Login

Welcome, Guest. Please login or register.

March 29, 2024, 04:58:12 pm

Author Topic: Mathematics Question Thread  (Read 1297060 times)  Share 

0 Members and 4 Guests are viewing this topic.

isaacdelatorre

  • HSC Lecturer
  • Forum Obsessive
  • ***
  • Posts: 303
  • Respect: +74
Re: Mathematics Question Thread
« Reply #555 on: October 17, 2016, 11:30:37 am »
0
Hey guys,

Just a question, regarding rounding.
I know that you shouldn't round any numbers until the last part of the question. But when it says round to 4dp for example, do you continue to use the whole decimal or just 4 decimal places?

E.g. rates of change when finding k - continue to use the whole thing or whatever decimal places they initially say
HSC 2016:   ATAR: 99+
Mathematics - 97    Economics - 96     Legal Studies - 95     Advanced English - 91    Business Studies - 95

2017: B Commerce/B Law @ UNSW  

imtrying

  • Trendsetter
  • **
  • Posts: 115
  • Respect: 0
Re: Mathematics Question Thread
« Reply #556 on: October 17, 2016, 12:02:16 pm »
0
Just needing some help with part ii of this question from the 2011 HSC.
I've done part i, the answer is (n+1)1/2 - n1/2.
Year 12 2016 (94.20)
English (Adv), Maths Ext.1, Modern History, Biology and Physics

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #557 on: October 17, 2016, 12:13:15 pm »
0
Hey guys,

Just a question, regarding rounding.
I know that you shouldn't round any numbers until the last part of the question. But when it says round to 4dp for example, do you continue to use the whole decimal or just 4 decimal places?

E.g. rates of change when finding k - continue to use the whole thing or whatever decimal places they initially say

Hey Isaac! If they say find to 4dp, and then the question continues, you can use that value!! :) but they would probably pay either or ;D

jakesilove

  • HSC Lecturer
  • Honorary Moderator
  • Part of the furniture
  • *******
  • Posts: 1941
  • "Synergising your ATAR potential"
  • Respect: +196
Mathematics Question Thread
« Reply #558 on: October 17, 2016, 12:53:19 pm »
0
Just needing some help with part ii of this question from the 2011 HSC.
I've done part i, the answer is (n+1)1/2 - n1/2.

Hey! Cool question, check out my solution below and let me know if I can clarify anything!



Jake

Annotation by Rui: In case his first line wasn't clear, Jake rationalised the denominator
       Annotation by Jake of Annotation by Rui: Cheers buddy
« Last Edit: October 17, 2016, 01:52:43 pm by jakesilove »
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

imtrying

  • Trendsetter
  • **
  • Posts: 115
  • Respect: 0
Re: Mathematics Question Thread
« Reply #559 on: October 17, 2016, 01:49:22 pm »
0
Hey! Cool question, check out my solution below and let me know if I can clarify anything!

(Image removed from quote.)

Jake

Annotation by Rui: In case his first line wasn't clear, Jake rationalised the denominator
Thanks so much! :)
Year 12 2016 (94.20)
English (Adv), Maths Ext.1, Modern History, Biology and Physics

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #560 on: October 17, 2016, 03:37:18 pm »
0
Hello, I'm not sure if this question has been answered before and I know it's been talked about in one of the ATARNotes Maths lectures but are we still allowed to use abbreviations in the reasonings (e.g. isosceles Δ abbreviated to isos.Δ / supplementary to supp.)? A friend of mine said that this year, we wouldn't be allowed to use them and I'm just a little confused.

Sorry cajama I missed this! Why does your friend say specifically this year? What do they think has changed? That's the curious bit to me :)

In general, you want to make your work as readable for the marker as is humanly possible. I am reasonably sure that abbreviations are fine, and that they would pay you for those that you've provided, but I was always hesitant to use them. Not because they wouldn't recognise them and not pay you for it intentionally, but more along Rui's line of thinking. It's about clarity and formality of proof, and basically, I wanted to take no chances that what I'd written had been misinterpreted.

My thinking is this. The BOSTES sample solutions don't use those abbreviations, so if you want to be 100% sure that you are okay, then take the 1 second to write the full word. Of course, symbols like Δ and // are universal and definitely acceptable :)

jakesilove

  • HSC Lecturer
  • Honorary Moderator
  • Part of the furniture
  • *******
  • Posts: 1941
  • "Synergising your ATAR potential"
  • Respect: +196
Re: Mathematics Question Thread
« Reply #561 on: October 17, 2016, 03:47:06 pm »
0
Sorry cajama I missed this! Why does your friend say specifically this year? What do they think has changed? That's the curious bit to me :)

In general, you want to make your work as readable for the marker as is humanly possible. I am reasonably sure that abbreviations are fine, and that they would pay you for those that you've provided, but I was always hesitant to use them. Not because they wouldn't recognise them and not pay you for it intentionally, but more along Rui's line of thinking. It's about clarity and formality of proof, and basically, I wanted to take no chances that what I'd written had been misinterpreted.

My thinking is this. The BOSTES sample solutions don't use those abbreviations, so if you want to be 100% sure that you are okay, then take the 1 second to write the full word. Of course, symbols like Δ and // are universal and definitely acceptable :)

I definitely used abbreviations for anything that was absolutely obvious (alt. angles on || are =, for instance), however if I thought there was a chance of confusion I would avoid abbreviations all together. I wouldn't say this makes much of a difference though!
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

olivercutbill

  • Forum Regular
  • **
  • Posts: 61
  • Monetary Policy is... an art not a science
  • Respect: +1
Re: Mathematics Question Thread
« Reply #562 on: October 17, 2016, 04:43:53 pm »
0
I've seen questions like this before but they've given a time constraint. How do I do 12?
2016 ATAR: 93.05

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #563 on: October 17, 2016, 05:01:18 pm »
0
I've seen questions like this before but they've given a time constraint. How do I do 12?

Are you an Extension student Oliver? Because I think this has strayed into that territory of difficulty :P

So we have this expression for cost in terms of speed, per hour:

$$c=150+\frac{v^2}{80}$$

What we want is the total cost for a 500km trip. To find how long THIS takes, we use our speed formula:

$$\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\v=\frac{500}{t}\\\therefore t=\frac{500}{v}$$

So our trip takes that many hours. To find our total cost, we multiply the cost per hour by the amount of hours taken that we just found.

$$C_\text{Total}=ct=\frac{500}{v}\left(50+\frac{v^2}{80}\right)$$

And now we're back to familiar territory, differentiate and find your minima! Does that help? :)

olivercutbill

  • Forum Regular
  • **
  • Posts: 61
  • Monetary Policy is... an art not a science
  • Respect: +1
Re: Mathematics Question Thread
« Reply #564 on: October 17, 2016, 05:45:32 pm »
0
Are you an Extension student Oliver? Because I think this has strayed into that territory of difficulty :P

So we have this expression for cost in terms of speed, per hour:

$$c=150+\frac{v^2}{80}$$

What we want is the total cost for a 500km trip. To find how long THIS takes, we use our speed formula:

$$\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\v=\frac{500}{t}\\\therefore t=\frac{500}{v}$$

So our trip takes that many hours. To find our total cost, we multiply the cost per hour by the amount of hours taken that we just found.

$$C_\text{Total}=ct=\frac{500}{v}\left(50+\frac{v^2}{80}\right)$$

And now we're back to familiar territory, differentiate and find your minima! Does that help? :)

No 2u, this was in the textbook :)

I get 63km/h as a minimum - textbook answer says 110km/h.

What am I doing wrong?
2016 ATAR: 93.05

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #565 on: October 17, 2016, 05:51:04 pm »
0
No 2u, this was in the textbook :)

I get 63km/h as a minimum - textbook answer says 110km/h.

What am I doing wrong?

Oh I mean like, it's strayed into that level of difficulty, definitely 2U content. I mean like, don't stress that it's hard for you, because it is a hard question, aha ;D

Snap a picture of your working? I'll see if I can spot ;D

olivercutbill

  • Forum Regular
  • **
  • Posts: 61
  • Monetary Policy is... an art not a science
  • Respect: +1
Re: Mathematics Question Thread
« Reply #566 on: October 17, 2016, 06:25:28 pm »
0
Oh I mean like, it's strayed into that level of difficulty, definitely 2U content. I mean like, don't stress that it's hard for you, because it is a hard question, aha ;D

Snap a picture of your working? I'll see if I can spot ;D

Figured it out, and did another similar question and got that too.

Thanks :)
2016 ATAR: 93.05

Rikahs

  • Forum Regular
  • **
  • Posts: 56
  • Respect: 0
Re: Mathematics Question Thread
« Reply #567 on: October 17, 2016, 07:37:01 pm »
0
Does anyone know how to answer the attached question (all parts please). Im super confused :(
Adv Eng
Mathematics
Mathematics Ext 1
Business Stds
Chemistry
Physics

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 #568 on: October 17, 2016, 07:54:44 pm »
0
Does anyone know how to answer the attached question (all parts please). Im super confused :(
Part (iii) was already addressed in post #533





_________________________________






_______


nibblez16

  • Forum Regular
  • **
  • Posts: 75
  • Respect: 0
  • School: Liverpool Girls
  • School Grad Year: 2016
Re: Mathematics Question Thread
« Reply #569 on: October 17, 2016, 09:59:50 pm »
0
Hello, can you please explain the last question... I always get confused on those types... Thanks :)