Mathematics Question Thread

[kauac]

\begin{align*} f(3) &\to \text{first}\\ f(3.2) &\to \text{odd}\\ f(3.4) &\to \text{even}\\ f(3.6)&\to \text{odd}\\ f(3.8 ) &\to \text{even}\\ f(4) &\to \text{odd}\\ f(4.2) &\to \text{even}\\ f(4.4) &\to \text{odd}\\ f(4.6) &\to \text{even}\\ f(4.8 )&\to \text{odd}\\ f(5)&\to \text{last} \end{align*}
That "mnemonic" is a very well known way of memorising the generalised Simpson's rule. Essentially your first function value is \(x_0 = 3\). The next function value, \(x_1 = 3.2\), is called "odd" in this context because the index is \(1\). The subsequent function value, \(x_2 = 3.4\), is called "even" in this context because the index is \(2\). And so on.

Essentially, you start counting after the "first". That one, will be the first "odd".

You should always end up with exactly one more "odd" than "even"

Thanks so much for your explanation! Everything is a lot more clear now. 

[Dragomistress]

I am confused on how I can convert the LHS into the RHS.

sin(pi-2x)=sin(2x)?

[RuiAce]

I am confused on how I can convert the LHS into the RHS.

sin(pi-2x)=sin(2x)?

Second quadrant angle.

[LaraC]

Hello

Could I please have help with this question:

Find lim (theta approaches 0) ((tan theta/3)/theta)

Hopefully you can decipher that! 

Thanks in advance! 

[clovvy]

Hello

Could I please have help with this question:

Find lim (theta approaches 0) ((tan theta/3)/theta)

Hopefully you can decipher that! 

Thanks in advance! 

[mirakhiralla]

Hey I have attempted this question multiple times but couldn't do it,
could someone please help/// I think it was from the 2007 HSC:

Mrs Cain decided to invest some money each year to help pay for her son's uni education.
She contributes $1000 on the day of her son's birth and increases her annual contribution by 6% each year.
Her investment also earns 6% compound interest p/a.
Find the total value of Mrs Cain's investment on her son's birthday (just before her fourth contribution)

[clovvy]

Hey I have attempted this question multiple times but couldn't do it,
could someone please help/// I think it was from the 2007 HSC:

Mrs Cain decided to invest some money each year to help pay for her son's uni education.
She contributes $1000 on the day of her son's birth and increases her annual contribution by 6% each year.
Her investment also earns 6% compound interest p/a.
Find the total value of Mrs Cain's investment on her son's birthday (just before her fourth contribution)

[RuiAce]

Hey I have attempted this question multiple times but couldn't do it,
could someone please help/// I think it was from the 2007 HSC:

Mrs Cain decided to invest some money each year to help pay for her son's uni education.
She contributes $1000 on the day of her son's birth and increases her annual contribution by 6% each year.
Her investment also earns 6% compound interest p/a.
Find the total value of Mrs Cain's investment on her son's birthday (just before her fourth contribution)

I found the question - I think you meant her son's third birthday.

Note that, because of what the question wants, we've set \(A_n\) to be the value right before we make the next deposit. So we need to ensure that after we compute \(A_1\), we deposit immediately after, before smacking on the interest factor of 1.06



Which you can put into your calculator.

The reason why this annuity turned out so surprisingly nicely is because the deposits were increasing alongside the interest accrued. This cleans up a lot of the mess for us.

[clovvy]

Oh lol I just realised I did the wrong question when I had a look at it lol, so as Rui says just said just sub them in to the calculator

That was embarrasing

[mirakhiralla]

Oh lol I just realised I did the wrong question when I had a look at it lol, so as Rui says just said just sub them in to the calculator

That was embarrasing

Ahahah I wrote the question wrong, all good.
Thank you both!

[ilikeapples]

Hi I am having difficulty with this series question:
A bandicoot population is decreasing by 5% each year. a) what % of population is left after 5 years. b) after how many years will the population only be 50%. c) how many years will I take for the population to decrease by 80%.

Thankyou

[jamonwindeyer]

Hi I am having difficulty with this series question:
A bandicoot population is decreasing by 5% each year. a) what % of population is left after 5 years. b) after how many years will the population only be 50%. c) how many years will I take for the population to decrease by 80%.

Thankyou

Welcome to the forums!! Let me give you a few hints!

-  For (a), a decrease of 5% is the same as there being 95% remaining. So, every year we are multiplying by 0.95. The number left after the first year is \(N=N_0(0.95)\), where \(N_0\) is the initial. The next year will be \(N=N_0(0.95)^2\). And so on!
-  For (b), you'll need to generalise the formula like this:



You want the value of N that leaves 50% of the initial, or \(0.5N_0\), generate a formula! And c) is the same, just you want it equal to \(0.2N_0\) (20% left since there is 80% gone!).

Hope this helps

[talitha_h]

Hi,
I have a cited task coming up for math - basically just a bunch of hsc past papers- and I was wondering what would be the best way to study for this (other than actually doing the papers)?
Thanks 

[RuiAce]

Hi,
I have a cited task coming up for math - basically just a bunch of hsc past papers- and I was wondering what would be the best way to study for this (other than actually doing the papers)?
Thanks 

Still not sure what you mean by "cited task". Is it just something like an in-class test?

[talitha_h]

Still not sure what you mean by "cited task". Is it just something like an in-class test?

sorry, I meant 'sighted' task, we get given a bunch of past papers to do before the exam and they select a number of them to be in the assessment