Login

Welcome, Guest. Please login or register.

March 29, 2024, 04:39:46 pm

Author Topic: QCE General Maths Questions Thread  (Read 13364 times)

0 Members and 1 Guest are viewing this topic.

RuiAce

  • ATAR Notes Lecturer
  • Moderator
  • Great Wonder of ATAR Notes
  • *****
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
QCE General Maths Questions Thread
« on: February 20, 2019, 06:11:09 pm »
+5
QCE GENERAL MATHS Q&A THREAD

What is this thread for?
If you have general questions about the QCE General Maths course (both Units 1&2 and 3&4) or how to improve in certain areas, this is the place to ask! 👌


Who can/will answer questions?
Everyone is welcome to contribute; even if you're unsure of yourself, providing different perspectives is incredibly valuable.

Please don't be dissuaded by the fact that you haven't finished Year 12, or didn't score as highly as others, or your advice contradicts something else you've seen on this thread, or whatever; none of this disqualifies you from helping others. And if you're worried you do have some sort of misconception, put it out there and someone else can clarify and modify your understanding! 

There'll be a whole bunch of other high-scoring students with their own wealths of wisdom to share with you, so you may even get multiple answers from different people offering their insights - very cool.


To ask a question or make a post, you will first need an ATAR Notes account. You probably already have one, but if you don't, it takes about four seconds to sign up - and completely free!

s110820

  • MOTM: April 20
  • QCE Moderator
  • Forum Obsessive
  • *****
  • Posts: 304
  • you'll be everything to the right someone
  • Respect: +151
Re: QCE General Maths Questions Thread
« Reply #1 on: May 14, 2020, 11:42:45 am »
0
Hi ATAR Notes community,

I was just wondering if anyone has any advice on how to memorise formulas for maths? I'm just worried that I'm going to forget about the ones that are not on the formula sheet.

Thank you so much and have a great week!

Darcy Dillon.
QUT 2021 - Bachelor of Education (Primary).

Bri MT

  • VIC MVP - 2018
  • Administrator
  • ATAR Notes Legend
  • *****
  • Posts: 4719
  • invest in wellbeing so it can invest in you
  • Respect: +3677
Re: QCE General Maths Questions Thread
« Reply #2 on: May 19, 2020, 11:30:58 am »
0
Hi ATAR Notes community,

I was just wondering if anyone has any advice on how to memorise formulas for maths? I'm just worried that I'm going to forget about the ones that are not on the formula sheet.

Thank you so much and have a great week!

Darcy Dillon.

Hey!

I find that making an effort to understand the formulas and what each part of it does really helps with this :)

hope this helps

s110820

  • MOTM: April 20
  • QCE Moderator
  • Forum Obsessive
  • *****
  • Posts: 304
  • you'll be everything to the right someone
  • Respect: +151
Re: QCE General Maths Questions Thread
« Reply #3 on: May 19, 2020, 11:49:17 am »
+1
Thanks so much, Bri! I really appreciated your help :)
QUT 2021 - Bachelor of Education (Primary).

Luke_8064

  • Trailblazer
  • *
  • Posts: 49
  • Respect: +12
Re: QCE General Maths Questions Thread
« Reply #4 on: July 25, 2020, 08:37:38 am »
0
I was wondering if someone could help me with two questions I am currently stuck on. Please find them in the two attached images.

Note: I have attempted question 1, I think I got roughly 57 km and just want to see what is right and question 2 my teacher roughly went over, but not directly so the solution is kind of hazy.

Thanks for the help,
Luke

QCE Class of 2021: Design | Digital Solutions | English | ICT | General Maths | Psychology

Luke_8064

  • Trailblazer
  • *
  • Posts: 49
  • Respect: +12
Re: QCE General Maths Questions Thread
« Reply #5 on: January 06, 2021, 10:20:38 am »
0
Hey,

I was just wondering if someone could help me with a couple of math problems that I have.

Number 1. A person of height 179 cm weighs 82 kg. If the regression equation is used to predict
their weight, weight = −96 + 0.95 × height, with r = 0.79, then the residual will be closest to...
For this I got 8 kg but my textbook is saying it is -3 kg.

Number 2. The rungs of a ladder diminish uniformly in length from 30 cm at the bottom of the
ladder to 22.5 cm at the top of the ladder. There are 16 rungs altogether. The length, in
centimetres, of the 10th rung up the ladder is...
I am pretty sure it is easier to calculate this with an arithmetic series than a sequence, but I am curious if/how it can be done through an arithmetic sequence formula.

Thanks in advanced ;D
Luke
QCE Class of 2021: Design | Digital Solutions | English | ICT | General Maths | Psychology

keltingmeith

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 5493
  • he/him - they is also fine
  • Respect: +1292
Re: QCE General Maths Questions Thread
« Reply #6 on: January 06, 2021, 02:00:03 pm »
+1
Hey,

I was just wondering if someone could help me with a couple of math problems that I have.

Number 1. A person of height 179 cm weighs 82 kg. If the regression equation is used to predict
their weight, weight = −96 + 0.95 × height, with r = 0.79, then the residual will be closest to...
For this I got 8 kg but my textbook is saying it is -3 kg.

Number 2. The rungs of a ladder diminish uniformly in length from 30 cm at the bottom of the
ladder to 22.5 cm at the top of the ladder. There are 16 rungs altogether. The length, in
centimetres, of the 10th rung up the ladder is...
I am pretty sure it is easier to calculate this with an arithmetic series than a sequence, but I am curious if/how it can be done through an arithmetic sequence formula.

Thanks in advanced ;D
Luke

Residual=difference between predicted y-value and actual y-value. At a quick glance, it looks like you calculated the residual for height - since the question is about predicting weight from height, you should calculate the residual for weight. (I also feel like they got the answer wrong, or they're using some weird formula I've never seen before)

I mean - the arithmetic series formula is just a special application of the arithmetic sequence formula - it's what you get when you add up the arithmetic sequence formula from your starting number up to n times. So they're not that different, really. Anyway, one approach could be to calculate the series up to 10 then subtract the same series up to 9, as you've suggested. I would instead suggest the following formula:

\[
a_n = a_1 + (n-1)d
\]

This formula predicts what the nth number in an arithmetic sequence will be. So, we're interested in the 10th rung - but we decrease instead of increase, so you need to remember to put a negative d, and we'll end up with:

\[
a_{10}=30+(10-1)(-0.5)=30-4.5=25.5
\]

Luke_8064

  • Trailblazer
  • *
  • Posts: 49
  • Respect: +12
Re: QCE General Maths Questions Thread
« Reply #7 on: January 30, 2021, 08:29:41 am »
0
Hey ATARNotes Community,

Could someone help me with the question below.

In the following, each pair of locations lie on the same latitude. Find the approximate
shortest distance between them travelling along the small circle.
X (158°15′E, 40°45′N), Y(26°45′E, 40°45′N)

This is what I have done so far and I am not sure where I am going wrong. First, I changed the latitude and longitude to their respective angle measurements, which I got as 40.75oN, 158.25oE, 26.75oE.

Then I calculated the distance with the following formula:
\[
D = 111.2cos() * Angular Distance
\]

Which resulted in:

\[
D = 111.2cos(40.75) * (158.25 - 26.75)
\]
\[
D = 11077.72 km
\]
However, my textbook is saying the answer is 9898 km and I can't figure out how they came to it. Any help will be greatly appreciated.

Kind regards,
Luke
QCE Class of 2021: Design | Digital Solutions | English | ICT | General Maths | Psychology

Luke_8064

  • Trailblazer
  • *
  • Posts: 49
  • Respect: +12
Re: QCE General Maths Questions Thread
« Reply #8 on: August 03, 2021, 02:12:07 pm »
0
Hey all,

I was just wondering if someone could do this question for me because I don't understand what it is asking me to find. Plus, I have never come across a question like this before.

The answer is D btw

Thanks in advanced,
Luke
« Last Edit: August 03, 2021, 02:15:47 pm by Luke_8064 »
QCE Class of 2021: Design | Digital Solutions | English | ICT | General Maths | Psychology

fun_jirachi

  • MOTM: AUG 18
  • HSC Moderator
  • Part of the furniture
  • *****
  • Posts: 1068
  • All doom and Gloom.
  • Respect: +710
Re: QCE General Maths Questions Thread
« Reply #9 on: August 03, 2021, 03:32:55 pm »
+1
The question doesn't tell you how often the rate compounds, etc. The only thing you actually know is that every month you pay $1485, for twenty years, which means you make 240 payments of 1485 for a total of 356400. It's also a safe assumption that the starting value will compound to become larger than all the options listed (unless there's been a mistake somewhere, which there isn't).

Hope this helps :)
« Last Edit: August 05, 2021, 10:00:45 am by fun_jirachi »
Spoiler
HSC 2018: Mod Hist [88] | 2U Maths [98]
HSC 2019: Physics [92] | Chemistry [93] | English Adv [87] | 3U Maths [98] | 4U Maths [97]
ATAR: 99.05

UCAT: 3310 - VR [740] | DM [890] | QR [880] | AR [800]
Guide Links:
Subject Acceleration (2018)
UCAT Question Compilation/FAQ (2020)
Asking good questions

Luke_8064

  • Trailblazer
  • *
  • Posts: 49
  • Respect: +12
Re: QCE General Maths Questions Thread
« Reply #10 on: August 05, 2021, 09:18:26 am »
0
How'd you get $356,400 because 360 X 1485 does not equal 356400?

Thanks,
Luke
QCE Class of 2021: Design | Digital Solutions | English | ICT | General Maths | Psychology

fun_jirachi

  • MOTM: AUG 18
  • HSC Moderator
  • Part of the furniture
  • *****
  • Posts: 1068
  • All doom and Gloom.
  • Respect: +710
Re: QCE General Maths Questions Thread
« Reply #11 on: August 05, 2021, 10:00:21 am »
+1
Oops, that is a typo - I'm correct in saying that you make monthly payments for twenty years which should have been 240 payments, rather than 360 as previously said. I'll fix that up. 240 * 1485 = 356400.
Spoiler
HSC 2018: Mod Hist [88] | 2U Maths [98]
HSC 2019: Physics [92] | Chemistry [93] | English Adv [87] | 3U Maths [98] | 4U Maths [97]
ATAR: 99.05

UCAT: 3310 - VR [740] | DM [890] | QR [880] | AR [800]
Guide Links:
Subject Acceleration (2018)
UCAT Question Compilation/FAQ (2020)
Asking good questions

Luke_8064

  • Trailblazer
  • *
  • Posts: 49
  • Respect: +12
Re: QCE General Maths Questions Thread
« Reply #12 on: August 05, 2021, 10:12:58 am »
0
Hey,

I am confused as to how to find the monthly repayments on reducing balance loans because every question I am doing is always a couple of dollars out. Could someone help me to figure out my issue.

The method I use is I sub in every value to the annuities formula and find M. However, doing it this way gave me $42.62 but the answer is $43.42.

Kind regards,
Luke
QCE Class of 2021: Design | Digital Solutions | English | ICT | General Maths | Psychology

Luke_8064

  • Trailblazer
  • *
  • Posts: 49
  • Respect: +12
Re: QCE General Maths Questions Thread
« Reply #13 on: August 05, 2021, 10:13:35 am »
0
Oops, that is a typo - I'm correct in saying that you make monthly payments for twenty years which should have been 240 payments, rather than 360 as previously said. I'll fix that up. 240 * 1485 = 356400.

Thanks! makes much more sense now.
QCE Class of 2021: Design | Digital Solutions | English | ICT | General Maths | Psychology

fun_jirachi

  • MOTM: AUG 18
  • HSC Moderator
  • Part of the furniture
  • *****
  • Posts: 1068
  • All doom and Gloom.
  • Respect: +710
Re: QCE General Maths Questions Thread
« Reply #14 on: August 05, 2021, 07:06:46 pm »
+1
-snip-

Using the formula, we have that \(500 = M \times \frac{1-(1+0.042)^{-1}}{0.042}\). This implies that the amount of money we have to pay is \(M = $521\). Since we have to make monthly payments, each payment is just \(\frac{521}{12} \approx $43.42\).

Hope this makes sense :)
Spoiler
HSC 2018: Mod Hist [88] | 2U Maths [98]
HSC 2019: Physics [92] | Chemistry [93] | English Adv [87] | 3U Maths [98] | 4U Maths [97]
ATAR: 99.05

UCAT: 3310 - VR [740] | DM [890] | QR [880] | AR [800]
Guide Links:
Subject Acceleration (2018)
UCAT Question Compilation/FAQ (2020)
Asking good questions