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June 20, 2021, 11:33:01 pm

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#### pans

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##### Re: VCE Methods Question Thread!
« Reply #18600 on: July 02, 2020, 11:57:38 am »
+1
Hello, I started methods 1/2 this year and Im kind of struggling. Like I can do the textbook questions but when it comes to my sacs, THEY ARE REAL HARD! Like I seriously cant! Ive been getting like 64%, 75%, 78% etc. Before my sacs I not only do practice tests from school but also from "edrolo" and random resources. Can anyone please give me some advice? Btw, I also go tuition.
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#### keltingmeith

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##### Re: VCE Methods Question Thread!
« Reply #18601 on: July 02, 2020, 12:15:56 pm »
+7
Hello, I started methods 1/2 this year and Im kind of struggling. Like I can do the textbook questions but when it comes to my sacs, THEY ARE REAL HARD! Like I seriously cant! Ive been getting like 64%, 75%, 78% etc. Before my sacs I not only do practice tests from school but also from "edrolo" and random resources. Can anyone please give me some advice? Btw, I also go tuition.

Work smarter, not harder.

You seem to be preparing by what I like to call, the "shotgun approach". Imagine being a shooting range, and you want to hit the centre of the target - instead of taking a second to think, and using just a handful of bullets to hit the centre, you're just taking out a shot-gun and firing. The truth is, with this method you'll always hit the target, but you'd have to be damn lucky to hit the centre. So the question is, how are you working?

What do you do when you finish a question? Do you immediately look up the answer? What do you do if it's wrong? Do you just look up a worked solution, or ask someone to solve it for you? What about when you get it right? Do you think about it all, or do you just do the next one? How many of these questions do you have a good think about? Do you ever try to use a different method to solve a question? Have you ever tried asking, "I could answer a question this way, but what if I change x and y to be z and f?" What do you do when you get a SAC back? Do you look at where you went wrong? What do you do then - again, do you just ask for the worked solution, and move on?

It's really easy to get stuck on, "I can answer these types of questions, or those types of questions, but I don't know the trick for *this* question!!" And here's the secret - there is no trick. There's never any trick. The "trick" is understanding the material, and taking time to understand how you tool box of maths works. For example, consider the following question:

$\text{Find the derivative of }\frac{x^2-4x}{x+3}\text{ without using the quotient rule}$

Some might say that the "trick" is to realise that:

$\frac{x^2-4x}{x+3}=(x^2-4x)(x+3)^{-1}$

and apply the product rule. I disagree - in this case, it's not a "trick". All you've done is realised you can use what you know about exponentials to help you answer this question. In fact, there's another "trick" you could use for this question - and I'll leave you to figure it out.

So, here's the question you need to ask yourself - are you truly understanding your material, and taking the effort after you get a question wrong to figure out why you got it wrong? Or are you just trying to do as many questions as possible, memorising "the trick" to all of them, and hoping that those questions end up on your exam?

Sorry if the tone of this post feels incredibly "called out" - I'm gonna be honest, I've made a lot of assumptions here about you that might not be true. So, if none of this is true - and you truly would consider yourself the kind of person that's working smarter, not harder - why don't you tell us about /how/ you go about using your study materials?

#### Azila2004

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##### Re: VCE Methods Question Thread!
« Reply #18602 on: July 05, 2020, 02:20:35 pm »
+1
Hello!

I have a question to ask on binomial distribution: What is the least number of times a fair die should be rolled in order to ensure that: a the probability of observing at least one 6 is more than 0.9 b the probability of observing more than one 6 is more than 0.9?

How do I use the formula Pr(X=x) = nCr(n,x) p^x (1-p)^(n-x) in my approach to this question?
'n' has to stay unknown, but I'm not sure how to format the probability being more than 0.9 and the value of x being between 1 and n.

Help would be appreciated!!
Just someone who likes to learn a lot of questions.

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#### keltingmeith

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##### Re: VCE Methods Question Thread!
« Reply #18603 on: July 05, 2020, 04:04:30 pm »
+7
Hello!

I have a question to ask on binomial distribution: What is the least number of times a fair die should be rolled in order to ensure that: a the probability of observing at least one 6 is more than 0.9 b the probability of observing more than one 6 is more than 0.9?

How do I use the formula Pr(X=x) = nCr(n,x) p^x (1-p)^(n-x) in my approach to this question?
'n' has to stay unknown, but I'm not sure how to format the probability being more than 0.9 and the value of x being between 1 and n.

Help would be appreciated!!

Okay, so I think for probability questions, it's often easier to have things make sense in your head BEFORE you worry about playing with equations. So, let's start by looking at a:

the probability of observing at least one 6 is more than 0.9

Okay, so we have the probability > 0.9
We want AT LEAST one 6. Here's the thing - working with "at least" is really hard, particularly when we don't know how many trials we have. But, we DO know from the law of total probability that the probability of getting "at least one 6" is the same as 1-P("at least one 6"s complement). Or, 1-P(no 6). So, this gives us:

P(at least one 6) > 0.9
1 - P(no 6) > 0.9
P(no 6) < 0.1

Okay, so what's the binomial distribution look like here? We don't know what n is... But, we do know what p is - it's the probability of either not getting a 6 (5/6) or the probability of getting a 6 (1/6). Since we're interested in NOT getting a 6 in our new equation, why don't we call the "success" not getting a 6 (5/6). So, this gives us the equation:

${n \choose x}\left(\frac{5}{6}\right)^x\left(\frac{1}{6}\right)^{n-x}<0.1$

Alright, so what's x? Well, x is the amount of times we DON'T roll a 6, and we DON'T want to roll a 6. It can get a little confusing with the more abstract "n" in there, so let's try using some actual numbers to try and understand what's going on:

If I roll a die 5 times, how many times do I want to NOT get a 6? 5 times
If I roll a die 3 times, how many times do I want to NOT get a 6? 3 times
So, if I roll a die n times, how many times do I want to NOT get a 6? Hopefully you see the pattern - and if you don't, please ask for us to try and explain again. But yes, it would be n times

So, now our equation is:

${n \choose n}\left(\frac{5}{6}\right)^n\left(\frac{1}{6}\right)^{n-n}<0.1$
$\left(\frac{5}{6}\right)^n<0.1$

Which can now be solved with the use of some logarithms. However, you could also make this easier on yourself, and just pick values of n until (5/6)^n is greater than 0.1 - I'm getting that n=13 by using this method on my calculator, and it only took me half a minute to do Of course, if you're convinced to doing it the method with logarithms:

$\log_{10}\left[\left(\frac{5}{6}\right)^n\right]<\log_{10}\left[10^{-1}\right]$
$n\log_{10}\left[\left(\frac{5}{6}\right)\right]<-1$
$n>\frac{-1}{\log_{10}\left[\left(\frac{5}{6}\right)\right]}$
$n>12.6$

Remember that log(1)=0 AND is strictly increasing for all numbers it's defined for, so log(<1)<0, which is why I needed to swap the sign. And, since the first integer (since n HAS to be a positive integer) greater than 12.6 is 13, the answer is 13. Also, the choice of base doesn't matter - what's important is that your calculator can do the maths to that logarithm. I used base 10 because it made my life easier as I no longer own a CAS calculator or program, and so had to use excel to calculate it for me

You should be able to apply this thinking to part b, so use that part to test your understanding. If you're still struggling, let us know what you're having problems with, and we'll take it from there

#### 1729

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##### Re: VCE Methods Question Thread!
« Reply #18604 on: July 05, 2020, 04:21:57 pm »
+3
Hello!

I have a question to ask on binomial distribution: What is the least number of times a fair die should be rolled in order to ensure that: a the probability of observing at least one 6 is more than 0.9 b the probability of observing more than one 6 is more than 0.9?

How do I use the formula Pr(X=x) = nCr(n,x) p^x (1-p)^(n-x) in my approach to this question?
'n' has to stay unknown, but I'm not sure how to format the probability being more than 0.9 and the value of x being between 1 and n.

Help would be appreciated!!
I would do guess or check.
Alternatively you could, graph/tabulate the result that's pretty quick, do you know how to find the greatest term in a binomial expansion by setting up inequality? $T_(n+1) > T_n$ that may help.

EDIT: Just read what keltingmeith did, I didn't see that he replied.
« Last Edit: July 05, 2020, 04:25:38 pm by 1729 »

#### The Cat In The Hat

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##### Re: VCE Methods Question Thread!
« Reply #18605 on: July 10, 2020, 12:32:08 pm »
+1
For my bound book I want to include when to use radians and when degrees on the CAS, because I'm always scared I'll get it wrong. As you may see I don't really understand them... anyway, when do I use them? I mean apart from circular functions, what do I use, because I guess circular functions (please correct me if I'm wrong...) if it has π in it it's a radian measure and if it doesn't it's degrees? Is that right?
Thanks
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#### Evolio

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##### Re: VCE Methods Question Thread!
« Reply #18606 on: July 10, 2020, 12:38:04 pm »
+3
Hello.

You may also use them when calculating the angle that the gradient of the tangent makes with the x axis (in differentiation), or the inverse, where you need to calculate the gradient of the tangent using the angle given. This concept was in one of the recent exams.
Yes, that is correct. Also, it'll be clear when they give it in degrees as there will be the degrees sign so that should be helpful to identify which is which
« Last Edit: July 10, 2020, 12:49:07 pm by Evolio »

#### The Cat In The Hat

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##### Re: VCE Methods Question Thread!
« Reply #18607 on: July 10, 2020, 12:40:02 pm »
+2
Hello.

You may also use them when calculating the angle that the gradient of the tangent makes with the x axis (in differentiation), or the inverse, where you need to calculate the gradient of the tangent using the angle given. This concept was in one of the recent exams.
Yes, that is correct. Also, it'll be clear when they give it in degree as there will be the degrees sign so that should be helpful to identify which is which
Thanks for the quick reply! Clear and concise. Thanks!
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#### S_R_K

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##### Re: VCE Methods Question Thread!
« Reply #18608 on: July 10, 2020, 01:33:30 pm »
+2
if it has π in it it's a radian measure and if it doesn't it's degrees? Is that right?
Thanks

Not necessarily. sin(90) ≠ sin(90°).

Evolio's approach is probably best: any angle measured in degrees will have the "°" symbol; otherwise, it's measured in radians.

#### The Cat In The Hat

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##### Re: VCE Methods Question Thread!
« Reply #18609 on: July 10, 2020, 02:43:32 pm »
+1
Thanks!
VCE 20
HHD MM Revs (F/R) Eng T&T
ATAR 85
Uni 21-24: BNursing/BMidwifery @ Deakin
Y1T1:
HNM101
HNN112
HNN120
HBS109
I hope I don't fail....
Listens to Amira Willighagen and Alma Deutscher and a little Marjolein Acke
~English - PM for P&P/creatives help~
Creative excerpts
Nur/Mid uni journal

For Narnia and for Aslan!

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#### svnflower

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##### Re: VCE Methods Question Thread!
« Reply #18610 on: July 11, 2020, 11:29:32 am »
+1
Hello all

I'm struggling with this question, what are the steps to solving this?

#### colline

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##### Re: VCE Methods Question Thread!
« Reply #18611 on: July 11, 2020, 11:59:48 am »
+2
Hello all

I'm struggling with this question, what are the steps to solving this?
You won't actually get those on the exam as absolute values are off the study design.

But to do this sort of question, just calculate the area below the graph for the interval specified. You can draw the graph first if it helps you visualise what it would look like.

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#### 1729

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##### Re: VCE Methods Question Thread!
« Reply #18612 on: July 11, 2020, 12:20:36 pm »
+5
Hello all

I'm struggling with this question, what are the steps to solving this?
You want to find the area under the curve until 1.5, first visualize the graph. Technically It would be an integral but since |1-x| is a triangle you can use triangle formula.

Do you understand how we get this weird graph looking thing?
You first graph the piecewise function as it says, then you want to find the area under it from x = negative infinity to x = 1.5.

From there you can do:

(0.5 * 1 * 1)+(0.5 * 0.5 * 0.5)
0.5 + 0.125
0.625

#### FrankieDens

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##### Re: VCE Methods Question Thread!
« Reply #18613 on: July 11, 2020, 10:37:55 pm »
0
Hi everyone!

I'm not really sure how to even begin working this question out since I always suck at questions that has only just variable letters *sigh*.

"For f(x)= 3ln(x+x/2),
- If f(u-2) + f(v-2)=f(auv+b) where u and v are positive real numbers, find the values of a and b.

- For what values of u does f(u)+f(-u)=f((u^2)/2) hold?"

Any help would be greatly appreciated! Do I start with equating equations or summ?
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#### keltingmeith

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##### Re: VCE Methods Question Thread!
« Reply #18614 on: July 11, 2020, 10:42:46 pm »
0
Hi everyone!

I'm not really sure how to even begin working this question out since I always suck at questions that has only just variable letters *sigh*.

"For f(x)= 3ln(x+x/2),
- If f(u-2) + f(v-2)=f(auv+b) where u and v are positive real numbers, find the values of a and b.

- For what values of u does f(u)+f(-u)=f((u^2)/2) hold?"

Any help would be greatly appreciated! Do I start with equating equations or summ?

I think the easiest way to approach these questions is to make them look less scary. Right now, you've got some alphabet soup and some really scary and complicated looking equations. So let's break it down and ask - what do you need to know?

Well, firstly, you need to know what f(u-2) is. Then, you need to know what f(v-2) is. Then, you need to find what f(auv+b) is.  Once you've got all of those, then you can think about what f(u-2)+f(v-2) is, and how that looks similar to f(auv+b).