VCE Specialist 3/4 Question Thread!

[Unsplash]

Hey Guys. I just finished my year 12 VCE but I'm deciding to take Specialist Maths 3/4 via Distance Education next year to boost my atar to 98-99 so I have a better chance of getting to Medicine. I'm decent at maths (not excellent by any means); I got a raw 39 in Methods without that much studying for it. Do you guys believe I might be able to survive Spesh 3/4 and get 40+ without doing 1/2 at all? I will take a gap year so I would have a lot of time in my hands. Thanks!!

I reckon it's possible, especially considering it will be your only subject. Will probably be a bit easier if you review fundamentals of 1/2 over the summer break.

I also just checked how much work I did across Units 1-4. I completed about 250 hours of homework in addition to about the same amount of in class time. This is about 500 hours over the year. So about 10 hours a week if you start now. Definitely a solid commitment but by all means doable if you are consistent and motivated enough.

EDIT: Forgot to mention, some of that unit 1/2 homework and classwork is not in 3/4 curriculum and therefore you will obviously require less work, in addition to the fact that 3/4 does go over a fair portion of unit 1/2 content. So you would not need that refresher like I did.

[Seno72]

I reckon it's possible, especially considering it will be your only subject. Will probably be a bit easier if you review fundamentals of 1/2 over the summer break.

I also just checked how much work I did across Units 1-4. I completed about 250 hours of homework in addition to about the same amount of in class time. This is about 500 hours over the year. So about 10 hours a week if you start now. Definitely a solid commitment but by all means doable if you are consistent and motivated enough.

EDIT: Forgot to mention, some of that unit 1/2 homework and classwork is not in 3/4 curriculum and therefore you will obviously require less work, in addition to the fact that 3/4 does go over a fair portion of unit 1/2 content. So you would not need that refresher like I did.

Thanks! Congrats on your spesh and methods scores!

[DBA-144]

Regarding geometric proofs with vectors, how much information and what information are we required to show by VCAA standards?

So, would saying that the diagonals of a rectangle bisect each other and there is one  pair of perpendicular vectors be sufficient for a rectangle? Could we do the same with squares?

And what about rhombuses and parrallelograms? What is the bare minimum of information we would need to show for these?

How often do vector proofs come up in exams?

And some more questions too:
-What are the applications of the geometric representation of the dot product, apart from being able to find the angle between 2 vectors and the magnitude of those vectors?
-If we can use vector projections (the vector resolute I mean) to decompose a vector into rectangular components, then how can we apply this to the i, j and k unit vectors, as these are also a form of vector projections? Does anyone have a link to a proof of this concept? I am not quite sure what to search for this topic.
-How is the formal definition of linear dependence derived? I understand the derivation of its practical definition but cannot seem to understand its formal defintion. Please help. :/

thanks.

[lzxnl]

Regarding geometric proofs with vectors, how much information and what information are we required to show by VCAA standards?

So, would saying that the diagonals of a rectangle bisect each other and there is one  pair of perpendicular vectors be sufficient for a rectangle? Could we do the same with squares?

And what about rhombuses and parrallelograms? What is the bare minimum of information we would need to show for these?

How often do vector proofs come up in exams?

thanks.

If the question says, 'prove that ABCD is a rectangle', then by all means, show that the diagonals bisect and two vectors are perpendicular. I doubt they will ask you to prove that the above criterion does give you a rectangle.

For a parallelogram, showing two pairs of equal vectors is sufficient. (equal means parallel and same length)
For a rhombus, showing two pairs of equal vectors of the same length suffices

Vector proofs will come up somewhere in the exam, in any section.

[studyingg]

Does anyone have any recommendations for good resources to use for spec to practice throughout the year? Preferably a resource that contains questions representative of what vcaa ask. Given that spec seems to be more content-heavy than methods, I'm afraid I may not finish the course in time to adequately prepare for the exam, so I'd like to prepare throughout the year. Is Checkpoints any good? Or would I be fine relying on the Quest textbook?

[dream chaser]

Does anyone have any recommendations for good resources to use for spec to practice throughout the year? Preferably a resource that contains questions representative of what vcaa ask. Given that spec seems to be more content-heavy than methods, I'm afraid I may not finish the course in time to adequately prepare for the exam, so I'd like to prepare throughout the year. Is Checkpoints any good? Or would I be fine relying on the Quest textbook?

Personally, I think checkpoints is good as checkpoints is based of past vcaa exams. If you are able to do the questions in it, it means that you will be prepared for the topic come exam time. Another thing you could do is ask your specialist teacher for company exams. This will also help you and throughout the year, do the questions related to the topics you have learnt. 

As for just relying on your Quest book, it really depends on the student in my opinion. I believe that if you are able to attempt every question in the book and get them correct, it means you are prepared. However, the exam will normally have different style of questions compared to the same structured questions in the books. So I do recommend that you use at least one other resource than just the text book(quest) for the entire year leading to your exam

Hope the advice helps  .

[studyingg]

Personally, I think checkpoints is good as checkpoints is based of past vcaa exams. If you are able to do the questions in it, it means that you will be prepared for the topic come exam time. Another thing you could do is ask your specialist teacher for company exams. This will also help you and throughout the year, do the questions related to the topics you have learnt. 

As for just relying on your Quest book, it really depends on the student in my opinion. I believe that if you are able to attempt every question in the book and get them correct, it means you are prepared. However, the exam will normally have different style of questions compared to the same structured questions in the books. So I do recommend that you use at least one other resource than just the text book(quest) for the entire year leading to your exam

Hope the advice helps  .

Ok, great! Thanks for the advice I'll probs use checkpoints along with quest

[dream chaser]

Ok, great! Thanks for the advice I'll probs use checkpoints along with quest

No problem. 

[lzxnl]

Regarding geometric proofs with vectors, how much information and what information are we required to show by VCAA standards?

So, would saying that the diagonals of a rectangle bisect each other and there is one  pair of perpendicular vectors be sufficient for a rectangle? Could we do the same with squares?

And what about rhombuses and parrallelograms? What is the bare minimum of information we would need to show for these?

How often do vector proofs come up in exams?

And some more questions too:
-What are the applications of the geometric representation of the dot product, apart from being able to find the angle between 2 vectors and the magnitude of those vectors? Is this not enough for you? You can use the geometric definition to write down an equation for a plane, given a normal vector, for instance, or find the minimum distance from a point to a line.
-If we can use vector projections (the vector resolute I mean) to decompose a vector into rectangular components, then how can we apply this to the i, j and k unit vectors, as these are also a form of vector projections? Does anyone have a link to a proof of this concept? I am not quite sure what to search for this topic.
Erm...you will find that the i, j, k components ARE the scalar resolutes in the i, j, k directions. Just use the formula or follow the derivation for them.
-How is the formal definition of linear dependence derived? I understand the derivation of its practical definition but cannot seem to understand its formal defintion. Please help. :/
Your question is a little confusing. One does not 'derive' definitions; you start off with them.

The idea is that a set of vectors is linearly dependent if you can write any one of them as a linear combination of the others. The problem is, if you pick a vector that isn't a linear combination of the others, then that cannot be done; you have to go through all of the vectors to ensure that none of them can be written as a linear combination of the others for linear independence. This is why the general definition involves writing a sum of vectors equalling the zero vector; this considers EVERY vector simultaneously.

thanks.

[Scribe]

How do you represent |2x - 8| = 6 graphically? What do you do with the 6?

Thanks 

[Bucket Hat]

How do you represent |2x - 8| = 6 graphically? What do you do with the 6?

Thanks 

Sketch y = |2x - 8|
Sketch y = 6
Find the intersection points.
The x-values of the intersection points are the solutions.

 

[Scribe]

Sketch y = |2x - 8|
Sketch y = 6
Find the intersection points.
The x-values of the intersection points are the solutions.

 

Ohhhh that's it. What was I thinking lol

Edit: Just to clarify, if you were to draw it, it would just be two lines x=1 and x=7?

[lzxnl]

How do you represent |2x - 8| = 6 graphically? What do you do with the 6?

Thanks 

|x-4| = 3. This means the set of all points that are a distance 3 away from 4. If x is a real number, then look at your number line and asking yourself, what happens if you go 3 units left and right from 4?

[DBA-144]

How are you guys finding the extended response questions from the textbook? I know that they are a poor indicator of what is required at times, but I am really struggling with the extended response questions, especially the longer ones where we need to combine info from multiple parts of the question eg. For vectors, as well as the ones where we have to prove theorems for trig. How are you guys finding these questions?

Thanks.

[TheAspiringDoc]

How are you guys finding the extended response questions from the textbook? I know that they are a poor indicator of what is required at times, but I am really struggling with the extended response questions, especially the longer ones where we need to combine info from multiple parts of the question eg. For vectors, as well as the ones where we have to prove theorems for trig. How are you guys finding these questions?

Thanks.

They're too obscure but also not interesting imo.

I'd recommend just reading about the basics of vectors in some commerical notes and the textbook (with reference to the study design),then making some draft notes with the basic rules (dot product formula etc) and then hit up checkpoints and learn about vectors from your approaches to these VCAA questions and comparing it to the suggested solutions at the end.

Also check out wormsmathsacademy (YouTube) and VicsMathsNotes