September 23, 2020, 06:27:53 pm

### AuthorTopic: VCE Specialist 3/4 Question Thread!  (Read 1322015 times) Tweet Share

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#### S_R_K

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9735 on: September 03, 2020, 11:16:16 am »
+2
Can someone explain to me what the scalar resolute shows in relation to the vector resolute/what is it used for? (general question because I don't understand the concept)

The absolute value of the scalar resolute is the magnitude of the vector resolute.

So, thinking of vectors as arrows, the absolute value of the scalar resolute of a in the direction of b gives the length of the component of a that is parallel to b.

#### czzn3

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9736 on: September 06, 2020, 09:32:10 pm »
0
Not a spesh ques, just here for some advices. So my school has finished teaching all the spesh content and I started doing practice papers. I did an insight one (im assuming they're pre basic ques) but I did so badly like I can barely answer the questions... I feel so shitty and dk what to do anymore should I be doing more papers and exercises or go through all my notes first? Iv also heard ppl saying going through notes isn't a great way to revise:( can I get some advice pls im rly struggling rn TY!!

#### keltingmeith

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9737 on: September 06, 2020, 09:59:59 pm »
+3
Not a spesh ques, just here for some advices. So my school has finished teaching all the spesh content and I started doing practice papers. I did an insight one (im assuming they're pre basic ques) but I did so badly like I can barely answer the questions... I feel so shitty and dk what to do anymore should I be doing more papers and exercises or go through all my notes first? Iv also heard ppl saying going through notes isn't a great way to revise:( can I get some advice pls im rly struggling rn TY!!

This question requires more introspection on your part. Here's a handy rule for going through papers - for every mark you lost, you should spend a timed 2-3 minutes on that mark trying to figure out why you lost those marks, and fixing it. It seems like a small amount of time, and why bother timing it, right? However, if in a 40 mark paper, you lost 30 marks, that means you should be spending over an hour on that paper figuring out where you went wrong - how long do you think you realistically spent on this paper going through why you lost marks?

Also, I want to clarify - I'm not talking as simple as, "oh no, I lost here because I did the wrong method. Oh well." Really /think/ about why you lost those marks. Why did you choose to use that particular method? Why did you interpret that question wrongly? What should you do next time to make sure you're doing that question correctly? For example, consider the following question:

$\text{Find the derivative of }y=\sin(2x)\times\cos(3x)$

Maybe the reason you got the answer wrong is because you divided by the coefficients instead of multiplying by the coefficients. So, in those 2-3 minutes, you should have identified that you mixed up the anti-derivative with the derivative. Is that because you remembered the rules wrong? Okay then, now you know you need to spend some time revising differentiation rules vs anti-differentiation rules. Maybe it's because you read the word derivative wrong? Okay, so come up with a strategy where you don't make that mistake - maybe you should start circling the key-words in a question. Maybe you applied the quotient rule, not the product rule? Cool, spend some time revising the product rule and how to use it.

The only thing this method doesn't help with, is it will tell you where you lost marks on this paper - not on future papers. However, by doing this, you should be able to pick up on all the non-specifics you're losing in your exam marks. Things not related to specific questions, but related to bad exam technique. Once you've picked those up, then you should start to assume if you're having issues with some topics, you likely need to revise that whole topic a bit better (eg, constantly getting differentiation questions wrong, revise all of differentiation)

People who say going through notes isn't a great way to revise are people who already know all of the content. If you're struggling to recall content that you need to know, it is 100% worth going through your notes again to revise. Yes, you can bring a book with all the information in the world written on it into this exam, but you need to recall that information under timed pressure. The best students aren't the ones who bring textbooks-worth of information into the final exam, it's the students who don't need to bring textbooks-worth of information into it.
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#### S_R_K

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9738 on: September 07, 2020, 05:02:34 pm »
+1
People who say going through notes isn't a great way to revise are people who already know all of the content.

Not necessarily - but it depends on how one "goes through notes". If you don't know all the content, simply re-reading or highlighting notes is unlikely to result in retaining any significant amount of it, or being able to apply it in the questions you're asked in exams.

The best thing to do is practice applying the content. If you don't remembers all of it, fine. When you come across a question that you don't remember how to do, try doing it by referring to your notes / textbook / worked examples, etc. You're more likely to retain the content you're reading from your notes when by trying to apply it.

#### p0kem0n21

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9739 on: September 09, 2020, 10:21:43 pm »
0
Hi guys, I was just looking at the 2019 exam 1 report and the response to question 6 kinda scared me. It revolves around solving for a variable with linearly dependent vectors. I just used simultaneous equations to get the answer, but apparently another method is using the determinant of a 3x3 matrix??? The reason I'm scared is because I never learnt how to evaluate such a determinant; is it actually in the study design/necessary knowledge?

#### Sine

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9740 on: September 09, 2020, 10:37:19 pm »
+4
Hi guys, I was just looking at the 2019 exam 1 report and the response to question 6 kinda scared me. It revolves around solving for a variable with linearly dependent vectors. I just used simultaneous equations to get the answer, but apparently another method is using the determinant of a 3x3 matrix??? The reason I'm scared is because I never learnt how to evaluate such a determinant; is it actually in the study design/necessary knowledge?
The formula for a 3x3 determinant is actually quite simple if you learn the formula. However, I don't think you need to know about it for spec.

The simultaneous equations is the classical way for solving that type of question in the context of a VCE exam and what they were expecting students to do.

#### keltingmeith

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9741 on: September 11, 2020, 08:58:38 am »
+3
A little separate to Sine's point (although I would like to add that the equation for a 3x3 determinant is anything but simple lol, though the algorithms typically aren't too bad):

I just used simultaneous equations to get the answer, but apparently another method is using the determinant of a 3x3 matrix??? The reason I'm scared is because I never learnt how to evaluate such a determinant; is it actually in the study design/necessary knowledge?

Never be scared because the method you used is different to the one that others used - if you've got the correct answer, you still have the correct answer. If you have the correct answer, and the maths you did was good and correct, that USUALLY means it's because your method is also good and correct. Sure, getting anxious because a technique you mentioned before isn't one you know, but remember that VCAA RARELY asks you to answer questions in a specific way (eg, they won't say, "find the integral of sin(x)cos(x) dx using a u-substitution"). In fact, for linear independence, VCAA only specifies that you should know "inear dependence and independence of a set of vectors and geometric interpretation" - there is no specification that you HAVE to solve these questions using matrices or by using simultaneous equations, and it's 99% likely that they will NOT ask you to use one or either of these methods (hell, there's a third method you could use based on the cosine rule, if you really wanted to do it that way!)

Just food for thought - this is true of I'd say 80% or more of the study design. We'll always happily answer questions based on if something is in the study design or not/if you HAVE to know something or not, so feel free to ask, but hopefully next time you won't get so anxious while waiting for a response But also, as Sine alluded to - sometimes these extra methods aren't so hard. The formula for a 3x3 determinant is messy, but finding it using a co-factor expansion isn't that hard at all, and answering this question using a 3x3 determinant is much quicker and less messier than doing it by simultaneous equations (although they're secretly the same method, just dressed up differently - don't tell anyone!). In fact, the hard part is figuring what determinant to take and what it should equal to - in this case, the determinant is just the vectors a, b, and c as the rows, and it should equal 0. The reasoning for this requires some linear algebra - which I'm happy to explain if you want, but can just leave on the back burner otherwise. Anyway, the matrix you're finding the determinant of would be:

$
\text{det}\left[
\begin{array}{c}
a\\
b\\
c
\end{array}
\right]=0\\

\text{det}\left[
\begin{array}{ccc}
2&-3&4\\
-2&4&-8\\
-6&2&d
\end{array}
\right]=0
$
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#### S_R_K

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9742 on: September 11, 2020, 03:54:56 pm »
+3
Even if you don't learn the formula for calculating a 3x3 determinant by hand, I'd recommend knowing the idea behind it, because it's useful for Exam 2.

In Exam 2 you might get a multiple choice question where you have 3 vectors, and you have to find an unknown component such that the vectors are linearly independent. This is most efficiently done on CAS by solving for when the determinant is zero.

#### Evolio

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9743 on: September 13, 2020, 03:35:25 pm »
0
Hi everyone.

For this question, I understand why the normal force is 2000g: 2000g-N=0 (since it's a constant velocity). However, since N=2000g and the weight force= 2000g, how is the balloon moving downwards? Doesn't there need to be a greater force magnitude in the downwards direction for the balloon to move downwards? Am I missing something here?
(Also, when they refer to upthrust here, are they referring to normal reaction force?)
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#### chemistrykind

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9744 on: September 13, 2020, 03:48:01 pm »
+1
Hi everyone.

For this question, I understand why the normal force is 2000g: 2000g-N=0 (since it's a constant velocity). However, since N=2000g and the weight force= 2000g, how is the balloon moving downwards? Doesn't there need to be a greater force magnitude in the downwards direction for the balloon to move downwards? Am I missing something here?
(Also, when they refer to upthrust here, are they referring to normal reaction force?)

hey op, good question!! firstly, make sure you understand the difference between moving and accelerating. when an object is moving at a constant velocity in one direction, it has NO net force acting on it. if a force DOES act on it, then it will begin to accelerate in the direction to force is acting until the force stops or is counteracted.
so for your example, the balloon was already moving downwards from an unbalanced force earlier! because the upthrust and gravitational force cancel out, the balloon moves at a constant velocity downwards, neither accelerating up or down.
[edit: this is just a precursor to the question! when the ballast is dropped, the upthrust force becomes stronger than the gravitational force downwards - think about what would happen and why]
« Last Edit: September 13, 2020, 03:51:28 pm by chemistrykind »
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#### ArtyDreams

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##### Re: VCE Specialist 3/4 Question Thread!
« Reply #9745 on: September 13, 2020, 03:48:21 pm »
+1
Hi everyone.

For this question, I understand why the normal force is 2000g: 2000g-N=0 (since it's a constant velocity). However, since N=2000g and the weight force= 2000g, how is the balloon moving downwards? Doesn't there need to be a greater force magnitude in the downwards direction for the balloon to move downwards? Am I missing something here?
(Also, when they refer to upthrust here, are they referring to normal reaction force?)

Please take my advice with a grain of salt because I'm terrible at this topic, but yes, you're right because at the start the Normal reaction at the beginning is 2000g, since it is not accelarating.
2000g-N=0, therefore N=2000g.

So in the second case, the N value is still the same, as it says to take the same value of upthrust (which I THINK is the same as NR)
But, the MASS of the BALLOON has changed, because it has let go of the object, that had a mass of 200. In the first instance, the combined mass is 2000, so the new mass of the balloon is 1800. (2000-200)

Therefore, an acceleration must be present now, as the normal reaction is not equal to the weight.
So the new equation would be:
1800g-2000g = 1800a, then solve for a

This might be wrong though - but I THINK this is what it is.
Let me know if you have any questions!
« Last Edit: September 13, 2020, 03:51:10 pm by ArtyDreams »
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