling with. So, if you're interested, post it in another thread. If you need help, post it here. Easy as that! 
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #294 on: July 10, 2016, 10:59:04 am »
0
Please reserve this thread for SOS pleas, not for tests.

Not sure how obvious it actually was but to me it was very clear that you just took the circle geometry questions straight out of maths in focus.

What is SOS? SO for tests I put it in the challenge thread

Yes it was from MIF but I had to crop the image

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #295 on: July 10, 2016, 11:00:26 am »
+1
What is SOS? SO for tests I put it in the challenge thread

Yes it was from MIF but I had to crop the image
Save our souls

In other words a plea for help.

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #296 on: July 10, 2016, 11:03:11 am »
0
Save our souls

In other words a plea for help.

Oh, okay  :D

humble mango

  • Adventurer
  • *
  • Posts: 5
  • Respect: 0
  • School Grad Year: 2017
Re: 3U Maths Question Thread
« Reply #297 on: July 13, 2016, 08:01:05 pm »
0
Hi! This is a very generic question compared to the others, but I'm doing Prelims next term, and i was wondering for all exams (HSC Trials,Prelims) involving 3D trigonometry, are diagrams always given?? I have done a lot of practice questions involving them but there are certain ones without diagrams and require you to draw them, and i really struggle at drawing the correct diagram whilst being crammed with tons of info on bearings, numbers and letters.

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #298 on: July 13, 2016, 08:15:10 pm »
+1
Hi! This is a very generic question compared to the others, but I'm doing Prelims next term, and i was wondering for all exams (HSC Trials,Prelims) involving 3D trigonometry, are diagrams always given?? I have done a lot of practice questions involving them but there are certain ones without diagrams and require you to draw them, and i really struggle at drawing the correct diagram whilst being crammed with tons of info on bearings, numbers and letters.
Generally, yes.

You don't know for sure ever, but every paper I've seen has given you the diagram for 3D trig.

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: 3U Maths Question Thread
« Reply #299 on: July 13, 2016, 11:55:50 pm »
+1
Hi! This is a very generic question compared to the others, but I'm doing Prelims next term, and i was wondering for all exams (HSC Trials,Prelims) involving 3D trigonometry, are diagrams always given?? I have done a lot of practice questions involving them but there are certain ones without diagrams and require you to draw them, and i really struggle at drawing the correct diagram whilst being crammed with tons of info on bearings, numbers and letters.

Hey there humble mango!! Aha Rui is right, although I have seen one question with it in a weird Trial, I remember thinking "wtf" when I saw it back in 2014  ;D but you are pretty safe I reckon!

Some tips on the diagram in case it does pop up; underline all the angles and data you are given and make sure that all of it goes in, don't miss anything, that's a good start. Besides that, draw the diagram in pieces, adding information piece at a time and crossing off as you go. Draw in pencil and fix mistakes. Or, alternatively, scribble a draft to make sure everything fits together nicely before the final version. Finally, take your time! The diagram is crucial for understanding and interpreting the question, best to spend some time to get it right  ;D