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November 28, 2020, 07:20:40 am

Author Topic: Maths Advanced - Discussion, Questions, Potential Solutions  (Read 1828 times)

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hooter03

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #15 on: October 26, 2020, 06:58:19 pm »
I heard there was a 23 mark cross over with the standard paper. It would be interesting to know which questions.

I know this is the advanced forum, but I thought I'd comment on what the standard paper had and you can check the cross over: the crickets, Wilma (i think that's her name) and the annuities table, the decagon,  the Z score question with Simon and his IQ... these were the difficult ones but I think there might be a couple more not entirely sure.

RuiAce

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #16 on: October 26, 2020, 10:51:02 pm »
This post will contain solutions to the common questions between standard and advanced. Again thanks to my love for handling the uploads.

Tank


Camping


Decagon


Tina's Withdrawals


Crickets chirping

« Last Edit: October 27, 2020, 10:34:21 am by RuiAce »

RuiAce

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #17 on: October 27, 2020, 01:37:42 am »
Some late night solutions to the whole paper. I'll continue these tomorrow. Edit: Complete now. (Note: I was doing the paper backwards)

Clicking an image can make it automatically resize into a more readable view.

Multiple Choice
Questions 1-10


Short Answer
Questions 11-14

Questions 15-18

Questions 19-21

Questions 22-25

Questions 26-28

Questions 29-31

« Last Edit: October 30, 2020, 11:13:44 pm by RuiAce »

sroe

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #18 on: October 27, 2020, 07:54:53 am »
Some late night solutions to the whole paper.

These are awesome, thank you!!
Just with Q27 (the crickets one) you've written =29.036... --> Hence 21 chirps...
Should it not also be 29?

BakerDad12

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #19 on: October 27, 2020, 08:16:05 am »
Oh no way, I got the cricket question!

RuiAce

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #20 on: October 27, 2020, 10:02:54 am »
These are awesome, thank you!!
Just with Q27 (the crickets one) you've written =29.036... --> Hence 21 chirps...
Should it not also be 29?
Oh dear haha.

Context: I screwed up the question a little in my first attempt. Found the mistake, and managed to get the correct 29.036. But then forgot to fix the conclusion! I'll make sure to fix that.

Natasack

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #21 on: October 27, 2020, 10:28:17 am »
I thought 8 and 10 were very hard, I was basically making an educated guess on both of them.
what was the answer for 10 multiple choice?

RuiAce

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #22 on: October 27, 2020, 10:36:20 am »
what was the answer for 10 multiple choice?
I will get to that.

rirerire

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #23 on: October 27, 2020, 02:07:32 pm »
reading these answers feels bad man

made sooooo many dumb errors I genuinely don't know if i even passed this paper. ugh I feel like i've completely jeopardised my atar with this one stupid exam

RuiAce

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #24 on: October 27, 2020, 04:39:36 pm »
reading these answers feels bad man

made sooooo many dumb errors I genuinely don't know if i even passed this paper. ugh I feel like i've completely jeopardised my atar with this one stupid exam
If they were silly mistakes I imagine you'd still get a reasonable amount of partial marks for your attempts. They shouldn't punish you that heavily if you showed reasonable understanding, even if there were errors along the way.

BakerDad12

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #25 on: October 27, 2020, 06:48:16 pm »
How hard was this exam compared to past exams?

RuiAce

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roy g biv

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #27 on: October 30, 2020, 10:56:45 pm »
Q10. Should be D, i think.
h(x) = f(g(x))
Examining around x = 3:

h(x) = f(g(2.9))
h(x) = ~ f(0.1)
h(x) = ~ 1.81

h(x) = f(g(3))
h(x) = ~ f(0)
h(x) = ~ 1.8

h(x) = f(g(3.1))
h(x) = ~ f(0.1)
h(x) = ~ 1.81

Clearly, there is a minimum point :-)

Therefore answer is D, not C. Other two max stationary points occur when ~f(0.8). i.e. we need g(x) to be 0.8 in order to get f(g(x)) to become f(0.8).
g(x) = 0.8 at 2 places. Therefore two stat points.

If you're still not convinced, try using desmos to experiment:
g(x) = 0.5(x-3)^2
f(x) = 2e^-(0.7x-0.5)^2
h(x) = f(g(x))

RuiAce

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #28 on: October 30, 2020, 11:05:30 pm »
Q10. Should be D, i think.
h(x) = f(g(x))
Examining around x = 3:

h(x) = f(g(2.9))
h(x) = ~ f(0.1)
h(x) = ~ 1.81

h(x) = f(g(3))
h(x) = ~ f(0)
h(x) = ~ 1.8

h(x) = f(g(3.1))
h(x) = ~ f(0.1)
h(x) = ~ 1.81

Clearly, there is a minimum point :-)

Therefore answer is D, not C. Other two max stationary points occur when ~f(0.8). i.e. we need g(x) to be 0.8 in order to get f(g(x)) to become f(0.8).
g(x) = 0.8 at 2 places. Therefore two stat points.

If you're still not convinced, try using desmos to experiment:
g(x) = 0.5(x-3)^2
f(x) = 2e^-(0.7x-0.5)^2
h(x) = f(g(x))
The stationary point at \(x=3\) was already located. There is nothing to convince me of here.

The mistake was that for the second part of the solution, I somehow borrowed the stationary point to \(y=g(x)\) instead of \(y=f(x)\). I do not need Desmos to convince me of that mistake.

(Mistake will be fixed soon)

roy g biv

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Re: Maths Advanced - Discussion, Questions, Potential Solutions
« Reply #29 on: October 31, 2020, 09:48:41 am »
Sorry!

To be honest, I saw that C had been put as the answer, and without reading your solution, I assumed you were missing the stat. pt. at x=3 similar to how many other students missed it.

My bad! Shouldn't have assumed :)