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March 29, 2024, 03:10:02 am

Author Topic: VCE Methods Question Thread!  (Read 4802519 times)  Share 

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Remy33

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Re: VCE Methods Question Thread!
« Reply #17925 on: May 19, 2019, 08:48:00 pm »
0
When finding inverse functions, do you always reject the negative? Or are there cases where you use both or reject the positive?
Cheers.
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AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17926 on: May 19, 2019, 08:57:31 pm »
+2
When finding inverse functions, do you always reject the negative? Or are there cases where you use both or reject the positive?
Cheers.

If we find we have to take a square root, we do not always take the positive one.

We also cannot take both roots as this wouldn't give us a function.

You need to take the sign that is consistent with its range (or the domain of the original function).

Here's an easy example question where we would take the negative root. Try sketching both roots and see which one produces a function that is symmetrical to the original about the line \(y=x\).

Question:    Let  \(f:(-\infty,\,0]\to\mathbb{R},\ f(x)=x^2\).  Find the rule, domain and range of \(f^{-1}\), the inverse function of \(f\).
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f0od

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Re: VCE Methods Question Thread!
« Reply #17927 on: May 24, 2019, 10:36:17 pm »
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For the question (1aiii) (and worked out answer) attached, I'm confused on how they converted the sin(x) to a cos(x)?

Additionally, could someone please explain the identity cos2(x) - sin2(x) = cos(2x)?

Thanks! :)
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AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17928 on: May 24, 2019, 11:31:43 pm »
+3
For the question (1aiii) (and worked out answer) attached, I'm confused on how they converted the sin(x) to a cos(x)?

Additionally, could someone please explain the identity cos2(x) - sin2(x) = cos(2x)?

Thanks! :)

That has got to be one of the stupidest solutions to a problem I've ever seen.

Clearly, the rule of \(d\) has the form  \(d(t)=a+b\cos(nt)\).  The amplitude gives the magnitude of \(b\),  the period gives \(n\),  and \(a\) is the average of the minimum and maximum distances.

Anyway, we can still learn something from this. They use complementary angle identities. The main complementary angle identities you should know are \[\boxed{\sin\left(\frac\pi 2-\theta\right)=\cos(\theta)\\
\cos\left(\frac\pi 2 -\theta\right)=\sin(\theta)}\] Then, you can just apply periodicity.

For a more intuitive outlook, sketch the graph of  \(y=\sin(x)\)  and translate it \(\dfrac{3\pi}{2}\) units to the left. You'll find that it becomes exactly the graph of  \(y=\cos(x)\).

The identity  \(\cos(2\theta)=\cos^2(\theta)-\sin^2(\theta)\)  is known as the cosine double angle formula, and is not a part of the Methods course.

I won't go into the details of how it can be used nor present a derivation here (since this is a Methods questions thread), but feel free to chuck a question in the Specialist Questions Thread if you're curious
« Last Edit: May 24, 2019, 11:33:27 pm by AlphaZero »
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DBA-144

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Re: VCE Methods Question Thread!
« Reply #17929 on: May 26, 2019, 09:05:18 am »
0
1. How formal do we need to be with our working out for methods? Not just prove and show that questions btw.
2. Do we get penalised 1 mark per paper or one mark per error for simplification?
3. How much working is required in exam 2, for non-show that/prove questions? For a 3 mark question, can't I just write 3 things, and so long as they fulfill the marking guide, I should get full marks right? I have heard that for 3 marks we should be showing plenty of working, but I am not sure if this is required given that essentially, 3 marks is just 3 things that we need to show/do.

Thanks.
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AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17930 on: May 26, 2019, 02:39:24 pm »
+2
1. How formal do we need to be with our working out for methods? Not just prove and show that questions btw.

You don't need to be able to present solutions is if they were for an academic paper, but you are expected to be able to communicate clearly what you are doing so that an examiner can follow your train of thought.

2. Do we get penalised 1 mark per paper or one mark per error for simplification?

Algebraic simplification and calculations are usually assigned to the final answer mark of a question. If you do not obtain the correct answer in the required form, you cannot be awarded the mark.

Please note, you are never penalised for mistakes. Depending on the error, you will just not obtain the mark that the working/answer is assigned to.

3. How much working is required in exam 2, for non-show that/prove questions? For a 3 mark question, can't I just write 3 things, and so long as they fulfill the marking guide, I should get full marks right? I have heard that for 3 marks we should be showing plenty of working, but I am not sure if this is required given that essentially, 3 marks is just 3 things that we need to show/do.

You need to show enough working to:
1.  allow the examiner to follow your train of though,  and
2.  show the examiner that you understand what the question is testing.

How much work you need to show depends on the question, but here's a good general rule:  Suppose you are showing your friend, who does not understand how to answer a question, your solution to it. Without you talking them through it, would they be able to understand the method just from what you wrote? If not, you probably haven't shown enough.
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Ansaki

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Re: VCE Methods Question Thread!
« Reply #17931 on: June 02, 2019, 02:22:56 pm »
0
hey guys! i got a question that is in conjunction with related rates of change, i dont quite understand how to tackle the question and also work through it.
Question:
"A spherical balloon is being inflated so that its radius is increasing at a rate of 5 cm/min. Find the rate at which the surface area is increasing when the radius is 10cm given the equation for the surface area is given by SA=4*pi*r^2.

thanks

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Re: VCE Methods Question Thread!
« Reply #17932 on: June 02, 2019, 02:37:49 pm »
+1
hey guys! i got a question that is in conjunction with related rates of change, i dont quite understand how to tackle the question and also work through it.
Question:
"A spherical balloon is being inflated so that its radius is increasing at a rate of 5 cm/min. Find the rate at which the surface area is increasing when the radius is 10cm given the equation for the surface area is given by SA=4*pi*r^2.

thanks
This is a related rates question which is not on the study design anymore but

We know that dr/dt = 5 cm/min
and dSA/dr=8 pi r
and we are trying to find dSA/dt
So dSA/dt = dSA/dr * dr/dt (chain rule)
= 8 pi r * 5
so when the radius = 10cm
dSA/dt = 8 pi 10 * 5
= 400pi cm^2 / min
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Ansaki

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Re: VCE Methods Question Thread!
« Reply #17933 on: June 02, 2019, 03:48:31 pm »
0
This is a related rates question which is not on the study design anymore but

We know that dr/dt = 5 cm/min
and dSA/dr=8 pi r
and we are trying to find dSA/dt
So dSA/dt = dSA/dr * dr/dt (chain rule)
= 8 pi r * 5
so when the radius = 10cm
dSA/dt = 8 pi 10 * 5
= 400pi cm^2 / min

thanks so much! your help is much appreciated!!!

Donut

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Re: VCE Methods Question Thread!
« Reply #17934 on: June 02, 2019, 10:27:24 pm »
0
Is there anyway to complete the square on the casio classpad. I only know how to do it on the tnspire

AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17935 on: June 02, 2019, 10:56:48 pm »
0
Is there anyway to complete the square on the casio classpad. I only know how to do it on the tnspire

I've been wondering this as well. I used the TI-nspire when I did VCE, and only recent bought a Casio Classpad to learn how to use it :/
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JR_StudyEd

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Re: VCE Methods Question Thread!
« Reply #17936 on: June 04, 2019, 06:44:14 pm »
0
How do transformations change the values of circular functions? E.g. I know that for the base function sin(x), when you dilate it for 2 units from the x-axis and dilate it for 1/3 units from the y-axis, you have the transformed function y=2sin(3x), but in terms of the values of x and y, how are they different? What do I change? How do I change it?
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AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17937 on: June 04, 2019, 11:42:00 pm »
+1
How do transformations change the values of circular functions? E.g. I know that for the base function sin(x), when you dilate it for 2 units from the x-axis and dilate it for 1/3 units from the y-axis, you have the transformed function y=2sin(3x), but in terms of the values of x and y, how are they different? What do I change? How do I change it?

I'm not sure I quite understand your question, so could you elaborate on what you mean by how transformations "change the values of circular functions"? And, when you say "how do I change it", what's it?

Edit: Are you asking about the overall effects of different transformations on the graphs of circular functions? Or, are you asking about how any given point say \((x,y)\) that is on the graph moves after a sequence of transformations are applied?
« Last Edit: June 04, 2019, 11:52:11 pm by AlphaZero »
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TyranT

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Re: VCE Methods Question Thread!
« Reply #17938 on: June 05, 2019, 07:35:24 am »
0
Hello,
Could i please get help with question 12b? I know the answer to question 12a but not 12b. The solutions say 19mm but with no working out; i want to understand the concept.
Thank you

MB_

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Re: VCE Methods Question Thread!
« Reply #17939 on: June 05, 2019, 09:47:30 am »
+1
Hello,
Could i please get help with question 12b? I know the answer to question 12a but not 12b. The solutions say 19mm but with no working out; i want to understand the concept.
Thank you
For part a, you get \(\sqrt[3]{7} \text{ cm}\). Part b is just asking you to evaluate that answer and round it so \(\sqrt[3]{7} \approx 1.9 \text{ cm} = 19 \text{ mm}\).
« Last Edit: June 05, 2019, 09:49:22 am by MB_ »
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