QCE Specialist Maths Questions Thread

[Joseph41]

QCE SPECIALIST MATHS Q&A THREAD

What is this thread for?
If you have general questions about the QCE Specialist 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!

[Twisty314]

Hey everyone! Need help with this question. Really troubling me. 

Using the formula for , prove that where 

I got mixed up so after so many attempts. Sorry about the formatting of nCr, but if it is confusing:

There is the combination, then there is the and lastly .

Thanks all!

[RuiAce]

Hey everyone! Need help with this question. Really troubling me. 

Using the formula for , prove that where 

I got mixed up so after so many attempts. Sorry about the formatting of nCr, but if it is confusing:

There is the combination, then there is the and lastly .

Thanks all!

For the \(^nC_r\) notation you're gonna require superscripts and subscripts. You can do a bit of exploring around if you're curious. Basically superscripts and subscripts are required because that notation isn't by default built into \(\LaTeX\), so you have to manually work around it.
\[ \text{We still need }n! = n(n-1)!\text{ for these problems.}\\ \text{Here it looks like we need that identity three times.} \]
\begin{align*}\binom{n-1}{r-1} + \binom{n-1}{r} &= \frac{(n-1)!}{(r-1)! ((n-1)-(r-1))!} + \frac{(n-1)!}{r! (n-1-r)!}\\ &= (n-1)! \left[ \frac{1}{(r-1)!(n-r)!} + \frac{1}{r!(n-r-1)!} \right]\\&= (n-1)! \left[ \frac{r}{r!(n-r)!} + \frac{n-r}{r!(n-r)!} \right]\\ &= (n-1)!\cdot \frac{r+n-r}{r!(n-r)!}\\ &= \frac{(n-1)! n}{r!(n-r)!}\\ &= \frac{n!}{r!(n-r)!}\\ &= \binom{n}{r} \end{align*}
The thing about that factorial identity is that it helps us make the whole 'lowest common denominator for adding fractions' idea work. It's really nifty when trying to prove results with \(^nP_r\) and \(^nC_r\) if we just want to use their respective formulas. Gotta be clever with using it

[Twisty314]

Thanks again Rui! That really helped a lot!

[WillHansen]

What marks are everybody sitting on? I am sitting on approx 70% for unit 1 and 2

[e_grace]

hey, i'm currently on a 76% with my assignment and exam combined... thinking of dropping however.

[e_grace]

Can someone please tell me how much specialist has scaled in the past? like in other states. has a 76% go up to a 96% in the past ? or yeah? Thank you!

[Joseph41]

Can someone please tell me how much specialist has scaled in the past? like in other states. has a 76% go up to a 96% in the past ? or yeah? Thank you!

It works a little differently in other states. For example, in Victoria, overall subject scores are out of 50. In 2018, a raw study score of 30 (which is the average) in Specialist Maths resulted in a scaled score of 41.

These numbers probably don't mean heaps to you because a) the system is entirely different, and b) they're not out of 100. But I think it's important to realise that even for QCE, subject scores aren't the same as percentages. For example, getting an average of 76% in Specialist Maths doesn't mean you'll get a subject score of 76 for Specialist Maths necessarily.

Ultimately, even if Spesh did scale that much in QCE, I don't think it's really worth considering. Getting high or low scaling doesn't reward or punish you; instead, it just negates a very competitive or less competitive cohort. What scaling does is actually equal the playing field across subjects, meaning you can simply choose subjects you enjoy, are passionate about, are good at, or need as university pre-requisites.

In general, I'd encourage you not to give too much weight to scaling in subject selection, particularly given we have absolutely zero relevant data to go off.

[Specialist_maths]

Can someone please tell me how much specialist has scaled in the past? like in other states. has a 76% go up to a 96% in the past ? or yeah? Thank you!

First, I would agree with Joseph's advice: don't worry too much about scaling - just focus on doing your best in all your subjects.

With regards to scaling for an ATAR, your overall results (/100) are used to determine your rank in the cohort. It doesn't really matter what your results are - it's how your results compare to the rest of the cohort (in each subject across the state). It's this percentile that is scaled.

If the 2020 Queensland Specialist Mathematics cohort has a similar distribution of results to what other cohorts typically achieve in other states, I would imagine 76/100 is an above average score and would scale well (possibly to about 95% - however, no one can say with any certainty at this point).

[A.Rose]

Hello
I am doing a PSMT about Leslie Matrices and I'm trying to talk about the properties of a Leslie matrix that causes a population to have high growth and one that causes a population to decline. What constitutes a high survival or birth rate? Is there somewhere I can find this information on the internet so I can reference it in my report? What are the features of a Leslie matrix that will cause that continuous increase? I know high survival and birth rates would contribute but what does it mean by a 'high' rate?
Thank you!

[Bri MT]

Hello
I am doing a PSMT about Leslie Matrices and I'm trying to talk about the properties of a Leslie matrix that causes a population to have high growth and one that causes a population to decline. What constitutes a high survival or birth rate? Is there somewhere I can find this information on the internet so I can reference it in my report? What are the features of a Leslie matrix that will cause that continuous increase? I know high survival and birth rates would contribute but what does it mean by a 'high' rate?
Thank you!

Hey!

You might find it easier to find/understand information by looking up life history tables as these display the same information (well, sometimes not fecundity/reproduction) but in a less mathematical way. There's not really set numbers for high vs low - it's all relative. In ecology, we talk about life history as involving trade-offs in somatic and gametic investment  - members of a population can't 100% put their resources to producing offspring or 100% to their own survival, it's a balancing act. I've written about life history a bit here (please note this is well outside the spec syllabus).

One thing you will want to consider is multiplying population size in each age class by fecundity in the corresponding age class to find the expected number of offspring produced in that age class. Comparison of this resulting distribution and the one you started with will help you with the insights you're interested in.


Hope this helps!

Ecology is my major at uni so definitely happy to talk about population ecology

[A.Rose]

Hi!
I doing Applications of integration in Specialist maths this term and I'm having trouble with this volumes of solids of revolutions question (see attached).
I don't have any worked solutions for this question so if you could step me through it that would be amazing.
Thank you!!

[A.Rose]

Hi, I have another question about finding the volume of a solid of revolution (see image). Do I have to differentiate to find max volume and if so at what point would I differentiate? I just need help with at least with how to start.
Thank you so much!

[A.Rose]

Sorry, I have another question!
I'm not quite sure how to do conditional probability for exponential probability distributions and I'm stuck on part c) of attached question.
Hopefully, that's my last question for now.
Much appreciated!

[fun_jirachi]

Not quite sure how to do exponential probability (never learnt that! or more accurately, haven't learnt that yet ), but I'll answer your other two questions. It's also better to edit in your extra questions into your original post instead of posting once per question, really helps declutter the forum!

For your first question, the integral is simplified quite a bit for you. Recall that when you rotate a curve around the x-axis, the volume is equal to \(\pi \int_a^b y^2 \ dx\). In both cases, a y² already appears, so all you have to do is find the point of intersection between the two curves, and then use the volume formula to integrate the correct curves within the upper and lower bounds you've found.

For your second question, it's a matter of rearranging the equation so you have a function of x in terms of y, so you can use the formula \(V = \pi \int_a^b x^2 \ dy\) for volumes around the y-axis. Make sure you have the correct upper and lower bounds as well so you get the correct answer!

If you need more assistance than this, don't hesitate to ask! It's just often a better idea to point you in the right direction as opposed to giving you the answer outright