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March 29, 2024, 04:58:28 am

Author Topic: VCE Specialist 3/4 Question Thread!  (Read 2164312 times)  Share 

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S_R_K

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9750 on: October 06, 2020, 02:32:04 pm »
+5
hello! could someone please explain the answer to Q4(f) from the 2017 VCAA Exam 2? /

i know that the line x=-2 is the perpendicular bisector so it is equidistant from a and b.
i did a+b/2 = -2 and solved for b which gave me b=-4-a but i don't know how to get the conjugate on the a.

thanks!

There are two ways to approach this, but the critical thing is to realise that \(a\) and \(b\) are complex numbers, so \(\frac{a+b}{2}\) finds the midpoint in two-dimensions, not the midpoint of their real parts.

Algebraic method: Let \(a=u+vi\) and \(b=w+vi\) - note they have the same imaginary part because we know that \(a\) and \(b\) are equidistant from a vertical line. Now we have \(\frac{u+vi+w+vi}{2}=-2+vi \Rightarrow w=-4-u\) and \(v\) can be any real number. Hence \(b = -4-u + vi = -4-(u-vi) = -4-\overline{a}\).

Geometric method: \(b\) is the reflection of \(a\) about the vertical line \(x=-2\). To achieve this transformation, apply the following sequence of transformations to the complex plane:
  • Translate 2 units right so the vertical line \(x=-2\) gets mapped to the imaginary axis. So \(a \rightarrow a + 2\)
  • Reflect around the imaginary axis. So \(a+2 \rightarrow \overline{-(a+2)}=-2-\overline{a}\)
  • Translate 2 units left, so the imaginary axis gets mapped back to the vertical line \(x=-2\). So \(-2-\overline{a} \rightarrow -4-\overline{a}\)

1292

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9751 on: October 11, 2020, 02:33:42 pm »
0
In questions where we are required to label forces, what is the best approach? For example, if there is 10kg object should we say 10g or 10g N or 98N? Probably a very trivial thing but I feel like they expect different things every year so I was just wondering what's "most correct":)

Evolio

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9752 on: October 11, 2020, 03:19:28 pm »
+2
Hey 1292!

I think it's alright to just label it as 10g for the weight force. Looking at past years' VCAA examination reports, they've just written it like that.

keltingmeith

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9753 on: October 11, 2020, 04:44:22 pm »
+6
In questions where we are required to label forces, what is the best approach? For example, if there is 10kg object should we say 10g or 10g N or 98N? Probably a very trivial thing but I feel like they expect different things every year so I was just wondering what's "most correct":)

Hey 1292!

I think it's alright to just label it as 10g for the weight force. Looking at past years' VCAA examination reports, they've just written it like that.

Just want to add on to this - VCAA will accept any number that is correct. Whether that be 10g, 98, or 9.8*10^1 - if it's mathematically correct, they will accept it. They will mark you wrong if your notation is wrong (eg, you say 10/g instead of 10g), but they won't mark you wrong because they prefer different notation.

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9754 on: October 12, 2020, 09:53:11 pm »
0
I'm not sure if this is the correct area to post.

My teacher gave our class this problem of deriving the derivatives of axioms, and then proving the axiom. I'm not sure how to continue from where I am.

My main question is could I take the derivative of the two parts and multiply them, or would that be incorrect? Any ideas?

I'm not expecting a full detailed proof, any help in the right direction would be appreciated.

keltingmeith

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9755 on: October 12, 2020, 10:18:02 pm »
+3
I'm not sure if this is the correct area to post.

My teacher gave our class this problem of deriving the derivatives of axioms, and then proving the axiom. I'm not sure how to continue from where I am.

My main question is could I take the derivative of the two parts and multiply them, or would that be incorrect? Any ideas?

I'm not expecting a full detailed proof, any help in the right direction would be appreciated.

These look nothing like axioms (and on that, axioms can't be proven - they're definitional), and the wording has confused me with what your teacher wants. If I understand right, put simply, you're trying to find the derivative of the function:



And you're asking if you can simply find the derivative of the numerator and denominator separately? The answer to that is no.

My initial gut reaction is quite simply - use the quotient rule, or the product rule. But unsure if your teacher is okay with this?

xpikachuzz

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9756 on: October 26, 2020, 03:34:26 pm »
0
had this question in the sac out of 4 marks.  how much would I have gotten if i messed up, im guessing i messed up because i did <i instead of <1 for set 'T'. https://imgur.com/dISPXPc

keltingmeith

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9757 on: October 26, 2020, 04:04:55 pm »
+1
had this question in the sac out of 4 marks.  how much would I have gotten if i messed up, im guessing i messed up because i did <i instead of <1 for set 'T'. https://imgur.com/dISPXPc

Not something any of us are going to know, sorry. How much marks a question is worth is HIGHLY subjective. You'll have to ask your teacher what the question is out of

xpikachuzz

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9758 on: October 26, 2020, 04:19:27 pm »
0
Not something any of us are going to know, sorry. How much marks a question is worth is HIGHLY subjective. You'll have to ask your teacher what the question is out of

did i get it wrong tho? just to be sure

Moonblossom

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9759 on: October 27, 2020, 03:33:58 pm »
0
Hey I'm doing 1/2 spec this year and we started doing kinematics recently. Is it true 3/4 spec is mostly physics? I didn't do physics 1/2 and don't really like that subject. Is it going to be hard to do 3/4 spec without prior physics knowledge?

keltingmeith

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9760 on: October 27, 2020, 03:54:44 pm »
+6
Hey I'm doing 1/2 spec this year and we started doing kinematics recently. Is it true 3/4 spec is mostly physics? I didn't do physics 1/2 and don't really like that subject. Is it going to be hard to do 3/4 spec without prior physics knowledge?

Not even close, no need to stress. Firstly, let me put your mind at ease about the content - there are 6 areas of study:

1. Functions and graphs. No physics here.
2. Algebra. Mostly complex numbers. No physics here.
3. Calculus. Applications of calculus can involve physics stuff, mostly kinematics, but it still feels like maths. You're still doing maths. Very little physics here.
4. Vectors. You can apply vectors to physics problems. VCE does not do this. It's all about the maths. SOMETIMES, there will be some motion questions that have a physics flavour, but it really is just about the maths. No physics here.
5. Mechanics. Yeah, look, this is all physics.
6. Probability and statistics. Again, there can be physics contexts, but it's all about the maths. No physics here.

You won't be disadvantaged if you haven't done physics. How do I know this? The amount of physics in the study design is the same amount of physics as when I did specialist maths. I did not do physics in VCE. I hadn't touched physics since year 9. I got full marks on the mechanics section of the exam. I got full marks on all my mechanics SACs. Did I study any extra physics? No, I only went over what my teacher taught, and did practice problems. I beat everybody in the class that did do physics.

I'm not going to say that doing physics doesn't help, because I'm sure it did. But it's not the physics they're testing you on, it's your ability to work with numbers and do maths. That's it. They will ask you to interpret equations, that usually only means describing the motion of a particle (eg, it's moving anti-clockwise in a circle). Mechanics, yeah, you might have to work a bit harder than your peers - but not much. So don't worry, you don't need to stress.

Sine

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9761 on: October 27, 2020, 04:24:19 pm »
+2
Hey I'm doing 1/2 spec this year and we started doing kinematics recently. Is it true 3/4 spec is mostly physics? I didn't do physics 1/2 and don't really like that subject. Is it going to be hard to do 3/4 spec without prior physics knowledge?
Nah it isn't mostly physics. It does help with kinematics and mechanics but not much else.

I completed spec 3/4 without doing any physics units and found it fine.

ArtyDreams

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9762 on: November 15, 2020, 07:25:58 pm »
0
If the stem of a question writes an inverse circular function as say, arcsin(x), am I allowed to write it in my working as sin-1(x). I just prefer the second notation as its quicker to write.

Thanks  :D

keltingmeith

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9763 on: November 16, 2020, 08:10:44 pm »
+4
If the stem of a question writes an inverse circular function as say, arcsin(x), am I allowed to write it in my working as sin-1(x). I just prefer the second notation as its quicker to write.

Thanks  :D

Look, it's probably fine, but if you can get into the habit of using the same notation as them, that would likely be better. For example, one time it wouldn't be fine:

\[
\text{If }y=x^2\text{ then evaluate }\frac{dy}{dx}
\]

And you respond with:

\[
f'(x)=2x
\]

This would not be fine, because you haven't defined what f(x) is. In the case of arcsin vs. \(\sin^{-1}\), it's predefined so probably not an issue, but it's safer to just go with whatever they go with.

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9764 on: December 05, 2020, 09:23:52 pm »
0
Hi guys,
Could someone explain this question to me please?

Let w = 2z. Describe the locus of w if z describes a circle with centre 1 + 2i and
radius 3.
soln is If w = 2z then w describes a circle with
centre (2, 4) and radius 6.

I don't get why u can just double everything and get the answer (esp the centre of the circle)
thanks!
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