Discussion and Suggested Solutions - Mathematics 2017

[jamonwindeyer]

Hey jamon, for question 16a) ii, instead of proving sin(alpha)=sin(beta), i proved tan(a)=tan(b), does that work as well?
Thanks!

I think for full marks you would need to hit the line, \(\therefore \sin{\alpha}=\sin{\beta}\), but you could get partial marks!

I am looking at around 85 raw for the exam and I finished 13/52, but the difference between me and 1st is quite a bit. I averaged 77% in internals and got 81% in trials. Do you think I can get a band 6 still?

Definitely possible!

[aadharmg]

There was this arithmetic and geometric sequences q that I couldn’t get for ages, had to cross out my working out multiple times  got it in the ens though :3 also the geometry proofs...

Which question was the geometric sequences one?

[Natasha.97]

Which question was the geometric sequences one?

I meant the limiting sum(16b) Arithmetic one was alright

[goodguy]

Hi,
For the loan repayments question if i have correctly summed up the geometric series however forgot to change the months to years, so just did it as n=4, and instead got an answer of $23000, do you think i would get 0,1, or 2/3. Also, if my x value was wrong for 16aiii, but i proved that it was a minimum through testing points on either side of the incorrect f'x equation, would i receive the mark for carry through error?
thanks

[NTK30]

Hey Jamon,

Thanks so much for the solution. I hope you didn't get anything wrong because I had the same answers for most of paper. Just a few doubts below.

I remembered that question 11h only asked for the domain. If it's not a problem, can you tell me where you got the paper from? I want to confirm whether the range was asked or not.

For question 14c part iii, I had 870 (to 2 sigfig) using exact value (ln0.5)/5730). There is a 10 years difference with your answer (I think you used -0.00012). Which answer is right? Or will both be accepted?

Finally for question 16a:
- Part ii I believe you're supposed to write equations for sin(alpha) and sin(beta), then substitute them in to dL/dx.
- Part iii, I stated that alpha and beta must be acute angles. Therefore if sin(alpha) = sin(beta) then alpha = beta and thus tan(alpha) = tan(beta). I solved for x from here which was much easier. I know you said below that partial marks might be awarded if I simply solved with the tan equation. Will I get the full mark with this explanation?
- Part iv instead of doing a table of x and dL/dx, I just did a table of x and L. I showed that the x values on either side of x = 15/4 ( e.g. 3.65 and 3.85) gave larger values for L than at the stationary point. Is this sufficient for the proof?

Sorry for the long post and looking forward to your response. Thanks again.

[jamonwindeyer]

Hi,
For the loan repayments question if i have correctly summed up the geometric series however forgot to change the months to years, so just did it as n=4, and instead got an answer of $23000, do you think i would get 0,1, or 2/3. Also, if my x value was wrong for 16aiii, but i proved that it was a minimum through testing points on either side of the incorrect f'x equation, would i receive the mark for carry through error?
thanks

If you just forgot to convert from months to years that should just be one mark gone, as long as your approach was otherwise correct! And I think you would get marks for that COE

Hey Jamon,

Thanks so much for the solution. I hope you didn't get anything wrong because I had the same answers for most of paper. Just a few doubts below.

You are welcome!

I remembered that question 11h only asked for the domain. If it's not a problem, can you tell me where you got the paper from? I want to confirm whether the range was asked or not.

Range wasn't asked, only domain - I was rushing and added work for myself

For question 14c part iii, I had 870 (to 2 sigfig) using exact value (ln0.5)/5730). There is a 10 years difference with your answer (I think you used -0.00012). Which answer is right? Or will both be accepted?

I've used the rounded, you've used the exact - I'm sure both will be paid

Finally for question 16a:
- Part ii I believe you're supposed to write equations for sin(alpha) and sin(beta), then substitute them in to dL/dx.
- Part iii, I stated that alpha and beta must be acute angles. Therefore if sin(alpha) = sin(beta) then alpha = beta and thus tan(alpha) = tan(beta). I solved for x from here which was much easier. I know you said below that partial marks might be awarded if I simply solved with the tan equation. Will I get the full mark with this explanation?
- Part iv instead of doing a table of x and dL/dx, I just did a table of x and L. I showed that the x values on either side of x = 15/4 ( e.g. 3.65 and 3.85) gave larger values for L than at the stationary point. Is this sufficient for the proof?

Sorry for the long post and looking forward to your response. Thanks again.

So Part (ii), yep that was definitely the intended approach - Again, me rushing I added work for myself (anyone who did what I did would absolutely get full marks as well). Part (iii), absolutely fine, provided you stepped through your logic as you have there!

Part (iv) is a little trickier, you would typically prove a minimum by table with the derivative. But, if you know the value of \(L\) then I see no reason that this proof wouldn't hold. So, I think you are okay there as well!

[blokefromthesky]

for the second part of the money question, I didnt create my own series (like using the sum formula to make the series). I just used the format of the series  like it was in the question but up to four not two to answer the question. would i lose a mark for not creating a series but getting the right answer?

[jamonwindeyer]

for the second part of the money question, I didnt create my own series (like using the sum formula to make the series). I just used the format of the series  like it was in the question but up to four not two to answer the question. would i lose a mark for not creating a series but getting the right answer?

It was compounded monthly so you would have needed 48 terms, which is next to impossible to do without using the sum formula. You might lose a mark or two

[Anfar3]

Hey Jamon,

For that same q^, I didn't get the answer coz i didn't do 2 sums i jst did the normal sum from the first part so got the wrong answer.

However, i created a series, used 48 terms, let A48= 80 000, did the algebra and calculations.

Only thing my sum missed the additional extra sum of the X deposit.

I kinda think ill only get 1/3 for that but any chance 2/3?

Thanks

[PrimalPancake92]

Overall, this test had some challenging questions. But Jamon, question 16aii,you could of ended it easily. Let dl/dx=0, drag the second expression over and say that theyre equal. Then find sin(a) and sin(b) from observation of diagram. They would match from the hypotenuse u found from parti). I am going to be honest. That question was pretty fun. Had a good ten minutes worth of staring.

It was just the last question, everything else was pretty okay, I don't think I did many mistakes, but geometry proofs are my weakness, and part of 16 was geometry I think I got 3/15 for 16, which REALLY bothers me :/ )

Dude why leave out 16?

[jamonwindeyer]

Hey Jamon,

For that same q^, I didn't get the answer coz i didn't do 2 sums i jst did the normal sum from the first part so got the wrong answer.

However, i created a series, used 48 terms, let A48= 80 000, did the algebra and calculations.

Only thing my sum missed the additional extra sum of the X deposit.

I kinda think ill only get 1/3 for that but any chance 2/3?

Thanks

I think it would depend how you framed the first part of that two part question, but I think you will probably only get 1 mark unfortunately - It's a misinterpretation of the question rather than just forgetting something, at least in their eyes, but fingers crossed you get lucky!

[Stefan Kolar]

Hey just to let u guys know, nesa released the paper

[jamonwindeyer]

Hey just to let u guys know, nesa released the paper

I've added a link to the OP

[Stefan Kolar]

hey Jamon just wanted to ask, for q16a ii) in the test i  differentiated the length formula in the above part to get dl/dx, then i was stuck and i couldnt find x when dl/dx = 0 so i left it until i finished the rest of the paper. When i came back i had about 15-20min remaining and couldnt for the life of me find x, and so i just guessed random numbers and i actually got the answer. SO without any working out after the differentiation i just wrote x = 3.75 (15/4). then i subbed it into sinalpha and sinbeta and showed that they are equal. How many marks do u think i'd get for that question.

[Anfar3]

Alright understandable Jamon, hope I get lucky hahaha!

Anyways if around 77-80 is raw b6 then what will an 86-88 raw get?