August 05, 2020, 08:11:29 pm

### AuthorTopic: VCE Specialist 3/4 Question Thread!  (Read 1300652 times) Tweet Share

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#### AlphaZero

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9540 on: October 17, 2019, 02:36:59 pm »
0
Speaking of 2018 NHT Exam 1 Question 2,
I can't seem to get the value of m no matter how many times I try.

The magnitude of the vector resolute of $\mathbf{a}$ parallel to $\mathbf{b}$ is given by $\left|(\mathbf{a}\cdot\hat{\mathbf{b}})\hat{\mathbf{b}}\right|=\left|\frac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{b}|}\right|,$ since $|\hat{\mathbf{b}}|=1$. Hence, $\pm\sqrt{14}=\frac{6+2+3m}{\sqrt{4+1+9}}\ \implies\ 3m+8=\pm 14\ \implies\ m=2,\ \frac{-22}{3}.$
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#### Tau

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9541 on: November 03, 2019, 10:09:21 pm »
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When following a slope field passing through a point, can our graph pass through the gradient segments? Or is that considered incorrect, and hence penalised?
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#### S_R_K

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9542 on: November 04, 2019, 03:35:22 pm »
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When following a slope field passing through a point, can our graph pass through the gradient segments? Or is that considered incorrect, and hence penalised?

If your solution curve passes through a point, then the slope segment at that point should be tangent to the graph.

There is some margin for error when drawing by hand, but if you curve is clearly travelling in the wrong direction when it touches/intersects a slope segment, then you will be penalised.

#### AnonymooseUser

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9543 on: November 04, 2019, 07:00:26 pm »
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The Cambridge textbook has a chapter about using definite integration to find solutions to differential equations where it basically eliminates the 'find +c' step of the process.

I was just wondering if this was valid in 'show that y=...' questions, or if making a point to show that there's a +c and then solving for it is necessary.

Thanks!

#### Tau

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9544 on: November 04, 2019, 07:58:12 pm »
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The Cambridge textbook has a chapter about using definite integration to find solutions to differential equations where it basically eliminates the 'find +c' step of the process.

I was just wondering if this was valid in 'show that y=...' questions, or if making a point to show that there's a +c and then solving for it is necessary.

Thanks!

I don’t see why not, it’s a valid approach. They might not have delineated marks for that, where a constant of integration is not present, but the if the working is solid... You should be fine.

I suppose it’s similar to omitting an extraneous constant when solving a separable equation, and missing the working Let C=c_1+c_2.... Most people don’t bother (they just keep one constant on one side), and it’s fine.
2018: Physics [46 ~ 48], Methods [41 ~ 46]
2019: UMEP Mathematics Extension [First Class Honours (H1)], English [44], Specialist [42 ~ 52], Algorithmics (HESS)
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#### lakvinu

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9545 on: November 05, 2019, 06:57:24 pm »
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Thx

#### Otter

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9546 on: November 08, 2019, 07:21:53 pm »
+1
If we are asked to plot a point such as 3+3i on a graph with Im(z) and Re(z) axes, do we label the points with (3,3) or simply 3+3i?

#### yplee0926

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9547 on: November 09, 2019, 02:03:40 pm »
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hey guys i was wondering if for the tension question in exam 1 this year, i labelled diagrams with t1 t2 etc but in my working out later i realised they were equal and just used T as the tension. Would they ignore my diagram or do they have marks allocated to it?
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#### AnonymooseUser

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9548 on: November 10, 2019, 06:16:32 pm »
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Can someone please explain the answers for 2019 nht exam 2 mcq 19 and 20?

#### AlphaZero

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9549 on: November 10, 2019, 06:26:40 pm »
+3
If we are asked to plot a point such as 3+3i on a graph with Im(z) and Re(z) axes, do we label the points with (3,3) or simply 3+3i?

Technically, it should be labeled as a complex number, but the meaning of cartesian coordinates is obvious too.

hey guys i was wondering if for the tension question in exam 1 this year, i labelled diagrams with t1 t2 etc but in my working out later i realised they were equal and just used T as the tension. Would they ignore my diagram or do they have marks allocated to it?

As long as you correctly came to the conclusion that the tension through the string is constant and you logically arrived at the correct answer, you should get the marks.
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#### AlphaZero

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9550 on: November 10, 2019, 06:54:49 pm »
+4
Can someone please explain the answers for 2019 nht exam 2 mcq 19 and 20?

Question 19

This is equivalent to having a margin of error of no more than 1 g. Where $a>0$, $\Pr(-a<Z<a)=0.98\implies a=-2.3263...,$ and so $2.3263...\frac{3}{\sqrt{n}}\leq 1\implies n_{\text{min}}=49.$
Question 20

Let $X_1,\,X_2\sim\mathcal{N}(0.875,\ 0.188^2)$ be independent random variables that denote the nitrogen oxide emissions of cars. We're looking for $\Pr(|X_1-X_2|\geq 0.5).$ We'll find the distribution of $X_1-X_2$: $\text{E}(X_1-X_2)=0.875-0.875=0$$\text{sd}(X_1-X_2)=\sqrt{0.188^2+0.188^2}=0.26587...$Thus, we have \begin{align*}\Pr(|X_1-X_2|\geq 0.5)&=\Pr\left(\left|\frac{(X_1-X_2)-0}{0.26587...}\right|\geq\frac{0.5-0}{0.26587...}\right)\\ &=\Pr(|Z|\geq 1.88060...)\\ &=1-\Pr(-1.88060...\leq Z\leq 1.88060...)\\ &=0.060026...\end{align*}
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#### AnonymooseUser

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9551 on: November 10, 2019, 11:17:03 pm »
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Question 19
Question 20

Thank you! I completely forgot about margin of error and distance being like a two tail test.

#### specialistmath123

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9552 on: December 11, 2019, 04:49:19 pm »
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When asked to sketch reciprocal trig functions (secant, cot etc) am I allowed to draw the normal trig function (e.g. tan) and draw the reciprocal function (e.g. cot) over the top of it?

Will I still get marks if both the tan and cot graph is present, but the question only asked for the cot graph?

#### Sine

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9553 on: December 11, 2019, 04:53:26 pm »
+1
When asked to sketch reciprocal trig functions (secant, cot etc) am I allowed to draw the normal trig function (e.g. tan) and draw the reciprocal function (e.g. cot) over the top of it?

Will I still get marks if both the tan and cot graph is present, but the question only asked for the cot graph?
It is a bit risky, giving assessors only the things they need to look at to mark makes their job easier. You could do a rough sketch on the side of the page and copy the inverse trig graph. Or you could draw the tan graph very lightly and rub it out once you are done. I personally wouldn't put both graphs down for a question that asks for only one of them.

If you decide to draw both make sure to label them - otherwise you will definitely lose marks.

#### TheEagle

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9554 on: December 22, 2019, 01:34:42 am »
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Hi
I'm having trouble with proving the following trig identities via the unit circle: sin (π/2 - θ) = cos θ      and         cos(π/2 - θ) = sin θ

Kindly appreciate it