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March 28, 2024, 11:30:22 pm

Author Topic: VCE Methods Question Thread!  (Read 4802320 times)  Share 

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milanander

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Re: VCE Methods Question Thread!
« Reply #18060 on: August 12, 2019, 01:45:36 pm »
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Just to be clear about what's on the study design: in Unit 2 you are required to know the application of differential calculus to rectilinear motion, with position/velocity/acceleration given as functions of time. Units 3 & 4 does not explicitly mention applications of differential calculus to kinematics, but Unit 2 is presumed knowledge. In addition Units 3 & 4 mentions the application of integration to finding the distance travelled using a speed-time graph.

This is pretty minimal, and to cover your bases you should do a few questions to consolidate your understanding – even if your school hasn't assigned any questions. I think the major textbooks also treat it pretty briefly. But you are correct, it is hardly assessed.

Ah, cheers mate, this is very helpful. Will definitely make sure I get down the foundations of this topic.

Thanks again.
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GodNifty

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Re: VCE Methods Question Thread!
« Reply #18061 on: August 12, 2019, 06:07:15 pm »
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Can someone help me with finding sample size?

I've attached question (https://imgur.com/a/C2WpKk8) and the solution (https://imgur.com/a/WfMhXem)
For question a, on the solution it says
Pr(X≯ 1)>0.95     but then the next step is
1-Pr(X=0)>0.95
I literally have no idea how it went from the first step to the second step... if x is equal to 1, then why can you take it out to make it zero?

Thank you!!!!

Sine

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Re: VCE Methods Question Thread!
« Reply #18062 on: August 12, 2019, 06:39:54 pm »
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Sorry for the dumb question, but how relevant are kinematics? My school skipped that chapter of the textbook completely and we never had any SAC questions on kinematics. I couldn't find much questions on this topic in past VCAA exams either, however it's on the study design.

Thanks.
You really don't need to know too much but wouldn't hurt to understand the relationship between displacement, velocity, acceleration and know how to logically think through those types of question. (definitely don't need to know to the extent that spec covers it).

Can someone help me with finding sample size?

I've attached question (https://imgur.com/a/C2WpKk8) and the solution (https://imgur.com/a/WfMhXem)
For question a, on the solution it says
Pr(X≯ 1)>0.95     but then the next step is
1-Pr(X=0)>0.95
I literally have no idea how it went from the first step to the second step... if x is equal to 1, then why can you take it out to make it zero?

Thank you!!!!
The min amount of times you can win is 0. The question basically wants to know how many games you need to play so the minimum times you win is 1. That includes 1,2,3,4 ... etc but doesn't include zero.
You should remember that all probabilities (the sum of them) is = 1.
So Pr(X = 0) + Pr(X >/1) = 1
Pr(X>/1) = 1 - Pr(X =0)
 and you should be able to complete the rest

GodNifty

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Re: VCE Methods Question Thread!
« Reply #18063 on: August 12, 2019, 07:06:55 pm »
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The min amount of times you can win is 0. The question basically wants to know how many games you need to play so the minimum times you win is 1. That includes 1,2,3,4 ... etc but doesn't include zero.
You should remember that all probabilities (the sum of them) is = 1.
So Pr(X = 0) + Pr(X >/1) = 1
Pr(X>/1) = 1 - Pr(X =0)
 and you should be able to complete the rest
Ok thanks kinda makes sense.
For Question b, why is Pr(X<2) = Pr(X=0) + Pr(X=1)

S_R_K

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Re: VCE Methods Question Thread!
« Reply #18064 on: August 12, 2019, 08:25:02 pm »
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Ok thanks kinda makes sense.
For Question b, why is Pr(X<2) = Pr(X=0) + Pr(X=1)

The random variable X can only take on non-negative whole number values. Hence, if X < 2, then X = 0 or X = 1, and these are mutually exclusive.

Ash Grey

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Re: VCE Methods Question Thread!
« Reply #18065 on: August 13, 2019, 12:22:13 pm »
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Can someone help me with finding the answer to this?

http://www.itute.com/wp-content/uploads/2018-Year-11-math-topic-test-exponential-and-logarithmic-functions.pdf
Qn 2(d).

Thank you so much

Sine

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Re: VCE Methods Question Thread!
« Reply #18066 on: August 13, 2019, 12:47:44 pm »
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Can someone help me with finding the answer to this?

http://www.itute.com/wp-content/uploads/2018-Year-11-math-topic-test-exponential-and-logarithmic-functions.pdf
Qn 2(d).

Thank you so much
The inverse function and the original function intersect with each other at the line y = x.

Hope this helps :)

VanessaS

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Re: VCE Methods Question Thread!
« Reply #18067 on: August 15, 2019, 04:31:42 pm »
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Hi, could someone please help me with this question:

The chance of winning a prize in the local raffle is 0.08. What is the least number of tickets Siena needs to purchase so that the chance of both her and her sister each winning at least one prize is more than 0.8?
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DrDusk

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Re: VCE Methods Question Thread!
« Reply #18068 on: August 17, 2019, 07:39:47 pm »
+1
I have a question regarding continuous random variables.

When evaluating a definite integral over unbounded intervals, can we just write infinity as one of the terminals or do we need to "lim k--> infinity" and then substitute infinity? (please have a look at the image I have attached for a better idea of what I am asking)




It is however important to note your not 'subbing in' infinity. Infinity is not a number. This would suggest it is better and more correct to use the former because its actually defined as a limit and not a number.

schoolstudent115

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Re: VCE Methods Question Thread!
« Reply #18069 on: August 17, 2019, 07:59:48 pm »
+1
I have a question regarding continuous random variables.

When evaluating a definite integral over unbounded intervals, can we just write infinity as one of the terminals or do we need to "lim k--> infinity" and then substitute infinity? (please have a look at the image I have attached for a better idea of what I am asking)

As Dr Dusk said, both notations are acceptable. And about the limit thing. What you do is you antidifferentiate, then when subbing in the bounds of integration, you solve the limit as k approaches infinity (or negative infinity in this case).
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blyatman

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Re: VCE Methods Question Thread!
« Reply #18070 on: August 17, 2019, 08:25:28 pm »
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I have a question regarding continuous random variables.

When evaluating a definite integral over unbounded intervals, can we just write infinity as one of the terminals or do we need to "lim k--> infinity" and then substitute infinity? (please have a look at the image I have attached for a better idea of what I am asking)

You should note that you can only do this if the interval over which you're integrating is continuous.
E.g.

The former is undefined, whereas the latter (known as the Cauchy Principal Value) is defined and is equal to 0.
« Last Edit: August 17, 2019, 08:28:02 pm by blyatman »
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kimokeeffe

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Re: VCE Methods Question Thread!
« Reply #18071 on: August 19, 2019, 05:50:40 pm »
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not really a specific question. just wondering if anyone has any good ways of remembering the circular functions exact values cause i feel like a bit of a idiot waving my fingers around during a test lol :)
thanks!!

Sine

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Re: VCE Methods Question Thread!
« Reply #18072 on: August 19, 2019, 05:55:57 pm »
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not really a specific question. just wondering if anyone has any good ways of remembering the circular functions exact values cause i feel like a bit of a idiot waving my fingers around during a test lol :)
thanks!!




for tan just find sin/cos.

This is really just for preliminary learning - ideally you won't have to think about it at the end of the year.

Source: https://atarnotes.com/forum/index.php?topic=161217.msg925985#msg925985

DrDusk

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Re: VCE Methods Question Thread!
« Reply #18073 on: August 20, 2019, 12:48:42 am »
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not really a specific question. just wondering if anyone has any good ways of remembering the circular functions exact values cause i feel like a bit of a idiot waving my fingers around during a test lol :)
thanks!!

There's a much easier way such that you won't even need to memorise it. All you need to do is firstly, type it into a calculator as you normally would, for e.g. cos(30). Then you will get a decimal number. You want to directly square this number. So for example if you square cos(30) your calculator will display 3/4. Now just by looking at the screen you can tell what cos(30) is... i.e. just it's square root sqrt(3)/2

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Re: VCE Methods Question Thread!
« Reply #18074 on: August 20, 2019, 01:13:17 am »
+1
not really a specific question. just wondering if anyone has any good ways of remembering the circular functions exact values cause i feel like a bit of a idiot waving my fingers around during a test lol :)
thanks!!

Not a fan of either of the above methods. Personally, I like these triangles:



If you can memorise these, then the exact values come from the trig ratios. Eg,

sin(30)=O/H=1/2

And if you can't remember them, you can also logic them.

The triangle on the left is an isosceles triangle with two 45 degree angles, so the last one HAS to be 90. Then, just make the two same side lengths to be 1, and use pythag to find the last.

The triangle on the right is an equilateral triangle, and we've decided that all side lengths are 2. Since it's equilateral, all angles are the same - 60 degrees. If you cut it in, then the bottom side becomes length 1, the top angle becomes 30 degrees, and you can use pythag again to find the final side.

Just draw these triangles on your exam, use logic and pythag to find the side lengths, and you're good to go!