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March 28, 2024, 08:32:41 pm

Author Topic: VCE Methods Question Thread!  (Read 4802202 times)  Share 

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KiNSKi01

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Re: VCE Methods Question Thread!
« Reply #18210 on: October 21, 2019, 08:01:32 pm »
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I don't know how to graph an exponential function graphically on the casio class pad.

Here is the equation:  2^-x = 1/10
I can do it using the solve setting:
solve(2^-x=1/10
                           {x=3.3219.....}
I don't know how to do it graphically. I entered the exact same equation into the graph section and it just drew a straight line. I believe it has something to do with there being a = sign in the equation.

So what do I do?

First of all I'm not familiar with casio class pad; however,I'll try help anyway

You can solve for when 2^-x = 1/10 by graphing two fucnctions: y=2^-x and y=1/10

Then just find the co-ordinates of where these two graphs intercept and take the x-value
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Re: VCE Methods Question Thread!
« Reply #18211 on: October 21, 2019, 08:36:21 pm »
+3
Hey can someone explain how the probability of A and B is 1/6 for MCQ 15 Exam 2 2008

If A = {1, 2} and B = {2, 4, 6}, then the intersection A&B is {2}. Hence Pr(A&B) = 1/6.

milanander

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Re: VCE Methods Question Thread!
« Reply #18212 on: October 21, 2019, 09:40:10 pm »
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Final question of VCAA 2018: does anyone know the mark allocation for it? It seemed like there was an insane amount of calculations and working out for a 2 marker!
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EllingtonFeint

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Re: VCE Methods Question Thread!
« Reply #18213 on: October 22, 2019, 09:22:49 am »
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Hey,
So I have three questions and I have no clue what to do :(
I know you guys on here like us to try to talk through our calculations or problem solving but with these three I am just totally stuck and would probably just write ??? and guess randomly.
Could somebody talk me through the qs please?

Thank you!!
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colline

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Re: VCE Methods Question Thread!
« Reply #18214 on: October 22, 2019, 10:20:31 am »
+4
Hey,
So I have three questions and I have no clue what to do :(
I know you guys on here like us to try to talk through our calculations or problem solving but with these three I am just totally stuck and would probably just write ??? and guess randomly.
Could somebody talk me through the qs please?

Thank you!!

I’m not too sure about the last question (gawd I hate transformations) but for the first one, to find the sample proportion you just take the number that is in the middle of the confidence interval range (aka find the average of the two numbers).

For the second question, here’s a picture of my working out (having trouble attaching the image so click on the link):
https://imgur.com/a/vtuY6Zh

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AlphaZero

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Re: VCE Methods Question Thread!
« Reply #18215 on: October 22, 2019, 10:31:16 am »
+3
Final question of VCAA 2018: does anyone know the mark allocation for it? It seemed like there was an insane amount of calculations and working out for a 2 marker!

You don't actually need to do many calculations. You can use your results from part a.

The line \(l_1\) has the equation \(y=3\pi-x\) (parts b and c), so it intersects the \(y\)-axis at \((0,\,3\pi)\).

Thus, we can write \begin{align*}A&=2\left[\frac12\times 3\pi\times 3\pi -\int_0^\pi f(x)\,\text{d}x-\int_\pi^{2\pi} g(x)\,\text{d}x-\int_{2\pi}^{3\pi} f(x)\,\text{d}x\right]\\ &=9\pi^2-2(2\times 0+1)\pi-2(2\times 1+1)\pi-2(2\times 2+1)\pi\\ &=9\pi^2-18\pi\ \text{units}^2\end{align*}
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AlphaZero

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Re: VCE Methods Question Thread!
« Reply #18216 on: October 22, 2019, 10:40:21 am »
+3
...

The transformation \(T\) gives \[\begin{cases}x'=2x\\ y'=\frac13 y\end{cases}\implies\,\begin{cases}x=\frac{x'}{2}\\ y=3y'\end{cases}.\] That is, \[3y'=3\sin\left(2\left(x'+\frac\pi 4\right)\right),\] and so dropping the dashes, we have \[y=\sin\left(x+\frac\pi 2\right)=\cos(x).\] Hence, the answer is D.

Alternatively, if you can, make the simplification \(y=3\sin\left(2\left(x+\frac\pi 4\right)\right)=3\cos(2x)\) first and read off the transformations. Ie, a dilation by factor \(1/3\) from the \(x\)-axis and a dilation by factor \(2\) from the \(y\)-axis.
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EllingtonFeint

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Re: VCE Methods Question Thread!
« Reply #18217 on: October 22, 2019, 02:36:36 pm »
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... so dropping the dashes, we have \[y=\sin\left(x+\frac\pi 2\right)=\cos(x).\] Hence, the answer is D.

Alternatively, if you can, make the simplification \(y=3\sin\left(2\left(x+\frac\pi 4\right)\right)=3\cos(2x)\) first and read off the transformations. Ie, a dilation by factor \(1/3\) from the \(x\)-axis and a dilation by factor \(2\) from the \(y\)-axis.

Wait but why does y=sin(x+π2)=cos(x) ??

Sorry :((
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Re: VCE Methods Question Thread!
« Reply #18218 on: October 22, 2019, 03:04:03 pm »
+4
Wait but why does y=sin(x+π2)=cos(x) ??

Think about it graphically. If you plot y=sin(x), then you shift the curve to the left by π/2, you will end up with y=cos(x).

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Coloratura

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Re: VCE Methods Question Thread!
« Reply #18219 on: October 22, 2019, 08:31:43 pm »
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If a question says write out a function that represents, for example, the distance between two graphs, is it enough just to write d(x) = f(x) - g(x)? Or do you have to write out the entire expression of f(x) and g(x) to get the mark, in a VCAA exam?
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Tau

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Re: VCE Methods Question Thread!
« Reply #18220 on: October 22, 2019, 08:36:04 pm »
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If a question says write out a function that represents, for example, the distance between two graphs, is it enough just to write d(x) = f(x) - g(x)? Or do you have to write out the entire expression of f(x) and g(x) to get the mark, in a VCAA exam?

I believe that should be sufficient. However, if they say ‘write an expression in terms of x’, then I’m not sure. Better safe than sorry to write out the expression explicitly.
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Coloratura

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Re: VCE Methods Question Thread!
« Reply #18221 on: October 22, 2019, 08:46:25 pm »
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I believe that should be sufficient. However, if they say ‘write an expression in terms of x’, then I’m not sure. Better safe than sorry to write out the expression explicitly.

Ok then. Thanks!
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DrDusk

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Re: VCE Methods Question Thread!
« Reply #18222 on: October 22, 2019, 08:52:41 pm »
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Ok then. Thanks!
Also sometimes the answer can be simplified to a special case or function or something, so if you just write f(x) - g(x) then it's not in simplified form.

At the end of the day the 20 extra seconds it takes to write it out fully is not gonna affect you, so I agree with Tau in that whenever your unsure just always write it out =).

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Re: VCE Methods Question Thread!
« Reply #18223 on: October 24, 2019, 07:46:22 pm »
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Since confidence intervals are intervals, we need to be using open brackets right?

I know its continuous (?) so if wouldn't really matter, but what is more correct? Pretty sure this isn't too important anyways :P

Like the above, is it ok if we just write f(t) etc for when we are integrating, differentiating, etc. there's the argument that you don't lose time, but if you do mess up with brackets or notation, then you lose marks, which is why I'm a bit concerned.

thanks.
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Tau

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Re: VCE Methods Question Thread!
« Reply #18224 on: October 24, 2019, 08:12:37 pm »
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Since confidence intervals are intervals, we need to be using open brackets right?

I know its continuous (?) so if wouldn't really matter, but what is more correct? Pretty sure this isn't too important anyways :P

Like the above, is it ok if we just write f(t) etc for when we are integrating, differentiating, etc. there's the argument that you don't lose time, but if you do mess up with brackets or notation, then you lose marks, which is why I'm a bit concerned.

thanks.

Correct, confidence intervals use open parentheses (). That’s also how it’s provided on the formula sheet.

As above, I would say it’s ok, but if they ask for an expression specifically /in terms of x, t.../ then perhaps better safe than sorry.

From VCAA 2018 examiner’s report:” If the functions have been defined at the start of the question, it is acceptable to use the function name, such as f(x), throughout the question rather than writing out the entire expression. This avoids transcription errors. ”
« Last Edit: October 24, 2019, 08:23:43 pm by Tau »
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